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Properties

Label 1600.4.s
Level $1600$
Weight $4$
Character orbit 1600.s
Rep. character $\chi_{1600}(207,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $212$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1600.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
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 220 1268
Cusp forms 1392 212 1180
Eisenstein series 96 8 88

Trace form

\( 212 q - 4 q^{3} - 4 q^{7} + 1836 q^{9} + O(q^{10}) \) \( 212 q - 4 q^{3} - 4 q^{7} + 1836 q^{9} + 4 q^{11} + 4 q^{17} + 48 q^{19} - 4 q^{21} - 4 q^{23} - 112 q^{27} + 4 q^{33} + 408 q^{47} + 1492 q^{51} + 4 q^{53} + 108 q^{57} - 1376 q^{59} + 1820 q^{61} - 108 q^{63} - 1164 q^{69} - 440 q^{71} - 296 q^{73} + 1376 q^{77} + 14572 q^{81} - 2684 q^{83} - 1292 q^{87} + 1700 q^{91} + 4 q^{97} - 5204 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)