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Properties

Label 3920.2.fx
Level $3920$
Weight $2$
Character orbit 3920.fx
Rep. character $\chi_{3920}(17,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $3984$
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.fx (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 16416 4080 12336
Cusp forms 15840 3984 11856
Eisenstein series 576 96 480

Trace form

\( 3984 q + 22 q^{3} - 22 q^{5} + 24 q^{7} + O(q^{10}) \) \( 3984 q + 22 q^{3} - 22 q^{5} + 24 q^{7} + 52 q^{11} - 28 q^{13} + 20 q^{15} - 22 q^{17} - 40 q^{21} + 14 q^{23} - 26 q^{25} + 28 q^{27} + 72 q^{31} + 2 q^{33} + 12 q^{35} - 26 q^{37} - 56 q^{41} + 20 q^{43} - 22 q^{45} + 58 q^{47} + 52 q^{51} - 26 q^{53} + 28 q^{55} + 10 q^{57} - 44 q^{61} - 32 q^{63} - 26 q^{65} + 24 q^{67} - 40 q^{71} - 22 q^{73} + 22 q^{75} - 38 q^{77} - 416 q^{81} + 28 q^{83} - 20 q^{85} + 40 q^{87} - 64 q^{91} - 56 q^{93} - 12 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1960, [\chi])\)\(^{\oplus 2}\)