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Properties

Label 2535.2.t
Level $2535$
Weight $2$
Character orbit 2535.t
Rep. character $\chi_{2535}(268,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $308$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 2535 = 3 \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2535.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(i)\)
Sturm bound: \(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2535, [\chi])\).

Total New Old
Modular forms 784 308 476
Cusp forms 672 308 364
Eisenstein series 112 0 112

Trace form

\( 308 q + 4 q^{2} + 308 q^{4} + 4 q^{5} + 12 q^{8} + O(q^{10}) \) \( 308 q + 4 q^{2} + 308 q^{4} + 4 q^{5} + 12 q^{8} + 8 q^{11} + 16 q^{12} + 4 q^{15} + 308 q^{16} - 28 q^{17} - 12 q^{20} - 8 q^{21} + 24 q^{22} + 16 q^{23} - 12 q^{25} + 16 q^{31} + 68 q^{32} + 8 q^{33} + 28 q^{34} + 56 q^{40} - 4 q^{41} + 8 q^{43} + 40 q^{44} + 8 q^{45} + 16 q^{46} + 32 q^{48} - 372 q^{49} - 4 q^{50} - 28 q^{53} + 8 q^{55} + 32 q^{59} + 60 q^{60} + 72 q^{62} + 308 q^{64} - 16 q^{66} - 32 q^{67} - 60 q^{68} + 16 q^{69} + 16 q^{70} - 40 q^{71} - 56 q^{73} - 32 q^{75} + 40 q^{76} - 48 q^{77} + 12 q^{80} - 308 q^{81} + 12 q^{82} - 32 q^{84} - 44 q^{85} - 16 q^{86} + 24 q^{87} + 64 q^{88} - 36 q^{89} - 20 q^{90} + 64 q^{92} + 48 q^{95} - 48 q^{97} + 12 q^{98} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2535, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2535, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2535, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(845, [\chi])\)\(^{\oplus 2}\)