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Properties

Label 1040.2.bb
Level $1040$
Weight $2$
Character orbit 1040.bb
Rep. character $\chi_{1040}(333,\cdot)$
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.bb (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

\( 328 q - 4 q^{2} - 4 q^{5} - 4 q^{6} - 4 q^{8} - 312 q^{9} + O(q^{10}) \) \( 328 q - 4 q^{2} - 4 q^{5} - 4 q^{6} - 4 q^{8} - 312 q^{9} - 8 q^{10} + 8 q^{12} - 4 q^{15} - 8 q^{16} + 12 q^{18} - 4 q^{20} - 32 q^{22} - 4 q^{24} - 12 q^{26} - 28 q^{30} - 8 q^{31} - 24 q^{32} - 8 q^{33} - 16 q^{34} - 4 q^{35} - 32 q^{36} + 4 q^{37} - 8 q^{38} + 24 q^{39} - 44 q^{40} + 8 q^{42} - 24 q^{44} + 12 q^{45} - 4 q^{46} + 8 q^{48} + 280 q^{49} - 32 q^{50} - 12 q^{52} - 8 q^{53} + 4 q^{54} - 56 q^{58} + 32 q^{59} + 4 q^{60} - 8 q^{61} - 44 q^{62} - 64 q^{63} + 4 q^{65} - 8 q^{66} - 4 q^{67} + 32 q^{68} + 52 q^{70} + 12 q^{72} - 16 q^{75} - 4 q^{76} + 56 q^{78} + 44 q^{80} + 248 q^{81} + 16 q^{82} + 44 q^{83} + 20 q^{84} - 20 q^{85} + 8 q^{86} + 24 q^{87} + 32 q^{90} - 20 q^{91} + 12 q^{92} + 16 q^{93} - 24 q^{96} - 8 q^{97} - 40 q^{98} + O(q^{100}) \)

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.