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Properties

Label 3332.2.t
Level $3332$
Weight $2$
Character orbit 3332.t
Rep. character $\chi_{3332}(373,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 1056 120 936
Cusp forms 960 120 840
Eisenstein series 96 0 96

Trace form

\( 120 q + 68 q^{9} + O(q^{10}) \) \( 120 q + 68 q^{9} - 8 q^{13} + 4 q^{15} - 3 q^{17} - 4 q^{19} + 46 q^{25} - 8 q^{33} - 20 q^{43} + 12 q^{47} - 13 q^{51} - 34 q^{53} - 48 q^{55} + 50 q^{67} + 4 q^{69} - 112 q^{81} + 64 q^{83} - 78 q^{85} + 18 q^{87} + 30 q^{89} + 100 q^{93} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3332, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(833, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1666, [\chi])\)\(^{\oplus 2}\)