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Properties

Label 3920.2.dj
Level $3920$
Weight $2$
Character orbit 3920.dj
Rep. character $\chi_{3920}(111,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $672$
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.dj (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 196 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 4104 672 3432
Cusp forms 3960 672 3288
Eisenstein series 144 0 144

Trace form

\( 672 q - 112 q^{9} + O(q^{10}) \) \( 672 q - 112 q^{9} - 20 q^{21} + 112 q^{25} - 60 q^{29} + 40 q^{37} + 20 q^{49} + 48 q^{53} - 16 q^{57} + 56 q^{61} + 24 q^{65} - 336 q^{69} - 24 q^{77} - 52 q^{81} - 80 q^{93} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1960, [\chi])\)\(^{\oplus 2}\)