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Properties

Label 3332.2.v
Level $3332$
Weight $2$
Character orbit 3332.v
Rep. character $\chi_{3332}(393,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $244$
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.v (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
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 2112 244 1868
Cusp forms 1920 244 1676
Eisenstein series 192 0 192

Trace form

\( 244 q - 4 q^{5} - 4 q^{9} + O(q^{10}) \) \( 244 q - 4 q^{5} - 4 q^{9} + 4 q^{15} + 4 q^{17} - 4 q^{19} - 16 q^{23} + 12 q^{25} + 36 q^{27} + 12 q^{29} + 24 q^{31} + 8 q^{33} + 4 q^{37} + 40 q^{39} + 12 q^{41} + 20 q^{43} - 28 q^{45} + 8 q^{51} - 44 q^{53} - 4 q^{57} - 44 q^{59} - 20 q^{61} - 8 q^{65} - 16 q^{67} + 8 q^{69} + 28 q^{73} - 96 q^{75} - 8 q^{79} - 28 q^{83} - 44 q^{85} + 44 q^{87} - 60 q^{93} + 100 q^{95} - 36 q^{97} + 132 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3332, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(833, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1666, [\chi])\)\(^{\oplus 2}\)