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Properties

Label 1456.2.dx
Level $1456$
Weight $2$
Character orbit 1456.dx
Rep. character $\chi_{1456}(367,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $112$
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.dx (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 364 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1456, [\chi])\).

Total New Old
Modular forms 472 112 360
Cusp forms 424 112 312
Eisenstein series 48 0 48

Trace form

\( 112 q + 112 q^{9} + O(q^{10}) \) \( 112 q + 112 q^{9} - 12 q^{13} + 8 q^{21} + 56 q^{25} - 8 q^{37} - 72 q^{41} + 4 q^{49} + 12 q^{53} - 32 q^{57} - 48 q^{65} + 72 q^{69} + 12 q^{73} + 36 q^{77} + 160 q^{81} + 20 q^{93} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)