Properties

Label 336.7.bp
Level $336$
Weight $7$
Character orbit 336.bp
Rep. character $\chi_{336}(67,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $768$
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.bp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 1552 768 784
Cusp forms 1520 768 752
Eisenstein series 32 0 32

Trace form

\( 768 q + 180 q^{4} + 3864 q^{8} + O(q^{10}) \) \( 768 q + 180 q^{4} + 3864 q^{8} - 756 q^{10} + 2720 q^{11} - 17056 q^{14} - 2820 q^{16} - 4860 q^{18} + 28000 q^{20} - 96480 q^{22} - 26240 q^{23} + 96120 q^{28} + 132800 q^{29} - 110880 q^{34} - 162336 q^{35} + 7200 q^{37} + 200200 q^{38} - 235956 q^{40} + 231660 q^{42} + 290880 q^{43} - 389572 q^{44} - 359100 q^{46} - 598752 q^{48} + 1580432 q^{50} + 1001448 q^{52} - 443680 q^{53} - 514360 q^{56} - 1237944 q^{58} - 886144 q^{59} + 627912 q^{60} - 1795248 q^{62} + 2286144 q^{64} + 775656 q^{66} - 1565952 q^{67} + 919100 q^{68} - 1229652 q^{70} - 1068032 q^{71} - 82620 q^{72} - 661584 q^{74} + 1242360 q^{76} + 277992 q^{78} - 1558172 q^{80} + 22674816 q^{81} + 1741740 q^{82} - 1312200 q^{84} + 400996 q^{86} + 848976 q^{88} - 775008 q^{91} - 5853976 q^{92} + 3244500 q^{94} + 2438100 q^{96} - 3017084 q^{98} - 1321920 q^{99} + O(q^{100}) \)

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

\( S_{7}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)