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Properties

Label 1456.2.gj
Level $1456$
Weight $2$
Character orbit 1456.gj
Rep. character $\chi_{1456}(53,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $768$
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.gj (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
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 912 768 144
Cusp forms 880 768 112
Eisenstein series 32 0 32

Trace form

\( 768 q + 4 q^{4} + 24 q^{8} + O(q^{10}) \) \( 768 q + 4 q^{4} + 24 q^{8} - 12 q^{10} + 8 q^{11} - 20 q^{16} - 40 q^{18} + 8 q^{22} - 40 q^{24} - 32 q^{29} - 40 q^{30} - 48 q^{31} - 20 q^{32} + 64 q^{34} - 24 q^{35} + 80 q^{36} + 16 q^{37} - 64 q^{40} - 40 q^{42} + 16 q^{43} + 40 q^{44} + 80 q^{47} - 16 q^{48} - 80 q^{50} - 40 q^{51} - 16 q^{53} - 144 q^{54} - 76 q^{56} + 24 q^{58} - 16 q^{60} + 88 q^{62} - 176 q^{64} + 28 q^{66} - 64 q^{67} - 120 q^{70} + 20 q^{72} + 16 q^{74} + 120 q^{76} + 100 q^{80} + 384 q^{81} - 80 q^{83} - 96 q^{84} + 100 q^{86} + 64 q^{88} - 112 q^{92} + 96 q^{94} - 48 q^{95} + 68 q^{96} + 20 q^{98} - 80 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1456, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)