Properties

Label 3960.2.bm
Level $3960$
Weight $2$
Character orbit 3960.bm
Rep. character $\chi_{3960}(1387,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $600$
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.bm (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 1760 600 1160
Cusp forms 1696 600 1096
Eisenstein series 64 0 64

Trace form

\( 600 q - 12 q^{8} + O(q^{10}) \) \( 600 q - 12 q^{8} + 8 q^{17} - 8 q^{25} - 8 q^{26} - 44 q^{28} - 40 q^{32} - 48 q^{35} + 40 q^{38} - 40 q^{40} + 24 q^{46} + 76 q^{50} + 4 q^{52} + 8 q^{56} + 56 q^{58} - 36 q^{62} - 8 q^{65} + 48 q^{67} + 52 q^{68} + 64 q^{70} - 40 q^{73} + 24 q^{76} + 56 q^{80} + 72 q^{82} - 48 q^{86} + 24 q^{88} + 32 q^{91} + 16 q^{92} - 8 q^{97} - 64 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1320, [\chi])\)\(^{\oplus 2}\)