Properties

Label 1456.2.gd
Level $1456$
Weight $2$
Character orbit 1456.gd
Rep. character $\chi_{1456}(309,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $672$
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.gd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
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 912 672 240
Cusp forms 880 672 208
Eisenstein series 32 0 32

Trace form

\( 672 q + 36 q^{6} + O(q^{10}) \) \( 672 q + 36 q^{6} - 56 q^{12} - 16 q^{22} - 96 q^{24} - 8 q^{26} + 48 q^{27} - 16 q^{30} - 120 q^{32} + 12 q^{36} + 40 q^{40} - 32 q^{43} - 52 q^{48} - 336 q^{49} + 60 q^{50} - 64 q^{52} + 36 q^{62} + 72 q^{64} - 16 q^{65} - 128 q^{66} + 28 q^{68} - 108 q^{72} - 68 q^{74} + 32 q^{75} + 96 q^{76} - 40 q^{78} + 160 q^{79} + 336 q^{81} - 4 q^{82} - 124 q^{88} - 80 q^{90} - 48 q^{92} - 32 q^{94} - 128 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)