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Properties

Label 3330.2.dx
Level $3330$
Weight $2$
Character orbit 3330.dx
Rep. character $\chi_{3330}(911,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $608$
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.dx (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 333 \)
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 608 2160
Cusp forms 2704 608 2096
Eisenstein series 64 0 64

Trace form

\( 608 q + O(q^{10}) \) \( 608 q - 16 q^{13} + 304 q^{16} - 8 q^{19} - 72 q^{23} + 72 q^{27} + 24 q^{28} + 8 q^{31} + 16 q^{37} + 40 q^{39} + 48 q^{41} - 48 q^{42} - 8 q^{43} + 16 q^{45} - 72 q^{47} + 592 q^{49} - 8 q^{51} + 16 q^{52} + 72 q^{54} - 96 q^{57} - 112 q^{61} - 72 q^{62} + 72 q^{63} + 48 q^{66} - 56 q^{69} + 96 q^{71} - 16 q^{76} - 8 q^{79} + 16 q^{81} + 120 q^{83} - 48 q^{87} + 72 q^{89} - 120 q^{91} - 8 q^{93} + 96 q^{95} + 8 q^{97} + 72 q^{99} + O(q^{100}) \)

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

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