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Properties

Label 2535.2.k
Level $2535$
Weight $2$
Character orbit 2535.k
Rep. character $\chi_{2535}(1282,\cdot)$
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.k (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

\( 308 q - 308 q^{4} - 8 q^{5} + O(q^{10}) \) \( 308 q - 308 q^{4} - 8 q^{5} + 8 q^{11} - 16 q^{12} - 4 q^{15} + 308 q^{16} + 28 q^{17} + 4 q^{18} - 8 q^{21} + 24 q^{22} - 16 q^{23} + 12 q^{25} + 16 q^{31} - 28 q^{34} - 32 q^{37} + 56 q^{40} - 4 q^{41} - 8 q^{43} - 40 q^{44} + 4 q^{45} + 16 q^{46} + 24 q^{47} + 32 q^{48} + 372 q^{49} + 32 q^{50} - 28 q^{53} + 8 q^{55} + 8 q^{58} - 32 q^{59} + 12 q^{60} - 72 q^{62} - 308 q^{64} - 16 q^{66} - 60 q^{68} - 16 q^{69} - 64 q^{70} - 40 q^{71} - 12 q^{72} + 32 q^{75} + 40 q^{76} + 48 q^{77} + 32 q^{80} - 308 q^{81} - 12 q^{82} + 104 q^{83} + 32 q^{84} + 4 q^{85} - 16 q^{86} + 24 q^{87} - 64 q^{88} + 36 q^{89} + 20 q^{90} + 64 q^{92} - 48 q^{95} - 8 q^{99} + O(q^{100}) \)

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

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