Properties

Label 1792.3.bg
Level $1792$
Weight $3$
Character orbit 1792.bg
Rep. character $\chi_{1792}(33,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $992$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1792.bg (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 224 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1792, [\chi])\).

Total New Old
Modular forms 4224 1056 3168
Cusp forms 3968 992 2976
Eisenstein series 256 64 192

Trace form

\( 992 q + 24 q^{5} - 8 q^{9} + O(q^{10}) \) \( 992 q + 24 q^{5} - 8 q^{9} + 16 q^{21} - 8 q^{25} + 32 q^{29} - 48 q^{33} + 8 q^{37} - 192 q^{45} - 312 q^{53} - 32 q^{57} + 24 q^{61} - 16 q^{65} - 24 q^{73} + 16 q^{77} - 368 q^{85} - 24 q^{89} + 152 q^{93} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1792, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1792, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1792, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 2}\)