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Properties

Label 3330.2.dk
Level $3330$
Weight $2$
Character orbit 3330.dk
Rep. character $\chi_{3330}(193,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $912$
Sturm bound $1368$

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Defining parameters

Level: \( N \) \(=\) \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3330.dk (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1665 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1368\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3330, [\chi])\).

Total New Old
Modular forms 2768 912 1856
Cusp forms 2704 912 1792
Eisenstein series 64 0 64

Trace form

\( 912 q - 4 q^{3} + 456 q^{4} + 4 q^{5} + O(q^{10}) \) \( 912 q - 4 q^{3} + 456 q^{4} + 4 q^{5} + 4 q^{12} - 456 q^{16} - 4 q^{20} + 24 q^{23} - 4 q^{27} - 12 q^{33} - 24 q^{35} - 12 q^{37} - 16 q^{39} - 48 q^{41} + 8 q^{42} - 16 q^{45} + 4 q^{47} + 8 q^{48} - 16 q^{50} - 16 q^{51} - 12 q^{53} + 12 q^{55} + 64 q^{59} - 12 q^{60} - 12 q^{62} - 912 q^{64} + 16 q^{66} + 36 q^{67} + 24 q^{69} - 16 q^{74} + 28 q^{75} - 16 q^{77} - 20 q^{78} - 8 q^{80} + 24 q^{81} - 48 q^{82} + 20 q^{83} + 12 q^{87} - 80 q^{89} + 40 q^{90} - 64 q^{95} - 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3330, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3330, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3330, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1665, [\chi])\)\(^{\oplus 2}\)