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Properties

Label 336.4.bq
Level $336$
Weight $4$
Character orbit 336.bq
Rep. character $\chi_{336}(37,\cdot)$
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.bq (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

\( 384 q + 20 q^{4} - 168 q^{8} + O(q^{10}) \) \( 384 q + 20 q^{4} - 168 q^{8} + 12 q^{10} + 40 q^{11} - 416 q^{14} + 60 q^{16} + 36 q^{18} - 160 q^{20} - 32 q^{22} + 344 q^{28} + 800 q^{29} + 1488 q^{31} - 288 q^{34} + 456 q^{35} - 16 q^{37} - 440 q^{38} + 492 q^{40} - 660 q^{42} + 1616 q^{43} - 1732 q^{44} - 700 q^{46} + 1056 q^{48} - 1456 q^{50} + 2376 q^{52} - 752 q^{53} + 3080 q^{56} + 2824 q^{58} - 1376 q^{59} + 1224 q^{60} + 1872 q^{62} - 1792 q^{64} - 1368 q^{66} - 1440 q^{67} - 2020 q^{68} - 3700 q^{70} + 612 q^{72} - 3472 q^{74} - 1224 q^{76} - 3672 q^{78} - 220 q^{80} + 15552 q^{81} + 1740 q^{82} - 1800 q^{84} - 8348 q^{86} + 496 q^{88} + 3496 q^{91} + 4648 q^{92} + 180 q^{94} - 7728 q^{95} + 2580 q^{96} - 796 q^{98} - 720 q^{99} + O(q^{100}) \)

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

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