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Properties

Label 2535.2.by
Level $2535$
Weight $2$
Character orbit 2535.by
Rep. character $\chi_{2535}(73,\cdot)$
Character field $\Q(\zeta_{52})$
Dimension $4368$
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.by (of order \(52\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 845 \)
Character field: \(\Q(\zeta_{52})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 8832 4368 4464
Cusp forms 8640 4368 4272
Eisenstein series 192 0 192

Trace form

\( 4368 q + 4 q^{2} - 364 q^{4} + 4 q^{5} + 12 q^{8} + O(q^{10}) \) \( 4368 q + 4 q^{2} - 364 q^{4} + 4 q^{5} + 12 q^{8} + 8 q^{11} + 4 q^{15} - 364 q^{16} - 28 q^{17} - 12 q^{20} - 8 q^{21} + 40 q^{22} + 4 q^{25} + 16 q^{31} + 68 q^{32} + 8 q^{33} + 28 q^{34} + 8 q^{39} + 40 q^{40} - 4 q^{41} + 260 q^{42} - 8 q^{43} + 40 q^{44} + 8 q^{45} + 16 q^{46} + 628 q^{49} - 4 q^{50} - 48 q^{52} - 324 q^{53} - 252 q^{55} - 384 q^{59} - 148 q^{60} - 16 q^{61} + 72 q^{62} - 364 q^{64} - 64 q^{65} - 16 q^{66} - 240 q^{67} - 60 q^{68} + 224 q^{70} - 40 q^{71} - 56 q^{73} + 260 q^{74} + 40 q^{76} - 48 q^{77} - 40 q^{78} + 12 q^{80} + 364 q^{81} - 4 q^{82} - 32 q^{84} - 44 q^{85} - 16 q^{86} + 232 q^{87} - 440 q^{88} - 36 q^{89} - 4 q^{90} + 56 q^{91} + 104 q^{94} + 64 q^{95} + 264 q^{97} + 12 q^{98} + 8 q^{99} + O(q^{100}) \)

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

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