↑

Properties

Label 3920.2.ds
Level $3920$
Weight $2$
Character orbit 3920.ds
Rep. character $\chi_{3920}(81,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1344$
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.ds (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 8208 1344 6864
Cusp forms 7920 1344 6576
Eisenstein series 288 0 288

Trace form

\( 1344 q + 4 q^{3} + 4 q^{7} + 112 q^{9} + O(q^{10}) \) \( 1344 q + 4 q^{3} + 4 q^{7} + 112 q^{9} - 4 q^{19} - 4 q^{21} + 112 q^{25} - 32 q^{27} + 20 q^{29} - 16 q^{31} - 32 q^{39} - 8 q^{41} + 32 q^{43} + 4 q^{45} - 20 q^{47} + 16 q^{49} + 20 q^{51} + 8 q^{53} + 16 q^{55} + 16 q^{57} + 8 q^{59} + 8 q^{61} - 56 q^{63} + 4 q^{65} - 4 q^{67} + 96 q^{69} + 40 q^{71} - 8 q^{73} + 4 q^{75} + 24 q^{77} - 4 q^{79} + 80 q^{81} - 112 q^{83} - 60 q^{87} - 12 q^{89} + 144 q^{91} + 16 q^{93} - 32 q^{97} + 72 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1960, [\chi])\)\(^{\oplus 2}\)