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Properties

Label 1456.2.gm
Level $1456$
Weight $2$
Character orbit 1456.gm
Rep. character $\chi_{1456}(397,\cdot)$
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.gm (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

\( 880 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 8 q^{8} + O(q^{10}) \) \( 880 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 8 q^{8} - 12 q^{10} - 24 q^{14} - 16 q^{15} + 26 q^{16} - 12 q^{17} + 26 q^{18} - 12 q^{19} - 18 q^{21} - 4 q^{22} - 24 q^{24} + 408 q^{25} - 6 q^{26} - 18 q^{28} - 4 q^{29} + 20 q^{30} - 12 q^{31} - 12 q^{32} - 12 q^{33} + 12 q^{34} - 32 q^{35} + 8 q^{36} - 6 q^{37} - 60 q^{38} - 72 q^{40} + 38 q^{42} - 12 q^{43} + 22 q^{44} - 6 q^{45} + 26 q^{46} - 12 q^{47} - 12 q^{49} - 2 q^{50} + 36 q^{51} + 48 q^{52} - 4 q^{53} + 30 q^{54} + 60 q^{55} - 26 q^{56} - 12 q^{57} - 34 q^{58} + 42 q^{59} - 6 q^{60} + 48 q^{63} + 48 q^{64} - 4 q^{65} - 36 q^{66} - 6 q^{68} + 76 q^{70} + 94 q^{72} + 30 q^{74} - 36 q^{75} - 24 q^{76} + 14 q^{77} - 28 q^{78} - 8 q^{79} + 108 q^{80} - 760 q^{81} - 12 q^{82} - 4 q^{84} - 42 q^{85} - 38 q^{86} + 32 q^{88} + 108 q^{90} - 58 q^{91} - 32 q^{92} + 30 q^{93} - 108 q^{94} - 12 q^{95} + 54 q^{96} - 82 q^{98} + 32 q^{99} + O(q^{100}) \)

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.