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Properties

Label 336.7.v
Level $336$
Weight $7$
Character orbit 336.v
Rep. character $\chi_{336}(83,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $760$
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.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 336 \)
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 776 776 0
Cusp forms 760 760 0
Eisenstein series 16 16 0

Trace form

\( 760 q - 8 q^{4} - 8 q^{7} + O(q^{10}) \) \( 760 q - 8 q^{4} - 8 q^{7} + 11272 q^{16} - 20560 q^{18} + 1456 q^{21} - 32768 q^{22} - 27008 q^{28} + 51360 q^{30} - 74920 q^{36} - 8 q^{37} - 8 q^{39} + 221560 q^{42} - 8 q^{43} + 504 q^{46} - 8 q^{49} - 770120 q^{51} - 1059896 q^{58} - 2294400 q^{60} - 577592 q^{64} + 1207672 q^{67} + 1162800 q^{70} - 621160 q^{72} - 1363264 q^{78} - 8 q^{81} + 1201232 q^{84} - 125008 q^{85} - 1366808 q^{88} - 1379808 q^{91} - 2920 q^{93} - 2125768 q^{99} + O(q^{100}) \)

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.