# Properties

 Label 1470.2.b Level $1470$ Weight $2$ Character orbit 1470.b Rep. character $\chi_{1470}(881,\cdot)$ Character field $\Q$ Dimension $56$ Newform subspaces $4$ Sturm bound $672$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1470.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$672$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$11$$, $$17$$

## Dimensions

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

Total New Old
Modular forms 368 56 312
Cusp forms 304 56 248
Eisenstein series 64 0 64

## Trace form

 $$56q - 56q^{4} + 4q^{9} + O(q^{10})$$ $$56q - 56q^{4} + 4q^{9} + 8q^{15} + 56q^{16} + 16q^{18} + 56q^{25} + 4q^{30} - 4q^{36} + 32q^{37} + 24q^{39} + 32q^{43} - 40q^{46} + 40q^{51} - 8q^{57} - 8q^{60} - 56q^{64} + 48q^{67} - 16q^{72} - 80q^{79} - 4q^{81} - 48q^{85} - 72q^{93} + 80q^{99} + O(q^{100})$$

## 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.b.a $$12$$ $$11.738$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$-4$$ $$12$$ $$0$$ $$q+\beta _{4}q^{2}-\beta _{1}q^{3}-q^{4}+q^{5}-\beta _{9}q^{6}+\cdots$$
1470.2.b.b $$12$$ $$11.738$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$4$$ $$-12$$ $$0$$ $$q+\beta _{4}q^{2}+\beta _{1}q^{3}-q^{4}-q^{5}+\beta _{9}q^{6}+\cdots$$
1470.2.b.c $$16$$ $$11.738$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$-8$$ $$-16$$ $$0$$ $$q-\beta _{9}q^{2}-\beta _{11}q^{3}-q^{4}-q^{5}+(-\beta _{5}+\cdots)q^{6}+\cdots$$
1470.2.b.d $$16$$ $$11.738$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$8$$ $$16$$ $$0$$ $$q-\beta _{9}q^{2}+\beta _{11}q^{3}-q^{4}+q^{5}+(\beta _{5}+\cdots)q^{6}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1470, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(294, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(735, [\chi])$$$$^{\oplus 2}$$