↑

Properties

Label 3330.2.cb
Level $3330$
Weight $2$
Character orbit 3330.cb
Rep. character $\chi_{3330}(181,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $372$
Sturm bound $1368$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3330.cb (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
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 4200 372 3828
Cusp forms 4008 372 3636
Eisenstein series 192 0 192

Trace form

\( 372 q - 24 q^{7} + O(q^{10}) \) \( 372 q - 24 q^{7} + 6 q^{10} + 12 q^{13} - 6 q^{14} - 18 q^{19} - 72 q^{23} + 12 q^{28} - 12 q^{29} + 36 q^{34} + 12 q^{35} + 60 q^{37} + 48 q^{38} - 60 q^{41} + 96 q^{43} + 6 q^{44} + 6 q^{46} - 12 q^{47} + 12 q^{49} - 24 q^{52} - 12 q^{55} - 48 q^{61} - 60 q^{62} - 186 q^{64} + 6 q^{65} + 72 q^{67} + 24 q^{68} - 84 q^{71} - 72 q^{73} + 60 q^{74} - 18 q^{76} - 12 q^{77} + 12 q^{79} - 48 q^{82} - 24 q^{83} + 12 q^{85} - 12 q^{86} + 54 q^{89} + 18 q^{91} + 12 q^{92} + 18 q^{94} + 48 q^{95} + 24 q^{97} + 48 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3330, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(666, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1665, [\chi])\)\(^{\oplus 2}\)