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Properties

Label 336.7.br
Level $336$
Weight $7$
Character orbit 336.br
Rep. character $\chi_{336}(59,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1520$
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.br (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 336 \)
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 1552 0
Cusp forms 1520 1520 0
Eisenstein series 32 32 0

Trace form

\( 1520 q - 6 q^{3} - 4 q^{4} - 16 q^{7} + O(q^{10}) \) \( 1520 q - 6 q^{3} - 4 q^{4} - 16 q^{7} - 12 q^{10} - 6 q^{12} - 11284 q^{16} - 9896 q^{18} - 12 q^{19} - 1462 q^{21} + 32744 q^{22} - 6 q^{24} + 26996 q^{28} - 51750 q^{30} - 12 q^{33} - 198992 q^{36} - 4 q^{37} - 4 q^{39} + 278448 q^{40} + 58370 q^{42} - 16 q^{43} - 6 q^{45} - 516 q^{46} - 16 q^{49} - 380686 q^{51} - 956352 q^{52} + 716766 q^{54} - 703108 q^{58} + 40470 q^{60} - 12 q^{61} + 577568 q^{64} + 2795094 q^{66} - 1207684 q^{67} + 913812 q^{70} - 951710 q^{72} - 93756 q^{75} + 1363252 q^{78} - 4 q^{81} + 5225976 q^{82} + 4851952 q^{84} + 124984 q^{85} - 12 q^{87} + 1366796 q^{88} + 2791584 q^{91} + 2914 q^{93} - 835392 q^{94} + 2781024 q^{96} + 2125756 q^{99} + O(q^{100}) \)

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.