↑

Properties

Label 1600.4.l
Level $1600$
Weight $4$
Character orbit 1600.l
Rep. character $\chi_{1600}(401,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $222$
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.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1488 234 1254
Cusp forms 1392 222 1170
Eisenstein series 96 12 84

Trace form

\( 222 q - 2 q^{3} + O(q^{10}) \) \( 222 q - 2 q^{3} - 14 q^{11} + 2 q^{13} + 4 q^{17} - 26 q^{19} - 60 q^{21} - 80 q^{27} - 198 q^{29} + 384 q^{31} + 4 q^{33} - 6 q^{37} - 30 q^{43} + 936 q^{47} - 9110 q^{49} - 92 q^{51} - 374 q^{53} - 334 q^{59} - 918 q^{61} + 108 q^{63} - 98 q^{67} - 364 q^{69} - 1636 q^{77} - 4416 q^{79} - 14106 q^{81} - 122 q^{83} - 260 q^{91} - 2080 q^{93} + 4 q^{97} + 3374 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)