↑

Properties

Label 1600.4.bg
Level $1600$
Weight $4$
Character orbit 1600.bg
Rep. character $\chi_{1600}(129,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $712$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1600.bg (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1600, [\chi])\).

Total New Old
Modular forms 2928 728 2200
Cusp forms 2832 712 2120
Eisenstein series 96 16 80

Trace form

\( 712 q + 8 q^{5} + 1560 q^{9} + O(q^{10}) \) \( 712 q + 8 q^{5} + 1560 q^{9} + 10 q^{13} - 10 q^{17} - 156 q^{21} - 52 q^{25} + 6 q^{29} - 10 q^{33} + 10 q^{37} + 466 q^{41} + 796 q^{45} - 32552 q^{49} + 10 q^{53} + 6 q^{61} - 1758 q^{65} + 1602 q^{69} - 10 q^{73} - 3420 q^{77} - 13236 q^{81} - 918 q^{85} - 138 q^{89} - 7450 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1600, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1600, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)