Properties

Label 3920.2.ea
Level $3920$
Weight $2$
Character orbit 3920.ea
Rep. character $\chi_{3920}(433,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $1992$
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.ea (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 8208 2040 6168
Cusp forms 7920 1992 5928
Eisenstein series 288 48 240

Trace form

\( 1992q + 14q^{3} - 14q^{5} + 12q^{7} + O(q^{10}) \) \( 1992q + 14q^{3} - 14q^{5} + 12q^{7} + 20q^{11} - 14q^{13} + 10q^{15} - 14q^{17} - 32q^{21} - 14q^{23} - 10q^{25} + 14q^{27} - 14q^{33} + 24q^{35} - 10q^{37} - 28q^{41} + 10q^{43} - 14q^{45} + 14q^{47} + 20q^{51} - 10q^{53} + 14q^{55} - 40q^{57} - 28q^{61} + 68q^{63} - 10q^{65} + 48q^{67} + 100q^{71} - 14q^{73} + 14q^{75} + 2q^{77} + 320q^{81} + 14q^{83} - 10q^{85} + 14q^{87} - 8q^{91} + 20q^{93} + 84q^{95} + O(q^{100}) \)

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

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