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Properties

Label 3330.2.ca
Level $3330$
Weight $2$
Character orbit 3330.ca
Rep. character $\chi_{3330}(571,\cdot)$
Character field $\Q(\zeta_{9})$
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.ca (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 333 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(1368\)

Dimensions

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

Total New Old
Modular forms 4152 912 3240
Cusp forms 4056 912 3144
Eisenstein series 96 0 96

Trace form

\( 912 q + 12 q^{7} + O(q^{10}) \) \( 912 q + 12 q^{7} + 12 q^{13} - 72 q^{21} - 72 q^{23} + 12 q^{28} - 72 q^{33} + 12 q^{37} + 72 q^{38} + 60 q^{39} - 96 q^{41} + 36 q^{42} - 24 q^{45} + 12 q^{49} + 12 q^{52} - 36 q^{54} + 72 q^{57} - 36 q^{62} + 60 q^{63} - 456 q^{64} - 168 q^{67} + 84 q^{69} - 48 q^{71} - 24 q^{74} - 168 q^{78} + 12 q^{79} - 96 q^{81} - 36 q^{83} + 84 q^{87} + 24 q^{90} + 84 q^{91} + 36 q^{93} - 24 q^{95} + 96 q^{98} + 72 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3330, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(666, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1665, [\chi])\)\(^{\oplus 2}\)