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Properties

Label 1600.4.cc
Level $1600$
Weight $4$
Character orbit 1600.cc
Rep. character $\chi_{1600}(47,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1424$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1600.cc (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 400 \)
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 5824 1456 4368
Cusp forms 5696 1424 4272
Eisenstein series 128 32 96

Trace form

\( 1424 q + 10 q^{3} - 8 q^{5} + 16 q^{7} + 3132 q^{9} + O(q^{10}) \) \( 1424 q + 10 q^{3} - 8 q^{5} + 16 q^{7} + 3132 q^{9} + 6 q^{11} - 6 q^{13} + 108 q^{15} - 16 q^{17} + 10 q^{19} - 276 q^{21} + 16 q^{23} + 10 q^{27} - 10 q^{29} - 16 q^{33} + 780 q^{35} - 6 q^{37} + 20 q^{39} + 880 q^{43} + 188 q^{45} - 408 q^{47} + 16 q^{51} - 10 q^{53} + 16 q^{55} - 108 q^{57} + 10 q^{59} - 6 q^{61} + 108 q^{63} - 16 q^{65} - 2766 q^{67} - 118 q^{69} + 12 q^{71} + 296 q^{73} - 486 q^{75} + 3420 q^{77} - 26256 q^{81} + 10 q^{83} + 242 q^{85} - 1272 q^{87} - 3424 q^{91} - 124 q^{93} - 4960 q^{95} - 16 q^{97} + 108 q^{99} + O(q^{100}) \)

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

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