Properties

Label 3960.2.dy
Level $3960$
Weight $2$
Character orbit 3960.dy
Rep. character $\chi_{3960}(829,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1424$
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.dy (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 440 \)
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 1456 2064
Cusp forms 3392 1424 1968
Eisenstein series 128 32 96

Trace form

\( 1424 q - 6 q^{4} + O(q^{10}) \) \( 1424 q - 6 q^{4} + 4 q^{10} + 10 q^{14} + 14 q^{16} + 26 q^{20} - 6 q^{25} + 8 q^{26} - 12 q^{31} - 40 q^{34} + 4 q^{40} + 12 q^{41} - 26 q^{44} + 42 q^{46} + 320 q^{49} - 4 q^{50} - 2 q^{55} + 112 q^{56} - 42 q^{64} - 4 q^{65} + 46 q^{70} + 28 q^{71} + 60 q^{74} + 12 q^{76} + 28 q^{79} + 40 q^{80} + 18 q^{86} + 32 q^{89} - 112 q^{94} - 34 q^{95} + O(q^{100}) \)

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

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