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Properties

Label 1600.4.cb
Level $1600$
Weight $4$
Character orbit 1600.cb
Rep. character $\chi_{1600}(209,\cdot)$
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.cb (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

\( 1424 q + 10 q^{3} - 8 q^{5} + O(q^{10}) \) \( 1424 q + 10 q^{3} - 8 q^{5} + 6 q^{11} - 10 q^{13} + 16 q^{15} - 20 q^{17} + 6 q^{19} - 168 q^{21} + 10 q^{27} - 6 q^{29} - 732 q^{31} - 20 q^{33} + 1236 q^{35} - 10 q^{37} - 312 q^{45} + 20 q^{47} + 65040 q^{49} + 124 q^{51} - 10 q^{53} + 6 q^{59} - 6 q^{61} + 6880 q^{63} + 1936 q^{65} + 4630 q^{67} + 102 q^{69} - 594 q^{75} - 3440 q^{77} - 3148 q^{79} + 26232 q^{81} + 10 q^{83} - 258 q^{85} + 2064 q^{91} + 3880 q^{95} - 20 q^{97} + 3040 q^{99} + O(q^{100}) \)

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

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