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Properties

Label 3332.2.x
Level $3332$
Weight $2$
Character orbit 3332.x
Rep. character $\chi_{3332}(195,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $1408$
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.x (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 476 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 2080 1472 608
Cusp forms 1952 1408 544
Eisenstein series 128 64 64

Trace form

\( 1408 q + 8 q^{2} - 16 q^{8} + 16 q^{9} + O(q^{10}) \) \( 1408 q + 8 q^{2} - 16 q^{8} + 16 q^{9} + 16 q^{16} + 16 q^{18} - 64 q^{22} + 16 q^{25} - 32 q^{29} - 32 q^{32} - 48 q^{36} + 16 q^{37} - 24 q^{44} + 8 q^{46} + 48 q^{50} + 16 q^{53} - 32 q^{57} + 8 q^{58} + 40 q^{60} + 96 q^{65} + 120 q^{74} - 64 q^{78} - 32 q^{85} + 160 q^{86} + 96 q^{88} + 128 q^{92} + 80 q^{93} + O(q^{100}) \)

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

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