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Properties

Label 336.7.z
Level $336$
Weight $7$
Character orbit 336.z
Rep. character $\chi_{336}(47,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 336.z (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(336, [\chi])\).

Total New Old
Modular forms 792 192 600
Cusp forms 744 192 552
Eisenstein series 48 0 48

Trace form

\( 192 q + O(q^{10}) \) \( 192 q - 24072 q^{21} - 335784 q^{25} - 27720 q^{37} - 693000 q^{45} + 236160 q^{49} - 849696 q^{57} - 385560 q^{73} - 210408 q^{81} - 1951776 q^{85} + 300720 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(336, [\chi])\) into newform subspaces

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

Decomposition of \(S_{7}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)