Properties

Label 3920.2.x
Level $3920$
Weight $2$
Character orbit 3920.x
Rep. character $\chi_{3920}(687,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $246$
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.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1440 246 1194
Cusp forms 1248 246 1002
Eisenstein series 192 0 192

Trace form

\( 246 q + O(q^{10}) \) \( 246 q - 6 q^{13} - 6 q^{17} - 6 q^{25} - 24 q^{33} + 30 q^{37} - 24 q^{41} + 30 q^{45} - 18 q^{53} + 48 q^{57} + 54 q^{65} + 30 q^{73} - 270 q^{81} - 54 q^{85} + 72 q^{93} + 30 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 3}\)