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Properties

Label 1040.2.ee
Level $1040$
Weight $2$
Character orbit 1040.ee
Rep. character $\chi_{1040}(379,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $656$
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.ee (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1040 \)
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 688 688 0
Cusp forms 656 656 0
Eisenstein series 32 32 0

Trace form

\( 656 q - 12 q^{4} - 8 q^{5} - 16 q^{6} + O(q^{10}) \) \( 656 q - 12 q^{4} - 8 q^{5} - 16 q^{6} - 10 q^{10} - 4 q^{11} - 32 q^{14} + 24 q^{15} - 28 q^{16} - 4 q^{19} - 10 q^{20} - 24 q^{26} - 4 q^{29} - 16 q^{30} - 16 q^{34} + 28 q^{35} + 4 q^{36} - 16 q^{39} + 32 q^{40} + 16 q^{44} - 36 q^{45} + 40 q^{46} - 24 q^{49} - 50 q^{50} + 88 q^{54} - 36 q^{55} - 12 q^{56} - 20 q^{59} - 8 q^{60} - 4 q^{61} - 96 q^{64} - 8 q^{65} - 16 q^{66} - 12 q^{69} - 100 q^{70} - 48 q^{71} - 52 q^{74} + 28 q^{75} - 48 q^{76} - 44 q^{80} + 256 q^{81} - 40 q^{84} + 24 q^{85} + 68 q^{86} - 16 q^{89} + 48 q^{90} - 68 q^{91} - 20 q^{94} - 20 q^{95} - 4 q^{96} + O(q^{100}) \)

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.