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Properties

Label 1040.2.cn
Level $1040$
Weight $2$
Character orbit 1040.cn
Rep. character $\chi_{1040}(27,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $288$
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.cn (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 344 288 56
Cusp forms 328 288 40
Eisenstein series 16 0 16

Trace form

\( 288 q - 8 q^{4} + 12 q^{8} + 288 q^{9} + O(q^{10}) \) \( 288 q - 8 q^{4} + 12 q^{8} + 288 q^{9} - 8 q^{12} + 8 q^{16} + 28 q^{18} + 16 q^{19} + 12 q^{20} - 8 q^{22} - 44 q^{28} - 80 q^{30} - 40 q^{32} - 32 q^{34} - 24 q^{35} - 32 q^{36} - 44 q^{38} - 28 q^{40} + 40 q^{42} + 48 q^{44} - 32 q^{46} - 48 q^{47} - 4 q^{48} + 28 q^{50} - 16 q^{51} - 8 q^{52} - 48 q^{56} - 60 q^{58} + 40 q^{60} - 32 q^{61} + 60 q^{62} - 32 q^{64} - 48 q^{66} + 72 q^{68} + 32 q^{69} + 72 q^{70} + 80 q^{72} + 56 q^{74} - 40 q^{75} - 32 q^{76} + 72 q^{80} + 288 q^{81} - 28 q^{82} - 48 q^{84} - 112 q^{87} + 76 q^{88} + 32 q^{90} - 36 q^{92} + 56 q^{94} + 56 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1040, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)