Properties

Label 1792.2.x
Level $1792$
Weight $2$
Character orbit 1792.x
Rep. character $\chi_{1792}(223,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $240$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1792.x (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 224 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1792, [\chi])\).

Total New Old
Modular forms 1088 272 816
Cusp forms 960 240 720
Eisenstein series 128 32 96

Trace form

\( 240q - 16q^{9} + O(q^{10}) \) \( 240q - 16q^{9} + 8q^{21} - 16q^{25} + 16q^{29} + 16q^{37} - 16q^{53} - 16q^{57} - 32q^{65} + 8q^{77} + 96q^{85} + 64q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1792, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1792, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1792, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 2}\)