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Properties

Label 3960.2.ds
Level $3960$
Weight $2$
Character orbit 3960.ds
Rep. character $\chi_{3960}(701,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $768$
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.ds (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 264 \)
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 768 2752
Cusp forms 3392 768 2624
Eisenstein series 128 0 128

Trace form

\( 768 q + O(q^{10}) \) \( 768 q - 16 q^{16} + 88 q^{22} - 192 q^{25} - 40 q^{28} + 48 q^{34} + 192 q^{49} + 80 q^{58} - 120 q^{64} + 72 q^{70} - 160 q^{79} + 216 q^{82} - 48 q^{88} + 240 q^{94} + O(q^{100}) \)

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

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