# Properties

 Label 630.2.ca Level 630 Weight 2 Character orbit ca Rep. character $$\chi_{630}(113,\cdot)$$ Character field $$\Q(\zeta_{12})$$ Dimension 144 Newform subspaces 2 Sturm bound 288 Trace bound 14

# Related objects

## Defining parameters

 Level: $$N$$ = $$630 = 2 \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 630.ca (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$45$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$2$$ Sturm bound: $$288$$ Trace bound: $$14$$ Distinguishing $$T_p$$: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(630, [\chi])$$.

Total New Old
Modular forms 608 144 464
Cusp forms 544 144 400
Eisenstein series 64 0 64

## Trace form

 $$144q - 8q^{3} + O(q^{10})$$ $$144q - 8q^{3} + 24q^{11} + 8q^{12} - 8q^{15} + 72q^{16} + 8q^{18} + 24q^{20} + 8q^{21} + 24q^{23} + 24q^{25} + 16q^{27} + 8q^{33} - 8q^{36} + 48q^{37} - 72q^{38} - 96q^{41} - 80q^{45} - 96q^{47} - 16q^{48} + 32q^{51} + 48q^{55} - 32q^{57} - 8q^{63} + 24q^{65} + 16q^{66} + 24q^{67} + 16q^{72} - 32q^{75} + 32q^{78} + 96q^{82} - 120q^{83} + 48q^{85} + 144q^{86} - 40q^{87} - 40q^{90} - 48q^{91} + 24q^{92} - 32q^{93} - 120q^{95} + 72q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(630, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
630.2.ca.a $$72$$ $$5.031$$ None $$0$$ $$-4$$ $$0$$ $$0$$
630.2.ca.b $$72$$ $$5.031$$ None $$0$$ $$-4$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(630, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(630, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database