# Properties

 Label 435.2.f Level $435$ Weight $2$ Character orbit 435.f Rep. character $\chi_{435}(289,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $6$ Sturm bound $120$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$435 = 3 \cdot 5 \cdot 29$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 435.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$145$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$120$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(435, [\chi])$$.

Total New Old
Modular forms 64 32 32
Cusp forms 56 32 24
Eisenstein series 8 0 8

## Trace form

 $$32 q + 36 q^{4} - 8 q^{5} - 4 q^{6} + 32 q^{9} + O(q^{10})$$ $$32 q + 36 q^{4} - 8 q^{5} - 4 q^{6} + 32 q^{9} + 44 q^{16} - 20 q^{20} - 12 q^{24} + 24 q^{25} - 12 q^{29} - 16 q^{30} - 32 q^{34} - 4 q^{35} + 36 q^{36} - 8 q^{45} - 32 q^{49} - 16 q^{51} - 4 q^{54} - 40 q^{59} - 12 q^{64} + 4 q^{65} + 8 q^{71} - 40 q^{74} - 72 q^{80} + 32 q^{81} - 40 q^{86} - 16 q^{91} - 88 q^{94} - 28 q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(435, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
435.2.f.a $2$ $3.473$ $$\Q(\sqrt{-1})$$ None $$-4$$ $$2$$ $$4$$ $$0$$ $$q-2q^{2}+q^{3}+2q^{4}+(2+i)q^{5}-2q^{6}+\cdots$$
435.2.f.b $2$ $3.473$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$-2$$ $$-2$$ $$0$$ $$q-q^{2}-q^{3}-q^{4}+(-1+i)q^{5}+q^{6}+\cdots$$
435.2.f.c $2$ $3.473$ $$\Q(\sqrt{-1})$$ None $$2$$ $$2$$ $$-2$$ $$0$$ $$q+q^{2}+q^{3}-q^{4}+(-1+i)q^{5}+q^{6}+\cdots$$
435.2.f.d $2$ $3.473$ $$\Q(\sqrt{-1})$$ None $$4$$ $$-2$$ $$4$$ $$0$$ $$q+2q^{2}-q^{3}+2q^{4}+(2+i)q^{5}-2q^{6}+\cdots$$
435.2.f.e $12$ $3.473$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$-12$$ $$-6$$ $$0$$ $$q+\beta _{5}q^{2}-q^{3}+(1-\beta _{3})q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots$$
435.2.f.f $12$ $3.473$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$12$$ $$-6$$ $$0$$ $$q-\beta _{5}q^{2}+q^{3}+(1-\beta _{3})q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(435, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(435, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(145, [\chi])$$$$^{\oplus 2}$$