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Properties

Label 3332.2.db
Level $3332$
Weight $2$
Character orbit 3332.db
Rep. character $\chi_{3332}(5,\cdot)$
Character field $\Q(\zeta_{336})$
Dimension $8064$
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.db (of order \(336\) and degree \(96\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 833 \)
Character field: \(\Q(\zeta_{336})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 48960 8064 40896
Cusp forms 47808 8064 39744
Eisenstein series 1152 0 1152

Trace form

\( 8064 q + O(q^{10}) \) \( 8064 q - 64 q^{11} - 48 q^{15} + 24 q^{21} - 8 q^{25} + 32 q^{35} + 32 q^{37} + 384 q^{49} + 48 q^{61} - 96 q^{63} + 224 q^{69} + 32 q^{71} - 120 q^{73} - 192 q^{75} - 16 q^{77} + 96 q^{85} - 144 q^{87} + 64 q^{91} + 80 q^{99} + O(q^{100}) \)

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

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