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Properties

Label 3960.2.j
Level $3960$
Weight $2$
Character orbit 3960.j
Rep. character $\chi_{3960}(1189,\cdot)$
Character field $\Q$
Dimension $300$
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.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
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 880 300 580
Cusp forms 848 300 548
Eisenstein series 32 0 32

Trace form

\( 300 q - 4 q^{4} + O(q^{10}) \) \( 300 q - 4 q^{4} - 6 q^{10} - 16 q^{14} - 8 q^{16} + 20 q^{20} + 4 q^{25} - 4 q^{26} - 8 q^{31} - 16 q^{34} - 4 q^{40} - 8 q^{41} - 4 q^{44} - 28 q^{46} - 300 q^{49} + 22 q^{50} + 32 q^{56} + 44 q^{64} - 24 q^{65} + 40 q^{70} - 40 q^{71} + 44 q^{74} + 16 q^{76} + 16 q^{79} - 52 q^{80} + 116 q^{86} - 24 q^{89} + 24 q^{94} + 24 q^{95} + O(q^{100}) \)

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

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