# Properties

 Label 1575.2.ef Level 1575 Weight 2 Character orbit ef Rep. character $$\chi_{1575}(92,\cdot)$$ Character field $$\Q(\zeta_{60})$$ Dimension 2880 Sturm bound 480

# Related objects

## Defining parameters

 Level: $$N$$ = $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1575.ef (of order $$60$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$225$$ 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 2880 1024
Cusp forms 3776 2880 896
Eisenstein series 128 0 128

## Trace form

 $$2880q - 4q^{3} + O(q^{10})$$ $$2880q - 4q^{3} + 16q^{12} - 16q^{15} - 360q^{16} + 64q^{18} + 48q^{20} + 24q^{23} - 48q^{25} + 32q^{27} + 20q^{30} + 60q^{32} + 16q^{33} + 24q^{37} - 72q^{38} + 40q^{39} - 160q^{42} - 40q^{45} - 12q^{47} + 156q^{48} + 260q^{54} + 24q^{55} + 4q^{57} - 60q^{59} - 188q^{60} + 32q^{63} + 72q^{65} + 12q^{67} - 216q^{72} + 108q^{75} - 272q^{78} + 40q^{81} + 96q^{82} - 120q^{83} + 48q^{85} - 216q^{87} + 48q^{88} - 252q^{90} - 156q^{92} + 24q^{93} + 240q^{94} - 120q^{95} + 60q^{97} + O(q^{100})$$

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

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

## Decomposition of $$S_{2}^{\mathrm{old}}(1575, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1575, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database