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Properties

Label 1040.2.et
Level $1040$
Weight $2$
Character orbit 1040.et
Rep. character $\chi_{1040}(11,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $448$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1040.et (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1040, [\chi])\).

Total New Old
Modular forms 688 448 240
Cusp forms 656 448 208
Eisenstein series 32 0 32

Trace form

\( 448 q - 12 q^{6} - 12 q^{8} + O(q^{10}) \) \( 448 q - 12 q^{6} - 12 q^{8} - 16 q^{14} - 24 q^{16} - 24 q^{18} - 16 q^{20} + 56 q^{24} - 448 q^{25} + 8 q^{26} - 64 q^{28} + 60 q^{34} + 20 q^{36} + 40 q^{38} + 40 q^{42} + 16 q^{44} + 52 q^{46} + 40 q^{48} + 52 q^{54} - 20 q^{56} + 68 q^{58} + 48 q^{59} - 36 q^{62} + 48 q^{64} + 80 q^{66} - 24 q^{68} - 8 q^{70} + 32 q^{71} + 40 q^{72} + 104 q^{74} + 24 q^{76} + 100 q^{78} + 48 q^{80} + 224 q^{81} + 116 q^{82} + 16 q^{84} - 100 q^{86} - 60 q^{88} - 16 q^{91} - 48 q^{92} - 96 q^{93} + 68 q^{94} - 92 q^{96} - 112 q^{98} - 128 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1040, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1040, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1040, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)