Properties

Label 2535.2.o
Level $2535$
Weight $2$
Character orbit 2535.o
Rep. character $\chi_{2535}(746,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $408$
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.o (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
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 784 408 376
Cusp forms 672 408 264
Eisenstein series 112 0 112

Trace form

\( 408 q - 12 q^{6} + 16 q^{7} + O(q^{10}) \) \( 408 q - 12 q^{6} + 16 q^{7} - 4 q^{15} - 384 q^{16} - 4 q^{18} + 16 q^{19} + 12 q^{21} - 8 q^{24} + 24 q^{27} - 32 q^{28} - 32 q^{31} + 4 q^{33} + 16 q^{34} - 32 q^{37} + 32 q^{42} + 8 q^{45} + 40 q^{46} + 32 q^{48} + 32 q^{54} - 16 q^{55} + 36 q^{57} - 24 q^{58} - 16 q^{60} - 16 q^{61} - 8 q^{63} + 24 q^{66} + 32 q^{67} - 132 q^{72} + 64 q^{73} - 16 q^{76} - 48 q^{79} - 88 q^{81} - 124 q^{84} + 24 q^{85} - 16 q^{87} + 108 q^{93} + 48 q^{94} + 76 q^{96} - 24 q^{97} + 20 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2535, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)