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Properties

Label 336.9.v
Level $336$
Weight $9$
Character orbit 336.v
Rep. character $\chi_{336}(83,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $1016$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 336.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 336 \)
Character field: \(\Q(i)\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(336, [\chi])\).

Total New Old
Modular forms 1032 1032 0
Cusp forms 1016 1016 0
Eisenstein series 16 16 0

Trace form

\( 1016 q - 8 q^{4} - 8 q^{7} + O(q^{10}) \) \( 1016 q - 8 q^{4} - 8 q^{7} - 222712 q^{16} + 578672 q^{18} + 13120 q^{21} + 909184 q^{22} - 1391168 q^{28} - 1984608 q^{30} - 1537960 q^{36} - 8 q^{37} - 8 q^{39} - 5150600 q^{42} - 8 q^{43} + 2040 q^{46} - 8 q^{49} + 30163192 q^{51} + 31405768 q^{58} + 47223360 q^{60} + 48383944 q^{64} - 74704392 q^{67} - 40464912 q^{70} - 107473192 q^{72} + 139676480 q^{78} - 8 q^{81} + 15433808 q^{84} - 3125008 q^{85} + 83571176 q^{88} + 198259584 q^{91} - 26248 q^{93} - 172186888 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(336, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.