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Properties

Label 3330.2.bq
Level $3330$
Weight $2$
Character orbit 3330.bq
Rep. character $\chi_{3330}(529,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $456$
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.bq (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1665 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1368\)

Dimensions

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

Total New Old
Modular forms 1384 456 928
Cusp forms 1352 456 896
Eisenstein series 32 0 32

Trace form

\( 456 q + 456 q^{4} - 8 q^{9} + O(q^{10}) \) \( 456 q + 456 q^{4} - 8 q^{9} + 8 q^{11} + 456 q^{16} - 24 q^{25} + 48 q^{26} - 12 q^{30} - 18 q^{35} - 8 q^{36} - 24 q^{39} - 48 q^{41} + 8 q^{44} - 12 q^{45} + 228 q^{49} + 36 q^{51} - 12 q^{59} + 456 q^{64} + 72 q^{66} - 36 q^{69} + 20 q^{71} + 8 q^{74} - 34 q^{75} + 16 q^{81} - 12 q^{85} - 40 q^{86} - 120 q^{89} + 12 q^{90} - 38 q^{95} - 96 q^{99} + O(q^{100}) \)

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

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