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Properties

Label 2640.2.bi
Level $2640$
Weight $2$
Character orbit 2640.bi
Rep. character $\chi_{2640}(571,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $384$
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.bi (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 176 \)
Character field: \(\Q(i)\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 1168 384 784
Cusp forms 1136 384 752
Eisenstein series 32 0 32

Trace form

\( 384 q + 16 q^{4} + O(q^{10}) \) \( 384 q + 16 q^{4} - 16 q^{11} - 32 q^{14} - 16 q^{16} + 16 q^{20} - 16 q^{22} - 64 q^{23} - 80 q^{34} - 64 q^{37} + 8 q^{44} - 384 q^{49} + 64 q^{53} + 16 q^{56} - 16 q^{58} - 32 q^{59} + 64 q^{64} - 24 q^{66} + 32 q^{67} - 16 q^{70} - 64 q^{71} - 32 q^{77} + 48 q^{78} - 384 q^{81} + 80 q^{82} + 112 q^{86} - 88 q^{88} + 64 q^{91} + 144 q^{92} - 16 q^{99} + O(q^{100}) \)

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

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