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Properties

Label 1456.2.fb
Level $1456$
Weight $2$
Character orbit 1456.fb
Rep. character $\chi_{1456}(45,\cdot)$
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.fb (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

\( 880 q - 2 q^{2} - 6 q^{3} - 12 q^{6} - 8 q^{8} + O(q^{10}) \) \( 880 q - 2 q^{2} - 6 q^{3} - 12 q^{6} - 8 q^{8} - 6 q^{10} + 2 q^{11} - 24 q^{14} - 16 q^{15} - 4 q^{16} - 24 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{21} - 4 q^{22} - 24 q^{24} - 408 q^{25} - 18 q^{26} - 6 q^{28} - 4 q^{29} + 4 q^{30} - 12 q^{31} - 22 q^{32} - 12 q^{33} - 12 q^{34} - 2 q^{35} - 32 q^{36} - 4 q^{37} + 60 q^{38} - 72 q^{40} - 10 q^{42} - 12 q^{43} + 30 q^{44} + 12 q^{46} - 12 q^{47} - 12 q^{49} + 2 q^{50} - 36 q^{51} - 6 q^{52} - 4 q^{53} + 6 q^{54} + 60 q^{55} - 16 q^{56} + 12 q^{57} + 18 q^{58} - 48 q^{60} - 6 q^{61} - 36 q^{63} - 48 q^{64} - 4 q^{65} - 36 q^{66} + 2 q^{67} - 24 q^{70} - 50 q^{72} - 60 q^{74} - 12 q^{75} - 24 q^{76} - 14 q^{77} - 188 q^{78} - 8 q^{79} + 48 q^{80} + 380 q^{81} + 24 q^{82} - 12 q^{84} + 6 q^{85} - 78 q^{86} + 10 q^{88} - 108 q^{90} + 42 q^{91} - 32 q^{92} - 28 q^{93} + 84 q^{94} - 6 q^{96} + 42 q^{98} + O(q^{100}) \)

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.