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Properties

Label 3960.2.z
Level $3960$
Weight $2$
Character orbit 3960.z
Rep. character $\chi_{3960}(1891,\cdot)$
Character field $\Q$
Dimension $240$
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.z (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 88 \)
Character field: \(\Q\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 880 240 640
Cusp forms 848 240 608
Eisenstein series 32 0 32

Trace form

\( 240 q + 4 q^{4} + O(q^{10}) \) \( 240 q + 4 q^{4} - 8 q^{11} - 4 q^{20} + 12 q^{22} - 240 q^{25} + 12 q^{26} + 40 q^{34} - 40 q^{38} + 16 q^{44} + 240 q^{49} - 16 q^{56} - 40 q^{58} + 16 q^{59} + 4 q^{64} - 16 q^{67} - 28 q^{70} + 16 q^{80} - 88 q^{82} + 76 q^{86} - 8 q^{88} + 80 q^{91} + 48 q^{92} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(792, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1320, [\chi])\)\(^{\oplus 2}\)