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Properties

Label 2535.2.m
Level $2535$
Weight $2$
Character orbit 2535.m
Rep. character $\chi_{2535}(677,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $576$
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.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
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 784 664 120
Cusp forms 672 576 96
Eisenstein series 112 88 24

Trace form

\( 576 q + 4 q^{3} + 8 q^{6} + 8 q^{7} + O(q^{10}) \) \( 576 q + 4 q^{3} + 8 q^{6} + 8 q^{7} - 8 q^{10} - 16 q^{12} + 4 q^{15} - 440 q^{16} + 28 q^{18} + 16 q^{21} + 8 q^{22} + 8 q^{25} + 4 q^{27} - 8 q^{28} - 40 q^{30} + 16 q^{31} - 4 q^{33} - 24 q^{36} - 40 q^{37} - 48 q^{40} + 8 q^{42} - 32 q^{43} + 44 q^{45} - 140 q^{48} + 48 q^{51} + 20 q^{57} + 88 q^{58} - 36 q^{60} + 16 q^{61} - 48 q^{63} - 152 q^{66} + 8 q^{67} + 120 q^{70} - 36 q^{72} - 8 q^{73} + 40 q^{75} + 16 q^{76} + 16 q^{81} - 68 q^{87} + 24 q^{88} - 8 q^{90} + 20 q^{93} + 96 q^{97} + O(q^{100}) \)

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

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