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Properties

Label 3330.2.bv
Level $3330$
Weight $2$
Character orbit 3330.bv
Rep. character $\chi_{3330}(1639,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
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.bv (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
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 1400 192 1208
Cusp forms 1336 192 1144
Eisenstein series 64 0 64

Trace form

\( 192 q - 96 q^{4} - 3 q^{5} + O(q^{10}) \) \( 192 q - 96 q^{4} - 3 q^{5} - 2 q^{10} + 4 q^{11} - 96 q^{16} - 6 q^{19} + 3 q^{20} - 7 q^{25} - 52 q^{26} + 6 q^{34} + 12 q^{35} + q^{40} - 34 q^{41} - 2 q^{44} - 10 q^{46} + 104 q^{49} + 3 q^{50} - 12 q^{55} - 6 q^{59} + 42 q^{61} + 192 q^{64} - 4 q^{65} + 4 q^{70} + 44 q^{71} + 18 q^{74} + 6 q^{76} - 36 q^{79} - 38 q^{85} + 20 q^{86} + 60 q^{89} + 36 q^{91} + 6 q^{94} + 16 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3330, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1665, [\chi])\)\(^{\oplus 2}\)