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Properties

Label 336.6.bj
Level $336$
Weight $6$
Character orbit 336.bj
Rep. character $\chi_{336}(95,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 336.bj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(336, [\chi])\).

Total New Old
Modular forms 664 160 504
Cusp forms 616 160 456
Eisenstein series 48 0 48

Trace form

\( 160 q + O(q^{10}) \) \( 160 q + 232 q^{13} - 2460 q^{21} + 54092 q^{25} + 1076 q^{37} + 17700 q^{45} - 34904 q^{49} - 123888 q^{57} - 50152 q^{61} - 314592 q^{69} + 45988 q^{73} + 118476 q^{81} - 298608 q^{85} + 222024 q^{93} - 50888 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(336, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)