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Properties

Label 3332.2.cw
Level $3332$
Weight $2$
Character orbit 3332.cw
Rep. character $\chi_{3332}(9,\cdot)$
Character field $\Q(\zeta_{168})$
Dimension $4032$
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.cw (of order \(168\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 833 \)
Character field: \(\Q(\zeta_{168})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 24480 4032 20448
Cusp forms 23904 4032 19872
Eisenstein series 576 0 576

Trace form

\( 4032 q - 4 q^{5} + O(q^{10}) \) \( 4032 q - 4 q^{5} + 32 q^{11} - 24 q^{15} + 8 q^{17} - 96 q^{23} + 4 q^{25} - 48 q^{27} + 48 q^{33} + 16 q^{35} - 16 q^{37} + 56 q^{41} - 12 q^{45} - 180 q^{49} + 104 q^{59} - 12 q^{61} + 24 q^{63} - 8 q^{67} + 48 q^{69} - 16 q^{71} + 20 q^{73} - 136 q^{75} - 24 q^{77} - 16 q^{79} - 44 q^{83} - 8 q^{85} + 96 q^{87} + 48 q^{91} - 224 q^{93} - 420 q^{95} - 96 q^{97} - 424 q^{99} + O(q^{100}) \)

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

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