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Properties

Label 1040.2.fd
Level $1040$
Weight $2$
Character orbit 1040.fd
Rep. character $\chi_{1040}(197,\cdot)$
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.fd (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

\( 656 q - 2 q^{2} - 8 q^{5} - 8 q^{6} - 8 q^{8} + 312 q^{9} + O(q^{10}) \) \( 656 q - 2 q^{2} - 8 q^{5} - 8 q^{6} - 8 q^{8} + 312 q^{9} + 2 q^{10} - 12 q^{11} + 16 q^{12} - 8 q^{15} - 28 q^{16} - 12 q^{17} - 12 q^{18} + 22 q^{20} - 4 q^{22} + 4 q^{24} - 6 q^{28} - 8 q^{30} - 16 q^{31} - 12 q^{32} - 4 q^{33} - 8 q^{34} + 28 q^{35} - 28 q^{36} - 4 q^{37} + 8 q^{38} - 24 q^{39} + 32 q^{40} + 76 q^{42} - 12 q^{43} + 24 q^{44} + 12 q^{45} - 8 q^{46} + 64 q^{48} - 280 q^{49} + 26 q^{50} + 6 q^{52} - 16 q^{53} + 20 q^{54} - 60 q^{55} - 12 q^{56} - 22 q^{58} + 16 q^{59} + 20 q^{60} - 4 q^{61} - 28 q^{62} + 52 q^{63} - 16 q^{65} - 16 q^{66} - 8 q^{67} + 40 q^{68} + 44 q^{70} + 30 q^{72} - 8 q^{75} - 8 q^{76} + 52 q^{78} + 34 q^{80} - 272 q^{81} - 22 q^{82} - 32 q^{83} - 20 q^{84} - 16 q^{85} - 44 q^{86} - 24 q^{87} - 30 q^{88} + 64 q^{90} - 40 q^{91} - 24 q^{92} + 20 q^{93} + 24 q^{94} - 12 q^{95} - 96 q^{96} - 4 q^{97} + 106 q^{98} + O(q^{100}) \)

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.