# Properties

 Label 1470.2.m Level $1470$ Weight $2$ Character orbit 1470.m Rep. character $\chi_{1470}(97,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $80$ Newform subspaces $6$ Sturm bound $672$ Trace bound $10$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1470.m (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(i)$$ Newform subspaces: $$6$$ Sturm bound: $$672$$ Trace bound: $$10$$ Distinguishing $$T_p$$: $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1470, [\chi])$$.

Total New Old
Modular forms 736 80 656
Cusp forms 608 80 528
Eisenstein series 128 0 128

## Trace form

 $$80q + O(q^{10})$$ $$80q - 16q^{11} + 8q^{15} - 80q^{16} - 24q^{22} - 48q^{23} - 16q^{30} - 80q^{36} + 64q^{37} + 16q^{43} + 16q^{46} - 32q^{51} - 80q^{53} + 16q^{57} - 56q^{58} + 64q^{65} - 32q^{67} - 32q^{78} - 80q^{81} - 80q^{85} - 32q^{86} + 24q^{88} - 48q^{92} + 16q^{93} + 16q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1470, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1470.2.m.a $$8$$ $$11.738$$ $$\Q(\zeta_{16})$$ None $$0$$ $$0$$ $$-8$$ $$0$$ $$q+\zeta_{16}^{3}q^{2}-\zeta_{16}^{3}q^{3}-\zeta_{16}^{2}q^{4}+\cdots$$
1470.2.m.b $$8$$ $$11.738$$ $$\Q(\zeta_{16})$$ None $$0$$ $$0$$ $$8$$ $$0$$ $$q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{3}q^{3}-\zeta_{16}^{2}q^{4}+\cdots$$
1470.2.m.c $$16$$ $$11.738$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$-8$$ $$0$$ $$q-\beta _{6}q^{2}-\beta _{6}q^{3}-\beta _{5}q^{4}+\beta _{3}q^{5}+\cdots$$
1470.2.m.d $$16$$ $$11.738$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{10}q^{2}-\beta _{10}q^{3}-\beta _{8}q^{4}+(1+2\beta _{1}+\cdots)q^{5}+\cdots$$
1470.2.m.e $$16$$ $$11.738$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{10}q^{2}+\beta _{10}q^{3}-\beta _{8}q^{4}+(-1+\cdots)q^{5}+\cdots$$
1470.2.m.f $$16$$ $$11.738$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$8$$ $$0$$ $$q-\beta _{6}q^{2}+\beta _{6}q^{3}-\beta _{5}q^{4}-\beta _{3}q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1470, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1470, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(245, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(490, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(735, [\chi])$$$$^{\oplus 2}$$