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Properties

Label 1456.2.fm
Level $1456$
Weight $2$
Character orbit 1456.fm
Rep. character $\chi_{1456}(3,\cdot)$
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.fm (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

\( 880 q + 2 q^{2} + 2 q^{4} - 12 q^{5} - 4 q^{7} - 16 q^{8} + O(q^{10}) \) \( 880 q + 2 q^{2} + 2 q^{4} - 12 q^{5} - 4 q^{7} - 16 q^{8} - 4 q^{11} - 12 q^{12} - 28 q^{14} + 2 q^{16} - 12 q^{17} + 4 q^{18} - 24 q^{20} - 2 q^{21} - 16 q^{22} + 4 q^{23} - 6 q^{26} + 28 q^{28} - 4 q^{29} - 20 q^{30} + 2 q^{32} + 8 q^{35} + 12 q^{36} + 2 q^{37} - 12 q^{38} - 4 q^{39} + 48 q^{40} - 86 q^{42} - 4 q^{43} - 12 q^{44} - 42 q^{45} + 8 q^{46} - 4 q^{49} - 8 q^{50} + 8 q^{51} - 96 q^{52} - 4 q^{53} + 66 q^{54} + 4 q^{56} - 4 q^{58} + 42 q^{59} - 36 q^{60} - 12 q^{62} - 16 q^{64} - 4 q^{65} + 48 q^{66} - 4 q^{67} - 66 q^{68} + 36 q^{69} + 8 q^{70} + 56 q^{71} + 140 q^{72} - 26 q^{74} + 24 q^{75} - 22 q^{77} + 100 q^{78} - 760 q^{81} - 64 q^{84} - 14 q^{85} - 20 q^{86} - 12 q^{87} - 4 q^{88} - 26 q^{91} + 40 q^{92} - 10 q^{93} + 48 q^{96} + 24 q^{98} + 32 q^{99} + O(q^{100}) \)

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.