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Properties

Label 3960.2.dn
Level $3960$
Weight $2$
Character orbit 3960.dn
Rep. character $\chi_{3960}(181,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $960$
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.dn (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 88 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 3520 960 2560
Cusp forms 3392 960 2432
Eisenstein series 128 0 128

Trace form

\( 960 q + 4 q^{2} - 4 q^{4} + 8 q^{7} + 4 q^{8} + O(q^{10}) \) \( 960 q + 4 q^{2} - 4 q^{4} + 8 q^{7} + 4 q^{8} + 2 q^{14} - 4 q^{20} - 48 q^{22} - 16 q^{23} + 240 q^{25} + 20 q^{26} + 18 q^{28} - 36 q^{32} - 60 q^{34} - 50 q^{38} - 16 q^{41} + 14 q^{44} + 30 q^{46} - 240 q^{49} - 4 q^{50} + 26 q^{52} - 128 q^{56} + 38 q^{58} + 64 q^{62} - 64 q^{64} - 78 q^{68} + 32 q^{70} - 40 q^{71} + 72 q^{74} - 192 q^{76} - 24 q^{79} - 24 q^{80} - 108 q^{82} + 100 q^{86} - 16 q^{88} + 24 q^{92} - 72 q^{94} + 32 q^{95} - 12 q^{98} + O(q^{100}) \)

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

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