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Properties

Label 1456.2.gg
Level $1456$
Weight $2$
Character orbit 1456.gg
Rep. character $\chi_{1456}(205,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $880$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.gg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1456 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1456, [\chi])\).

Total New Old
Modular forms 912 912 0
Cusp forms 880 880 0
Eisenstein series 32 32 0

Trace form

\( 880 q + 2 q^{3} - 4 q^{4} - 12 q^{6} + O(q^{10}) \) \( 880 q + 2 q^{3} - 4 q^{4} - 12 q^{6} + 2 q^{10} - 6 q^{11} - 4 q^{12} - 8 q^{13} + 4 q^{14} - 24 q^{15} - 4 q^{16} - 8 q^{17} - 24 q^{18} - 6 q^{19} + 12 q^{20} - 18 q^{21} + 8 q^{22} - 6 q^{24} - 2 q^{26} - 4 q^{27} + 30 q^{28} - 4 q^{29} + 10 q^{30} - 12 q^{33} + 18 q^{35} + 12 q^{36} - 24 q^{38} - 24 q^{40} + 82 q^{42} - 4 q^{43} - 24 q^{44} - 44 q^{48} - 4 q^{49} - 24 q^{50} - 16 q^{51} - 62 q^{52} - 4 q^{53} + 24 q^{56} - 6 q^{58} - 96 q^{60} + 2 q^{61} - 44 q^{62} - 12 q^{63} - 16 q^{64} - 4 q^{65} + 24 q^{66} - 6 q^{67} - 28 q^{68} + 8 q^{69} - 96 q^{70} - 54 q^{72} - 60 q^{74} - 8 q^{75} - 12 q^{76} - 22 q^{77} + 52 q^{78} - 8 q^{79} - 6 q^{80} + 380 q^{81} - 46 q^{82} - 6 q^{84} - 42 q^{85} + 2 q^{88} + 44 q^{90} - 54 q^{91} - 72 q^{92} + 22 q^{94} - 8 q^{95} + 60 q^{96} - 24 q^{97} - 6 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1456, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.