Was it serious at all? Many argue that the invasion was merely just a small series of raids on coastal towns.
This question is somewhat difficult to answer given the great deal of ambiguity surrounding the Chola invasion of Srivijaya – there has been extensive debate as to the aim, purpose, timing and even the number of raids undertaken!
The most direct evidence for a Chola invasion of Southeast Asia comes from a temple inscription commissioned by Rajendra Chola. This inscription claims that Rajendra had defeated a king called Sangrama-Vijayottungavarman and had accumulated a great deal of treasure overthrowing thirteen places (Srivijaya, Pannai, Malaiyur, Mayirudingam, Ilangasoka, Mappappalam, Mevilimbangam, Valaippanduru, Talaittakkolam, Madamalingam, Ilamuri-desam, Nakkavaram, Kadaram). As with every other aspect of the invasion, the identity of these locations is up for debate though most have been associated with the Malay Peninsula, Sumatra and the Nicobar Islands. As mentioned earlier, when this happened is also up for question. The conventional date is given as around 1025 CE, though there is a school of thought represented by historian R.C. Majumdar that posits that there were two invasions with the first occurring in 1017-1018 (based on copper plate inscriptions also commissioned by Rajendra). There is also a theory of a later invasion in 1068-1069.
There are also multiple theories as to why these raids happened. One is the so-called trade strangulation hypothesis forwarded by scholars such as K.A. Nilakanta Sastri and Tansen Sen who attribute the raids to the Chola kingdom attempting to break Srivijaya’s hold on the trade routes to China. On the other hand, you have scholars such as George W. Spencer who attribute the raids as a bid to generate loot and prestige. This point requires some explanation: there is debate as to how centralized the Chola polity actually was; historians such as K.A. Nilakanta Sastri saw it as a centralized despotic kingdom while scholars such as Burton Stein cite the Chola polity as an example of a segmentary state – an entity where the ruler does not have absolute coercive dominance over his subjects and so relies on soft power such as ritual to maintain control. George W. Spencer argues that as the Chola king did not have absolute coercive power over his subjects, there was a limit to the amount of resources he could coax out of them. An alternate source of revenue was raiding. Loot from successful raids could be leveraged as donations to temples, gifts to foreign rulers and local subjects which enhanced the prestige of the ruler and elevated him in the eyes of his subjects; as already mentioned, successful raids could also be recorded for posterity on the walls of temples or on copper plates and these could serve as fantastic propaganda. Southeast Asia wasn’t the only target of Chola raids; northern Sri Lanka had been raided and occupied and Rajendra had sent Chola armies as far north as the Ganges River (supposedly to get water from said river to inaugurate his capital which was appropriately named Gangaikondacholapuram (the city of the Ganges conquering Chola)).
In the end, did the Chola raid have any effect on Southeast Asia? It certainly left an impression, as the memory of the Chola raids persisted in the minds of the Malays even after the dynasty had fallen. A fifteenth century genealogy of the sultans of Malacca claimed several Chola rulers as ancestors. There is also the ambiguous evidence of the Song Shi (the dynastic records of the Song Dynasty) which mentions a joint Srivijaya-Chola trade mission to the Song court and identifies the Chola kingdom as the vassal of Srivijaya. This is supplemented from an inscription from a Daoist temple in Guangzhou which records how the Paramount chief of Srivijaya – one Di-hua-jia-luo (who is also identified in the Song Shi as the ruler of the Chola kingdom) restored the crumbling temple. This evidence has been interpreted several ways – one (forwarded by Tan Yeok Seong) is that Di-hua-jia-luo was Rajendra Deva Kullottunga who ruled both empires from Sumatra briefly. Other explanations have been forwarded by George W. Spencer and Tansen Sen. Spencer posits a marriage alliance between the two kingdoms while Sen theorizes that Srivijiya was engaged in a bit of diplomatic chicanery, misrepresenting their position vis a vis the Chola kingdom to secure greater trading rights than their Chola rivals. Whatever the truth, the Chola raid into Southeast Asia is a fascinating subject.