↑

Properties

Label 3920.2.da
Level $3920$
Weight $2$
Character orbit 3920.da
Rep. character $\chi_{3920}(717,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1888$
Sturm bound $1344$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3920.da (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 560 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 2752 1952 800
Cusp forms 2624 1888 736
Eisenstein series 128 64 64

Trace form

\( 1888 q + 2 q^{2} + 12 q^{3} + 6 q^{5} - 4 q^{8} + 912 q^{9} + O(q^{10}) \) \( 1888 q + 2 q^{2} + 12 q^{3} + 6 q^{5} - 4 q^{8} + 912 q^{9} + 6 q^{10} + 4 q^{11} + 6 q^{12} - 32 q^{15} + 4 q^{16} + 12 q^{17} + 12 q^{18} - 24 q^{22} + 36 q^{24} + 12 q^{26} - 46 q^{30} + 24 q^{31} - 38 q^{32} + 12 q^{33} - 64 q^{36} + 4 q^{37} - 12 q^{38} - 24 q^{39} + 36 q^{40} + 48 q^{44} + 24 q^{45} + 4 q^{46} + 12 q^{47} - 16 q^{50} + 4 q^{51} + 36 q^{52} - 24 q^{54} + 24 q^{57} + 62 q^{58} + 48 q^{59} - 12 q^{60} + 12 q^{61} + 4 q^{65} + 84 q^{66} + 72 q^{68} + 64 q^{72} + 4 q^{74} + 6 q^{75} - 88 q^{78} - 108 q^{80} - 808 q^{81} + 78 q^{82} + 4 q^{85} - 4 q^{86} + 36 q^{87} + 12 q^{88} - 68 q^{92} - 44 q^{93} - 72 q^{94} + 28 q^{95} + 12 q^{96} + 24 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)