Properties

Label 3920.2.fr
Level $3920$
Weight $2$
Character orbit 3920.fr
Rep. character $\chi_{3920}(131,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $10752$
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.fr (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 784 \)
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 16224 10752 5472
Cusp forms 16032 10752 5280
Eisenstein series 192 0 192

Trace form

\( 10752q + O(q^{10}) \) \( 10752q + 16q^{14} - 20q^{18} - 48q^{22} - 124q^{28} - 20q^{32} + 60q^{42} + 108q^{44} + 20q^{46} - 40q^{51} + 72q^{52} + 84q^{54} - 184q^{56} + 28q^{58} + 48q^{59} + 224q^{60} - 48q^{64} - 88q^{66} + 60q^{68} + 16q^{70} + 160q^{71} - 48q^{78} - 896q^{81} + 452q^{84} + 20q^{86} + 304q^{91} - 56q^{92} + 264q^{94} - 1000q^{96} - 160q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)