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Properties

Label 3332.2.i
Level $3332$
Weight $2$
Character orbit 3332.i
Rep. character $\chi_{3332}(1157,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $108$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 1056 108 948
Cusp forms 960 108 852
Eisenstein series 96 0 96

Trace form

\( 108 q - 2 q^{3} - 4 q^{5} - 52 q^{9} + O(q^{10}) \) \( 108 q - 2 q^{3} - 4 q^{5} - 52 q^{9} + 4 q^{11} + 24 q^{15} - 4 q^{17} + 6 q^{19} - 8 q^{23} - 46 q^{25} + 16 q^{27} - 24 q^{29} + 18 q^{31} - 2 q^{33} - 26 q^{37} - 48 q^{39} + 28 q^{41} + 4 q^{43} + 28 q^{45} + 10 q^{47} - 4 q^{55} + 56 q^{57} - 10 q^{59} - 16 q^{61} + 2 q^{65} - 28 q^{67} - 40 q^{69} - 20 q^{71} - 4 q^{73} - 40 q^{75} + 12 q^{79} - 74 q^{81} - 24 q^{83} + 42 q^{87} - 8 q^{89} + 10 q^{93} - 8 q^{95} + 12 q^{97} - 84 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3332, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(833, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1666, [\chi])\)\(^{\oplus 2}\)