# Properties

 Label 1470.2.d Level $1470$ Weight $2$ Character orbit 1470.d Rep. character $\chi_{1470}(1469,\cdot)$ Character field $\Q$ Dimension $80$ Newform subspaces $8$ 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.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$105$$ Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$672$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$11$$, $$13$$, $$23$$

## Dimensions

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

Total New Old
Modular forms 368 80 288
Cusp forms 304 80 224
Eisenstein series 64 0 64

## Trace form

 $$80q + 80q^{4} + 4q^{9} + O(q^{10})$$ $$80q + 80q^{4} + 4q^{9} + 4q^{15} + 80q^{16} + 4q^{25} + 4q^{30} + 4q^{36} + 56q^{39} + 40q^{46} + 40q^{51} + 4q^{60} + 80q^{64} + 8q^{79} - 92q^{81} - 56q^{85} - 96q^{99} + O(q^{100})$$

## 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.d.a $$4$$ $$11.738$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$-4$$ $$-1$$ $$3$$ $$0$$ $$q-q^{2}-\beta _{1}q^{3}+q^{4}+(1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$$
1470.2.d.b $$4$$ $$11.738$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$-4$$ $$1$$ $$-3$$ $$0$$ $$q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
1470.2.d.c $$4$$ $$11.738$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$4$$ $$-1$$ $$-3$$ $$0$$ $$q+q^{2}-\beta _{1}q^{3}+q^{4}+(-2\beta _{2}-\beta _{3})q^{5}+\cdots$$
1470.2.d.d $$4$$ $$11.738$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$4$$ $$1$$ $$3$$ $$0$$ $$q+q^{2}+\beta _{1}q^{3}+q^{4}+(2\beta _{2}+\beta _{3})q^{5}+\cdots$$
1470.2.d.e $$8$$ $$11.738$$ 8.0.3317760000.3 None $$-8$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+(\beta _{2}+\beta _{5})q^{3}+q^{4}+(\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots$$
1470.2.d.f $$8$$ $$11.738$$ 8.0.3317760000.3 None $$8$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+(\beta _{2}+\beta _{5})q^{3}+q^{4}+(-\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots$$
1470.2.d.g $$24$$ $$11.738$$ None $$-24$$ $$0$$ $$0$$ $$0$$
1470.2.d.h $$24$$ $$11.738$$ None $$24$$ $$0$$ $$0$$ $$0$$

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

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