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Properties

Label 2535.2.ch
Level $2535$
Weight $2$
Character orbit 2535.ch
Rep. character $\chi_{2535}(112,\cdot)$
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.ch (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

\( 4368 q + 364 q^{4} - 8 q^{5} + O(q^{10}) \) \( 4368 q + 364 q^{4} - 8 q^{5} + 8 q^{11} + 12 q^{13} - 4 q^{15} - 364 q^{16} + 28 q^{17} + 4 q^{18} - 8 q^{21} + 40 q^{22} - 4 q^{25} + 16 q^{31} - 28 q^{34} - 32 q^{37} - 8 q^{39} + 40 q^{40} - 4 q^{41} - 260 q^{42} + 8 q^{43} - 40 q^{44} + 4 q^{45} + 16 q^{46} + 24 q^{47} - 628 q^{49} + 32 q^{50} - 52 q^{52} + 144 q^{53} - 148 q^{55} + 8 q^{58} + 384 q^{59} - 196 q^{60} - 16 q^{61} - 72 q^{62} + 364 q^{64} + 8 q^{65} - 16 q^{66} - 208 q^{67} - 60 q^{68} + 144 q^{70} - 40 q^{71} - 12 q^{72} - 260 q^{74} + 40 q^{76} + 48 q^{77} - 8 q^{78} + 32 q^{80} + 364 q^{81} + 4 q^{82} + 104 q^{83} + 32 q^{84} + 4 q^{85} - 16 q^{86} - 184 q^{87} + 440 q^{88} + 36 q^{89} + 4 q^{90} + 56 q^{91} - 104 q^{94} - 64 q^{95} + 312 q^{97} - 8 q^{99} + O(q^{100}) \)

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

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