Properties

Label 1792.2.bh
Level $1792$
Weight $2$
Character orbit 1792.bh
Rep. character $\chi_{1792}(289,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $480$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1792.bh (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 224 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(512\)

Dimensions

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

Total New Old
Modular forms 2176 544 1632
Cusp forms 1920 480 1440
Eisenstein series 256 64 192

Trace form

\( 480q + 8q^{5} - 8q^{9} + O(q^{10}) \) \( 480q + 8q^{5} - 8q^{9} + 32q^{13} + 16q^{21} - 8q^{25} + 32q^{29} - 16q^{33} + 8q^{37} - 32q^{41} - 16q^{45} + 40q^{53} - 32q^{57} + 8q^{61} - 16q^{65} + 32q^{69} - 8q^{73} + 16q^{77} + 112q^{85} - 8q^{89} - 40q^{93} - 64q^{97} + O(q^{100}) \)

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

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