Weight 2 Newforms of large level computations.

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I am stuck with some weight $2$ newform computations of large level. For example I want to compute newforms of level $11520$. Can anyone suggest me a way to do it? I need it to solve some diophantine equations.

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There are computer packages that will do this for you using modular symbols. The "industry standard" implementations are in Sage and Magma. Level 11520 isn't that large; I fired up Sage and it did level 1520 in under a minute, so level 11520 shouldn't be more than a few hours. (John Cremona's elliptic curve tables use modular symbol computations in levels up to around 400,000.)