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Properties

Label 304.7.q
Level $304$
Weight $7$
Character orbit 304.q
Rep. character $\chi_{304}(159,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
Sturm bound $280$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 304.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(304, [\chi])\).

Total New Old
Modular forms 492 120 372
Cusp forms 468 120 348
Eisenstein series 24 0 24

Trace form

\( 120 q + 15960 q^{9} + O(q^{10}) \) \( 120 q + 15960 q^{9} - 2520 q^{13} - 20520 q^{17} - 9720 q^{21} - 187500 q^{25} - 62100 q^{33} - 55440 q^{37} + 90012 q^{41} - 1912008 q^{49} - 182280 q^{53} + 118272 q^{57} + 362880 q^{61} - 268032 q^{65} + 405540 q^{73} - 1518528 q^{77} - 2790780 q^{81} - 1748520 q^{85} - 1080504 q^{89} - 4737528 q^{93} - 2276460 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

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

Decomposition of \(S_{7}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(304, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)