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Properties

Label 1456.2.gu
Level $1456$
Weight $2$
Character orbit 1456.gu
Rep. character $\chi_{1456}(219,\cdot)$
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.gu (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

\( 880 q - 2 q^{2} + 2 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{8} + O(q^{10}) \) \( 880 q - 2 q^{2} + 2 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{8} + 2 q^{10} - 6 q^{11} - 8 q^{13} + 8 q^{14} - 24 q^{15} - 4 q^{16} - 4 q^{18} - 6 q^{19} - 40 q^{20} - 14 q^{21} - 4 q^{22} + 4 q^{24} + 408 q^{25} - 38 q^{26} - 4 q^{27} - 22 q^{28} - 4 q^{29} - 16 q^{30} - 22 q^{32} - 4 q^{33} - 12 q^{34} - 2 q^{35} + 8 q^{36} - 4 q^{37} - 72 q^{38} - 4 q^{39} + 16 q^{40} - 10 q^{42} - 12 q^{43} - 2 q^{44} - 68 q^{45} + 4 q^{46} - 44 q^{48} - 12 q^{49} - 38 q^{50} + 36 q^{51} - 6 q^{52} - 4 q^{53} - 42 q^{54} - 8 q^{55} + 4 q^{56} + 12 q^{57} - 30 q^{58} - 64 q^{60} + 2 q^{61} - 12 q^{62} + 12 q^{63} + 48 q^{64} - 4 q^{65} - 60 q^{66} - 6 q^{67} + 60 q^{68} - 12 q^{69} + 44 q^{70} + 16 q^{71} - 50 q^{72} + 52 q^{74} + 20 q^{75} + 14 q^{77} - 92 q^{78} - 80 q^{80} + 380 q^{81} + 4 q^{82} - 164 q^{84} - 14 q^{85} - 70 q^{86} - 8 q^{87} - 22 q^{88} - 48 q^{90} - 50 q^{91} - 28 q^{93} - 64 q^{94} - 80 q^{95} - 10 q^{96} - 16 q^{97} - 90 q^{98} + 8 q^{99} + O(q^{100}) \)

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.