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Properties

Label 2760.2.cl
Level $2760$
Weight $2$
Character orbit 2760.cl
Rep. character $\chi_{2760}(451,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1920$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2760.cl (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 184 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2760, [\chi])\).

Total New Old
Modular forms 5840 1920 3920
Cusp forms 5680 1920 3760
Eisenstein series 160 0 160

Trace form

\( 1920 q - 8 q^{2} + 12 q^{4} - 4 q^{6} - 8 q^{8} - 192 q^{9} + O(q^{10}) \) \( 1920 q - 8 q^{2} + 12 q^{4} - 4 q^{6} - 8 q^{8} - 192 q^{9} + 12 q^{16} - 8 q^{18} - 4 q^{24} - 192 q^{25} - 40 q^{26} + 32 q^{32} + 22 q^{34} - 32 q^{36} + 220 q^{38} - 22 q^{40} - 44 q^{44} + 140 q^{46} - 144 q^{48} - 192 q^{49} + 36 q^{50} + 32 q^{52} + 18 q^{54} - 220 q^{56} + 12 q^{58} - 22 q^{60} - 48 q^{62} - 36 q^{64} - 8 q^{72} + 44 q^{74} - 192 q^{81} + 224 q^{82} + 352 q^{88} + 356 q^{92} + 308 q^{94} - 4 q^{96} + 256 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2760, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2760, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2760, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(552, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(920, [\chi])\)\(^{\oplus 2}\)