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Properties

Label 336.4.bs
Level $336$
Weight $4$
Character orbit 336.bs
Rep. character $\chi_{336}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $384$
Sturm bound $256$

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Defining parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.bs (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(256\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(336, [\chi])\).

Total New Old
Modular forms 784 384 400
Cusp forms 752 384 368
Eisenstein series 32 0 32

Trace form

\( 384 q + 20 q^{4} + 168 q^{8} + O(q^{10}) \) \( 384 q + 20 q^{4} + 168 q^{8} - 36 q^{10} - 40 q^{11} + 416 q^{14} + 60 q^{16} - 36 q^{18} - 976 q^{22} + 656 q^{23} + 416 q^{28} - 800 q^{29} + 456 q^{35} + 16 q^{37} - 2340 q^{40} + 660 q^{42} - 1616 q^{43} - 732 q^{44} - 700 q^{46} + 4256 q^{50} + 2160 q^{52} - 752 q^{53} + 3080 q^{56} + 808 q^{58} + 4128 q^{59} + 1224 q^{60} - 7840 q^{64} + 4104 q^{66} + 2256 q^{67} - 6060 q^{68} - 6220 q^{70} - 896 q^{71} - 612 q^{72} + 840 q^{74} + 3672 q^{78} - 7524 q^{80} + 15552 q^{81} - 5220 q^{82} - 1800 q^{84} + 8348 q^{86} - 496 q^{88} - 3496 q^{91} - 11432 q^{92} + 7020 q^{94} + 7740 q^{96} + 5516 q^{98} - 720 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(336, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)