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Properties

Label 3960.2.fm
Level $3960$
Weight $2$
Character orbit 3960.fm
Rep. character $\chi_{3960}(613,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2848$
Sturm bound $1728$

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Defining parameters

Level: \( N \) \(=\) \( 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3960.fm (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 440 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 7040 2912 4128
Cusp forms 6784 2848 3936
Eisenstein series 256 64 192

Trace form

\( 2848 q + 10 q^{2} - 20 q^{7} + 10 q^{8} + O(q^{10}) \) \( 2848 q + 10 q^{2} - 20 q^{7} + 10 q^{8} - 20 q^{16} + 20 q^{17} - 40 q^{20} - 22 q^{22} + 32 q^{23} - 12 q^{25} - 28 q^{26} - 10 q^{28} - 24 q^{31} - 14 q^{38} - 10 q^{40} + 40 q^{41} - 140 q^{46} + 12 q^{47} + 10 q^{50} - 50 q^{52} - 36 q^{55} - 8 q^{56} + 38 q^{58} + 160 q^{62} + 10 q^{68} + 14 q^{70} - 8 q^{71} - 20 q^{73} - 54 q^{80} - 10 q^{82} - 28 q^{86} + 94 q^{88} + 108 q^{92} + 20 q^{95} - 44 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1320, [\chi])\)\(^{\oplus 2}\)