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Properties

Label 3920.2.bw
Level $3920$
Weight $2$
Character orbit 3920.bw
Rep. character $\chi_{3920}(2529,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $232$
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.bw (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1440 248 1192
Cusp forms 1248 232 1016
Eisenstein series 192 16 176

Trace form

\( 232 q + q^{5} + 110 q^{9} + O(q^{10}) \) \( 232 q + q^{5} + 110 q^{9} - 2 q^{11} + 2 q^{15} - 14 q^{19} + 5 q^{25} - 24 q^{29} - 14 q^{31} + 28 q^{39} + 16 q^{41} - 12 q^{45} - 2 q^{51} + 18 q^{55} - 30 q^{59} + 2 q^{61} + 12 q^{65} + 36 q^{69} + 80 q^{71} - 25 q^{75} - 26 q^{79} - 116 q^{81} + 34 q^{85} - 10 q^{89} - 69 q^{95} - 8 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1960, [\chi])\)\(^{\oplus 2}\)