Properties

Label 3920.2.ef
Level $3920$
Weight $2$
Character orbit 3920.ef
Rep. character $\chi_{3920}(251,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $5376$
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.ef (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 784 \)
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 8112 5376 2736
Cusp forms 8016 5376 2640
Eisenstein series 96 0 96

Trace form

\( 5376q + O(q^{10}) \) \( 5376q + 8q^{14} - 40q^{18} + 48q^{22} + 124q^{28} - 40q^{32} - 60q^{42} + 48q^{44} + 40q^{46} - 80q^{51} + 268q^{56} + 56q^{58} - 140q^{60} + 48q^{64} + 280q^{66} + 8q^{70} - 160q^{71} + 48q^{78} + 896q^{81} + 340q^{84} - 44q^{86} - 304q^{91} - 28q^{92} - 336q^{94} - 224q^{96} + 76q^{98} + O(q^{100}) \)

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

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