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Properties

Label 1040.2.bs
Level $1040$
Weight $2$
Character orbit 1040.bs
Rep. character $\chi_{1040}(499,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $328$
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.bs (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1040 \)
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 344 344 0
Cusp forms 328 328 0
Eisenstein series 16 16 0

Trace form

\( 328 q - 12 q^{6} + O(q^{10}) \) \( 328 q - 12 q^{6} - 16 q^{10} + 8 q^{14} - 12 q^{15} - 8 q^{16} + 16 q^{20} + 16 q^{21} + 24 q^{24} + 12 q^{26} - 8 q^{29} + 20 q^{30} - 4 q^{34} - 4 q^{35} - 32 q^{36} - 8 q^{39} - 44 q^{40} + 36 q^{44} + 4 q^{45} + 28 q^{46} + 20 q^{50} - 52 q^{54} + 24 q^{55} + 56 q^{60} - 8 q^{61} - 96 q^{64} - 4 q^{65} - 8 q^{66} - 36 q^{70} + 24 q^{71} - 8 q^{74} + 16 q^{75} + 48 q^{76} - 12 q^{80} - 280 q^{81} - 100 q^{84} - 24 q^{85} + 32 q^{86} - 16 q^{89} - 12 q^{90} - 48 q^{91} - 40 q^{94} + 40 q^{95} + 76 q^{96} + 24 q^{99} + O(q^{100}) \)

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.