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Properties

Label 2640.2.fw
Level $2640$
Weight $2$
Character orbit 2640.fw
Rep. character $\chi_{2640}(181,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1536$
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.fw (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 176 \)
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 1536 3136
Cusp forms 4544 1536 3008
Eisenstein series 128 0 128

Trace form

\( 1536 q - 16 q^{4} + O(q^{10}) \) \( 1536 q - 16 q^{4} - 16 q^{11} + 40 q^{14} + 16 q^{16} - 24 q^{18} + 16 q^{20} + 104 q^{22} - 48 q^{28} - 64 q^{29} + 80 q^{32} + 80 q^{34} + 96 q^{37} + 32 q^{43} + 8 q^{44} + 64 q^{46} + 384 q^{49} - 16 q^{50} + 112 q^{52} - 96 q^{53} + 16 q^{56} - 16 q^{58} + 32 q^{59} + 32 q^{63} - 88 q^{64} + 24 q^{66} + 32 q^{67} - 16 q^{70} + 24 q^{72} + 136 q^{74} + 256 q^{76} + 32 q^{77} + 48 q^{78} + 384 q^{81} + 120 q^{82} + 144 q^{84} + 176 q^{86} - 8 q^{88} - 176 q^{91} + 208 q^{92} + 192 q^{94} + 120 q^{96} + 64 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(880, [\chi])\)\(^{\oplus 2}\)