Properties

Label 1600.4.br
Level $1600$
Weight $4$
Character orbit 1600.br
Rep. character $\chi_{1600}(107,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $3440$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1600.br (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 320 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 5808 3472 2336
Cusp forms 5712 3440 2272
Eisenstein series 96 32 64

Trace form

\( 3440 q + 8 q^{2} + 8 q^{3} - 16 q^{6} + 8 q^{7} + 8 q^{8} + O(q^{10}) \) \( 3440 q + 8 q^{2} + 8 q^{3} - 16 q^{6} + 8 q^{7} + 8 q^{8} - 16 q^{11} - 88 q^{12} + 8 q^{13} - 832 q^{14} - 16 q^{16} + 16 q^{17} + 8 q^{18} - 16 q^{21} - 856 q^{22} + 8 q^{23} - 1824 q^{24} - 16 q^{26} + 8 q^{27} + 8 q^{28} - 32 q^{31} + 8 q^{32} - 128 q^{34} - 16 q^{36} + 8 q^{37} - 2400 q^{38} - 16 q^{41} + 8 q^{42} + 8 q^{43} - 16 q^{46} - 4880 q^{48} + 5936 q^{51} + 8 q^{52} + 8 q^{53} - 352 q^{56} + 8 q^{57} - 4024 q^{58} - 16 q^{61} + 72 q^{62} + 10928 q^{66} + 8 q^{67} + 3488 q^{68} + 4224 q^{69} - 912 q^{71} + 2768 q^{72} + 8 q^{73} - 11920 q^{76} + 8 q^{77} + 11712 q^{78} + 11328 q^{79} - 16 q^{81} + 1128 q^{82} + 8 q^{83} - 16 q^{86} + 2584 q^{87} - 608 q^{88} - 16 q^{91} - 18152 q^{92} + 224 q^{93} + 128 q^{94} - 16 q^{96} - 6368 q^{98} + 21248 q^{99} + O(q^{100}) \)

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

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