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Properties

Label 2535.2.bm
Level $2535$
Weight $2$
Character orbit 2535.bm
Rep. character $\chi_{2535}(418,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $616$
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.bm (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 1568 616 952
Cusp forms 1344 616 728
Eisenstein series 224 0 224

Trace form

\( 616 q + 308 q^{4} + 8 q^{5} + O(q^{10}) \) \( 616 q + 308 q^{4} + 8 q^{5} - 8 q^{11} - 32 q^{12} + 4 q^{15} - 308 q^{16} + 20 q^{17} + 8 q^{18} - 24 q^{19} + 8 q^{21} + 36 q^{22} + 16 q^{23} + 36 q^{25} + 8 q^{31} + 60 q^{32} - 12 q^{33} + 4 q^{34} + 20 q^{37} - 8 q^{40} + 4 q^{41} + 60 q^{42} + 20 q^{43} + 40 q^{44} + 8 q^{45} + 8 q^{46} - 24 q^{47} - 32 q^{48} - 300 q^{49} + 124 q^{50} - 20 q^{53} - 32 q^{55} - 72 q^{56} + 4 q^{58} - 64 q^{59} + 48 q^{60} - 24 q^{61} - 108 q^{62} - 616 q^{64} + 16 q^{66} - 12 q^{68} + 16 q^{69} - 80 q^{70} + 16 q^{71} + 12 q^{72} + 36 q^{74} - 32 q^{75} - 112 q^{76} - 48 q^{77} - 164 q^{80} + 308 q^{81} + 60 q^{82} - 104 q^{83} - 32 q^{84} - 16 q^{85} + 64 q^{86} - 36 q^{87} + 16 q^{88} - 12 q^{89} + 28 q^{90} + 128 q^{92} - 24 q^{94} - 48 q^{95} + 108 q^{97} + 96 q^{98} + 8 q^{99} + O(q^{100}) \)

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

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