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Properties

Label 2535.2.bl
Level $2535$
Weight $2$
Character orbit 2535.bl
Rep. character $\chi_{2535}(653,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1152$
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.bl (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 195 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 1568 1312 256
Cusp forms 1344 1152 192
Eisenstein series 224 160 64

Trace form

\( 1152 q + 2 q^{3} + 4 q^{6} + 4 q^{7} + O(q^{10}) \) \( 1152 q + 2 q^{3} + 4 q^{6} + 4 q^{7} + 20 q^{10} + 28 q^{12} + 2 q^{15} + 464 q^{16} - 16 q^{18} + 8 q^{21} + 4 q^{22} + 16 q^{25} + 8 q^{27} + 44 q^{28} + 16 q^{30} - 16 q^{31} + 46 q^{33} + 36 q^{36} - 20 q^{37} - 24 q^{40} + 4 q^{42} + 32 q^{43} + 22 q^{45} + 8 q^{48} - 48 q^{51} - 68 q^{57} + 20 q^{58} - 96 q^{60} + 8 q^{61} + 18 q^{63} - 160 q^{66} + 52 q^{67} + 24 q^{70} - 6 q^{72} - 64 q^{73} - 64 q^{75} + 104 q^{76} - 16 q^{81} - 36 q^{82} + 108 q^{85} + 74 q^{87} - 156 q^{88} + 92 q^{90} - 32 q^{93} + 240 q^{96} - 48 q^{97} + O(q^{100}) \)

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

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