Properties

Label 392.6.l
Level $392$
Weight $6$
Character orbit 392.l
Rep. character $\chi_{392}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $0$
Newform subspaces $0$
Sturm bound $336$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 392.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 0 \)
Sturm bound: \(336\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(392, [\chi])\).

Total New Old
Modular forms 592 0 592
Cusp forms 528 0 528
Eisenstein series 64 0 64

Decomposition of \(S_{6}^{\mathrm{old}}(392, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(392, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)