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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

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

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

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