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Properties

Label 2640.2.fo
Level $2640$
Weight $2$
Character orbit 2640.fo
Rep. character $\chi_{2640}(613,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2304$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2640.fo (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 880 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2640, [\chi])\).

Total New Old
Modular forms 4672 2304 2368
Cusp forms 4544 2304 2240
Eisenstein series 128 0 128

Trace form

\( 2304 q - 576 q^{9} + O(q^{10}) \) \( 2304 q - 576 q^{9} - 16 q^{12} - 28 q^{22} + 40 q^{30} + 64 q^{34} - 56 q^{38} + 140 q^{40} - 192 q^{44} - 140 q^{50} + 40 q^{52} - 96 q^{56} - 80 q^{58} + 32 q^{59} + 24 q^{66} - 88 q^{70} - 48 q^{75} + 96 q^{78} - 16 q^{80} - 576 q^{81} + 16 q^{82} + 400 q^{83} + 16 q^{86} - 12 q^{88} - 32 q^{91} + 20 q^{92} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2640, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2640, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(880, [\chi])\)\(^{\oplus 2}\)