# Properties

 Label 1470.2.n Level $1470$ Weight $2$ Character orbit 1470.n Rep. character $\chi_{1470}(79,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $80$ Newform subspaces $12$ Sturm bound $672$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1470.n (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$12$$ Sturm bound: $$672$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$11$$, $$17$$, $$19$$, $$31$$

## 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

 $$80 q + 40 q^{4} + 4 q^{5} - 8 q^{6} + 40 q^{9} + O(q^{10})$$ $$80 q + 40 q^{4} + 4 q^{5} - 8 q^{6} + 40 q^{9} + 2 q^{10} - 4 q^{11} - 4 q^{15} - 40 q^{16} - 20 q^{19} + 8 q^{20} - 4 q^{24} + 10 q^{25} + 4 q^{26} + 80 q^{29} - 8 q^{30} - 12 q^{31} + 32 q^{34} + 80 q^{36} - 8 q^{39} - 2 q^{40} + 72 q^{41} + 4 q^{44} - 4 q^{45} + 20 q^{46} + 64 q^{50} + 8 q^{51} - 4 q^{54} - 20 q^{55} + 16 q^{59} - 2 q^{60} + 8 q^{61} - 80 q^{64} - 16 q^{65} + 16 q^{66} + 48 q^{69} - 112 q^{71} + 60 q^{74} + 8 q^{75} - 40 q^{76} - 28 q^{79} + 4 q^{80} - 40 q^{81} + 104 q^{85} - 40 q^{86} - 8 q^{89} + 4 q^{90} - 20 q^{94} - 44 q^{95} + 4 q^{96} - 8 q^{99} + O(q^{100})$$

## 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.n.a $4$ $11.738$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$
1470.2.n.b $4$ $11.738$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+(1+\cdots)q^{4}+\cdots$$
1470.2.n.c $4$ $11.738$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+(1+\cdots)q^{4}+\cdots$$
1470.2.n.d $4$ $11.738$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+\zeta_{12}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$
1470.2.n.e $4$ $11.738$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}q^{3}+(1+\cdots)q^{4}+\cdots$$
1470.2.n.f $4$ $11.738$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$
1470.2.n.g $4$ $11.738$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$
1470.2.n.h $4$ $11.738$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+(1+\cdots)q^{4}+\cdots$$
1470.2.n.i $4$ $11.738$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+\zeta_{12}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$
1470.2.n.j $12$ $11.738$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}-\beta _{1}q^{3}+\beta _{8}q^{4}+\beta _{5}q^{5}+\cdots$$
1470.2.n.k $16$ $11.738$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{2}q^{2}+\beta _{5}q^{3}+(1+\beta _{3})q^{4}-\beta _{7}q^{5}+\cdots$$
1470.2.n.l $16$ $11.738$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q-\beta _{2}q^{2}+\beta _{5}q^{3}+(1+\beta _{3})q^{4}-\beta _{8}q^{5}+\cdots$$

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

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