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Properties

Label 3920.2.q
Level $3920$
Weight $2$
Character orbit 3920.q
Rep. character $\chi_{3920}(961,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $160$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3920.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3920, [\chi])\).

Total New Old
Modular forms 1440 160 1280
Cusp forms 1248 160 1088
Eisenstein series 192 0 192

Trace form

\( 160 q + 4 q^{3} - 80 q^{9} + O(q^{10}) \) \( 160 q + 4 q^{3} - 80 q^{9} - 8 q^{11} - 4 q^{19} - 8 q^{23} - 80 q^{25} - 32 q^{27} - 40 q^{29} - 16 q^{31} + 16 q^{37} + 20 q^{39} - 8 q^{41} + 48 q^{43} + 4 q^{45} - 20 q^{47} + 44 q^{51} + 24 q^{53} + 16 q^{55} + 16 q^{57} + 8 q^{59} + 8 q^{61} + 4 q^{65} - 44 q^{67} - 16 q^{69} - 48 q^{71} - 8 q^{73} + 4 q^{75} - 44 q^{79} - 84 q^{81} - 112 q^{83} - 60 q^{87} - 12 q^{89} + 16 q^{93} - 32 q^{97} + 104 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3920, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3920, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)