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Properties

Label 2760.2.cs
Level $2760$
Weight $2$
Character orbit 2760.cs
Rep. character $\chi_{2760}(49,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $720$
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.cs (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
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 5920 720 5200
Cusp forms 5600 720 4880
Eisenstein series 320 0 320

Trace form

\( 720 q + 72 q^{9} + O(q^{10}) \) \( 720 q + 72 q^{9} - 8 q^{11} + 32 q^{19} + 8 q^{21} - 8 q^{25} - 8 q^{31} - 8 q^{35} - 36 q^{39} + 24 q^{41} + 48 q^{49} - 24 q^{51} - 8 q^{55} - 68 q^{59} + 24 q^{61} - 24 q^{65} + 16 q^{71} - 16 q^{75} + 8 q^{79} - 72 q^{81} - 132 q^{85} - 24 q^{89} + 496 q^{91} - 224 q^{95} + 8 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2760, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(920, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1380, [\chi])\)\(^{\oplus 2}\)