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Properties

Label 3332.2.f
Level $3332$
Weight $2$
Character orbit 3332.f
Rep. character $\chi_{3332}(783,\cdot)$
Character field $\Q$
Dimension $320$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3332.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3332, [\chi])\).

Total New Old
Modular forms 520 320 200
Cusp forms 488 320 168
Eisenstein series 32 0 32

Trace form

\( 320 q + 4 q^{2} - 4 q^{4} + 16 q^{8} + 320 q^{9} + O(q^{10}) \) \( 320 q + 4 q^{2} - 4 q^{4} + 16 q^{8} + 320 q^{9} - 20 q^{16} + 20 q^{18} - 16 q^{22} - 304 q^{25} + 16 q^{29} + 20 q^{30} - 16 q^{32} + 40 q^{36} + 48 q^{37} + 20 q^{44} + 48 q^{46} - 32 q^{50} - 32 q^{53} + 16 q^{57} + 24 q^{58} - 44 q^{60} + 32 q^{64} - 48 q^{65} + 56 q^{72} - 88 q^{74} + 12 q^{78} + 432 q^{81} - 172 q^{86} + 120 q^{88} - 96 q^{92} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3332, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3332, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3332, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 2}\)