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Properties

Label 1040.2.fa
Level $1040$
Weight $2$
Character orbit 1040.fa
Rep. character $\chi_{1040}(69,\cdot)$
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.fa (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

\( 656 q - 4 q^{4} - 12 q^{6} + O(q^{10}) \) \( 656 q - 4 q^{4} - 12 q^{6} - 2 q^{10} - 12 q^{11} - 48 q^{14} - 12 q^{15} - 4 q^{16} - 12 q^{19} - 6 q^{20} - 60 q^{24} - 64 q^{26} - 4 q^{29} + 14 q^{30} + 8 q^{35} - 36 q^{36} - 68 q^{40} - 36 q^{45} - 12 q^{46} + 272 q^{49} - 48 q^{50} - 40 q^{51} - 12 q^{54} + 24 q^{56} - 60 q^{59} - 4 q^{61} - 16 q^{64} - 16 q^{65} + 64 q^{66} + 20 q^{69} - 4 q^{74} + 8 q^{75} - 12 q^{76} - 192 q^{79} - 6 q^{80} + 256 q^{81} - 96 q^{84} - 36 q^{85} - 108 q^{90} - 4 q^{91} - 28 q^{94} - 4 q^{95} + O(q^{100}) \)

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.