↑

Properties

Label 3960.2.fs
Level $3960$
Weight $2$
Character orbit 3960.fs
Rep. character $\chi_{3960}(41,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1152$
Sturm bound $1728$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3960.fs (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3960, [\chi])\).

Total New Old
Modular forms 7040 1152 5888
Cusp forms 6784 1152 5632
Eisenstein series 256 0 256

Trace form

\( 1152 q - 4 q^{3} - 12 q^{9} + O(q^{10}) \) \( 1152 q - 4 q^{3} - 12 q^{9} - 6 q^{11} + 60 q^{19} - 144 q^{25} + 8 q^{27} - 4 q^{33} + 120 q^{39} - 144 q^{49} - 70 q^{51} + 60 q^{57} - 18 q^{59} - 80 q^{63} - 12 q^{67} - 120 q^{69} - 6 q^{75} - 72 q^{77} - 20 q^{81} + 32 q^{93} + 54 q^{97} + 76 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3960, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3960, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(792, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(990, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1980, [\chi])\)\(^{\oplus 2}\)