# Properties

 Label 1600.2.cs Level $1600$ Weight $2$ Character orbit 1600.cs Rep. character $\chi_{1600}(67,\cdot)$ Character field $\Q(\zeta_{80})$ Dimension $7616$ Sturm bound $480$

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## Defining parameters

 Level: $$N$$ $$=$$ $$1600 = 2^{6} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1600.cs (of order $$80$$ and degree $$32$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1600$$ Character field: $$\Q(\zeta_{80})$$ Sturm bound: $$480$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1600, [\chi])$$.

Total New Old
Modular forms 7744 7744 0
Cusp forms 7616 7616 0
Eisenstein series 128 128 0

## Trace form

 $$7616q - 32q^{2} - 32q^{3} - 40q^{4} - 32q^{5} - 24q^{6} - 32q^{7} - 32q^{8} - 40q^{9} + O(q^{10})$$ $$7616q - 32q^{2} - 32q^{3} - 40q^{4} - 32q^{5} - 24q^{6} - 32q^{7} - 32q^{8} - 40q^{9} - 32q^{10} - 24q^{11} - 64q^{12} - 32q^{13} - 40q^{14} - 32q^{15} - 24q^{16} - 40q^{17} - 32q^{18} - 40q^{19} - 32q^{20} - 24q^{21} - 32q^{23} - 32q^{25} - 64q^{26} - 32q^{27} - 32q^{28} - 40q^{29} + 32q^{30} - 48q^{31} - 32q^{32} - 72q^{34} - 32q^{35} - 24q^{36} - 32q^{37} - 256q^{38} - 40q^{39} - 128q^{40} - 24q^{41} - 32q^{42} - 32q^{43} - 40q^{44} - 8q^{45} - 24q^{46} - 24q^{47} - 136q^{48} - 136q^{50} - 64q^{51} - 32q^{52} - 32q^{53} - 40q^{54} - 32q^{55} - 24q^{56} - 32q^{57} + 32q^{58} - 40q^{59} - 256q^{60} - 24q^{61} - 16q^{62} - 40q^{64} - 64q^{65} - 24q^{66} - 32q^{67} - 120q^{68} - 40q^{69} - 32q^{70} - 24q^{71} + 88q^{72} - 32q^{73} - 32q^{75} - 64q^{76} - 32q^{77} + 120q^{78} - 40q^{79} - 32q^{80} - 24q^{81} - 32q^{82} - 32q^{83} - 40q^{84} - 72q^{85} - 24q^{86} + 80q^{87} + 320q^{88} - 40q^{89} - 32q^{90} - 24q^{91} - 168q^{92} - 8q^{93} - 8q^{94} - 64q^{95} + 376q^{96} + 8q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1600, [\chi])$$ into newform subspaces

The newforms in this space have not yet been added to the LMFDB.