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Properties

Label 1792.3.o
Level $1792$
Weight $3$
Character orbit 1792.o
Rep. character $\chi_{1792}(639,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $248$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1792.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 1072 264 808
Cusp forms 976 248 728
Eisenstein series 96 16 80

Trace form

\( 248 q - 344 q^{9} + O(q^{10}) \) \( 248 q - 344 q^{9} - 4 q^{17} + 544 q^{25} - 76 q^{33} + 16 q^{41} - 72 q^{49} - 296 q^{57} - 104 q^{65} - 316 q^{73} - 796 q^{81} + 4 q^{89} - 1808 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{3}^{\mathrm{old}}(1792, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 3}\)