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Properties

Label 1040.2.cj
Level $1040$
Weight $2$
Character orbit 1040.cj
Rep. character $\chi_{1040}(213,\cdot)$
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.cj (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

\( 328 q - 8 q^{3} - 4 q^{5} - 4 q^{6} + 312 q^{9} + O(q^{10}) \) \( 328 q - 8 q^{3} - 4 q^{5} - 4 q^{6} + 312 q^{9} - 8 q^{10} - 8 q^{12} - 4 q^{13} - 4 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{20} + 8 q^{22} + 4 q^{24} - 12 q^{26} - 32 q^{27} + 12 q^{28} - 12 q^{30} - 8 q^{31} + 16 q^{34} - 4 q^{35} - 32 q^{36} - 4 q^{37} - 8 q^{38} - 24 q^{39} - 44 q^{40} - 16 q^{42} + 32 q^{43} + 24 q^{44} - 12 q^{45} - 4 q^{46} - 8 q^{47} - 16 q^{48} - 280 q^{49} + 12 q^{50} + 4 q^{52} - 4 q^{54} - 24 q^{57} - 4 q^{58} - 32 q^{59} + 16 q^{60} - 8 q^{61} + 44 q^{62} - 12 q^{65} - 8 q^{66} + 4 q^{67} - 72 q^{68} + 40 q^{70} - 36 q^{72} + 16 q^{73} + 16 q^{75} - 4 q^{76} + 56 q^{77} + 36 q^{78} - 32 q^{80} + 248 q^{81} - 44 q^{83} - 20 q^{84} + 20 q^{85} + 8 q^{86} - 24 q^{87} + 64 q^{88} - 32 q^{90} - 20 q^{91} + 12 q^{92} - 16 q^{93} - 24 q^{96} + 20 q^{98} + O(q^{100}) \)

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.