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Properties

Label 336.7.t
Level $336$
Weight $7$
Character orbit 336.t
Rep. character $\chi_{336}(29,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $576$
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.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 776 576 200
Cusp forms 760 576 184
Eisenstein series 16 0 16

Trace form

\( 576 q - 1020 q^{6} + O(q^{10}) \) \( 576 q - 1020 q^{6} - 3000 q^{10} - 8580 q^{12} - 9432 q^{16} + 7872 q^{19} + 51408 q^{22} - 52256 q^{24} + 68640 q^{27} + 204304 q^{30} - 145464 q^{34} - 237160 q^{36} + 390528 q^{43} - 301944 q^{46} + 349492 q^{48} - 9680832 q^{49} + 882288 q^{52} + 1654680 q^{58} - 1228216 q^{60} + 652992 q^{61} + 1081080 q^{64} + 885308 q^{66} - 1207680 q^{67} - 568008 q^{70} + 1185800 q^{72} - 2762144 q^{75} + 5689416 q^{76} - 4320280 q^{78} - 1721856 q^{79} + 1341600 q^{82} - 744000 q^{85} - 1151928 q^{88} + 8442344 q^{90} + 2349600 q^{93} - 1254384 q^{94} - 104992 q^{96} + 5970688 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{7}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)