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Properties

Label 2960.2.ee
Level $2960$
Weight $2$
Character orbit 2960.ee
Rep. character $\chi_{2960}(251,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1216$
Sturm bound $912$

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Defining parameters

Level: \( N \) \(=\) \( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2960.ee (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 592 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(912\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2960, [\chi])\).

Total New Old
Modular forms 1840 1216 624
Cusp forms 1808 1216 592
Eisenstein series 32 0 32

Trace form

\( 1216 q + 8 q^{2} + 12 q^{4} + 8 q^{8} + O(q^{10}) \) \( 1216 q + 8 q^{2} + 12 q^{4} + 8 q^{8} + 16 q^{11} + 60 q^{12} - 16 q^{14} + 20 q^{16} - 20 q^{18} - 36 q^{22} - 16 q^{23} - 56 q^{24} - 608 q^{25} - 20 q^{28} + 32 q^{29} - 16 q^{30} + 28 q^{32} - 32 q^{36} - 32 q^{37} + 20 q^{42} + 12 q^{44} - 60 q^{46} - 608 q^{49} - 4 q^{50} - 20 q^{52} - 48 q^{53} + 28 q^{54} - 24 q^{56} + 28 q^{60} - 56 q^{62} - 48 q^{64} + 52 q^{66} + 64 q^{68} + 40 q^{72} - 68 q^{74} - 92 q^{76} + 48 q^{77} + 80 q^{79} + 608 q^{81} - 32 q^{82} + 120 q^{83} - 112 q^{84} + 32 q^{86} + 68 q^{88} - 104 q^{92} + 136 q^{94} - 24 q^{96} + 12 q^{98} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2960, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2960, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(592, [\chi])\)\(^{\oplus 2}\)