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Properties

Label 336.7.r
Level $336$
Weight $7$
Character orbit 336.r
Rep. character $\chi_{336}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $384$
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.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
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 776 384 392
Cusp forms 760 384 376
Eisenstein series 16 0 16

Trace form

\( 384 q - 180 q^{4} + 3864 q^{8} + O(q^{10}) \) \( 384 q - 180 q^{4} + 3864 q^{8} + 2720 q^{11} + 8528 q^{14} + 2820 q^{16} - 4860 q^{18} + 64620 q^{22} - 74880 q^{28} - 66400 q^{29} + 162336 q^{35} + 7200 q^{37} + 231660 q^{42} - 145440 q^{43} - 538644 q^{44} - 718200 q^{46} + 1142932 q^{50} + 443680 q^{53} - 257180 q^{56} - 211812 q^{58} - 627912 q^{60} - 2014740 q^{64} + 2829984 q^{67} - 1190808 q^{70} - 82620 q^{72} + 2785244 q^{74} + 575424 q^{78} - 22674816 q^{81} + 1312200 q^{84} - 4734092 q^{86} - 672852 q^{88} - 775008 q^{91} - 4404344 q^{92} - 7171584 q^{95} + 4673408 q^{98} - 660960 q^{99} + O(q^{100}) \)

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

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