↑

Properties

Label 1600.4.by
Level $1600$
Weight $4$
Character orbit 1600.by
Rep. character $\chi_{1600}(63,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1424$
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.by (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 5856 1456 4400
Cusp forms 5664 1424 4240
Eisenstein series 192 32 160

Trace form

\( 1424 q + 16 q^{5} - 20 q^{9} + O(q^{10}) \) \( 1424 q + 16 q^{5} - 20 q^{9} + 16 q^{13} - 120 q^{17} + 12 q^{21} + 72 q^{25} + 20 q^{29} - 124 q^{33} + 16 q^{37} - 12 q^{41} + 516 q^{45} + 832 q^{53} + 92 q^{57} + 12 q^{61} - 1064 q^{65} + 20 q^{69} - 312 q^{73} - 2116 q^{77} + 26232 q^{81} - 2336 q^{85} + 420 q^{89} + 5068 q^{93} + 10072 q^{97} + O(q^{100}) \)

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

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