# Properties

 Label 1575.2.eb Level 1575 Weight 2 Character orbit eb Rep. character $$\chi_{1575}(187,\cdot)$$ Character field $$\Q(\zeta_{60})$$ Dimension 3776 Sturm bound 480

# Related objects

## Defining parameters

 Level: $$N$$ = $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1575.eb (of order $$60$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$1575$$ Character field: $$\Q(\zeta_{60})$$ Sturm bound: $$480$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1575, [\chi])$$.

Total New Old
Modular forms 3904 3904 0
Cusp forms 3776 3776 0
Eisenstein series 128 128 0

## Trace form

 $$3776q + 8q^{2} - 24q^{3} + 10q^{4} - 8q^{7} - 72q^{8} - 10q^{9} + O(q^{10})$$ $$3776q + 8q^{2} - 24q^{3} + 10q^{4} - 8q^{7} - 72q^{8} - 10q^{9} - 48q^{10} - 12q^{11} - 24q^{12} - 10q^{14} - 38q^{15} - 442q^{16} - 30q^{17} + 16q^{18} - 60q^{19} + 48q^{20} - 12q^{21} - 8q^{22} - 32q^{23} - 16q^{25} - 96q^{26} - 36q^{27} - 44q^{28} - 20q^{29} + 34q^{30} - 18q^{31} - 20q^{32} - 54q^{33} + 4q^{35} - 40q^{36} - 16q^{37} + 30q^{39} - 10q^{42} - 16q^{43} - 20q^{44} - 42q^{45} - 12q^{46} - 24q^{47} - 42q^{48} + 8q^{50} - 16q^{51} - 36q^{53} - 30q^{54} + 26q^{56} + 32q^{57} + 24q^{58} - 30q^{59} + 100q^{60} - 18q^{61} + 26q^{63} - 80q^{64} - 16q^{65} + 54q^{66} + 8q^{67} - 210q^{69} + 32q^{70} - 48q^{71} - 20q^{72} - 48q^{73} - 24q^{75} + 48q^{76} - 64q^{77} - 38q^{78} + 10q^{79} - 72q^{80} - 6q^{81} - 36q^{82} + 336q^{83} + 220q^{84} - 16q^{85} - 12q^{86} - 6q^{87} + 64q^{88} - 210q^{89} - 144q^{90} - 24q^{91} - 12q^{92} - 38q^{93} - 30q^{94} + 60q^{95} - 18q^{96} - 140q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1575, [\chi])$$ into newform subspaces

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

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database