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Properties

Label 3332.2.k
Level $3332$
Weight $2$
Character orbit 3332.k
Rep. character $\chi_{3332}(1959,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $704$
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.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 476 \)
Character field: \(\Q(i)\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 1040 736 304
Cusp forms 976 704 272
Eisenstein series 64 32 32

Trace form

\( 704 q + 8 q^{4} + O(q^{10}) \) \( 704 q + 8 q^{4} + 8 q^{16} + 40 q^{18} + 24 q^{22} - 16 q^{29} + 128 q^{30} + 8 q^{37} + 52 q^{44} - 32 q^{46} - 72 q^{50} - 40 q^{57} + 32 q^{64} - 32 q^{65} - 16 q^{72} + 8 q^{74} - 44 q^{78} - 560 q^{81} + 16 q^{85} + 88 q^{86} - 56 q^{88} + 32 q^{92} + O(q^{100}) \)

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

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