# Properties

 Label 630.2.d Level $630$ Weight $2$ Character orbit 630.d Rep. character $\chi_{630}(629,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $4$ Sturm bound $288$ Trace bound $23$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$630 = 2 \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 630.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$105$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$288$$ Trace bound: $$23$$ Distinguishing $$T_p$$: $$11$$, $$23$$

## Dimensions

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

Total New Old
Modular forms 160 16 144
Cusp forms 128 16 112
Eisenstein series 32 0 32

## Trace form

 $$16 q + 16 q^{4} + O(q^{10})$$ $$16 q + 16 q^{4} + 16 q^{16} + 16 q^{46} + 8 q^{49} + 16 q^{64} + 40 q^{70} + 16 q^{79} - 80 q^{85} - 40 q^{91} + O(q^{100})$$

## 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.d.a $4$ $5.031$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots$$
630.2.d.b $4$ $5.031$ $$\Q(\sqrt{-2}, \sqrt{5})$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots$$
630.2.d.c $4$ $5.031$ $$\Q(\sqrt{-2}, \sqrt{5})$$ None $$4$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots$$
630.2.d.d $4$ $5.031$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$4$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+q^{4}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(630, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 2}$$