# Properties

 Label 450.2.w Level 450 Weight 2 Character orbit w Rep. character $$\chi_{450}(23,\cdot)$$ Character field $$\Q(\zeta_{60})$$ Dimension 480 Newform subspaces 1 Sturm bound 180 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$450 = 2 \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 450.w (of order $$60$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$225$$ Character field: $$\Q(\zeta_{60})$$ Newform subspaces: $$1$$ Sturm bound: $$180$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(450, [\chi])$$.

Total New Old
Modular forms 1504 480 1024
Cusp forms 1376 480 896
Eisenstein series 128 0 128

## Trace form

 $$480q - 4q^{3} + O(q^{10})$$ $$480q - 4q^{3} + 4q^{12} + 8q^{15} - 60q^{16} + 8q^{18} + 12q^{20} + 24q^{23} - 48q^{25} + 8q^{27} + 24q^{30} - 16q^{33} + 24q^{37} - 36q^{38} + 40q^{39} - 44q^{42} + 12q^{45} - 48q^{47} - 8q^{48} - 48q^{50} + 24q^{55} + 28q^{57} - 12q^{58} - 60q^{59} - 24q^{60} + 20q^{63} + 24q^{65} + 12q^{67} - 144q^{68} - 140q^{69} + 16q^{72} - 168q^{75} - 432q^{77} - 76q^{78} + 40q^{81} + 48q^{82} - 60q^{83} - 60q^{84} + 24q^{85} - 44q^{87} - 52q^{90} + 24q^{92} - 72q^{93} - 60q^{95} + 36q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(450, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
450.2.w.a $$480$$ $$3.593$$ None $$0$$ $$-4$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(450, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(450, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database