# Properties

 Label 435.3.b Level $435$ Weight $3$ Character orbit 435.b Rep. character $\chi_{435}(434,\cdot)$ Character field $\Q$ Dimension $116$ Newform subspaces $5$ Sturm bound $180$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$435 = 3 \cdot 5 \cdot 29$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 435.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$435$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$180$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$, $$11$$, $$23$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(435, [\chi])$$.

Total New Old
Modular forms 124 124 0
Cusp forms 116 116 0
Eisenstein series 8 8 0

## Trace form

 $$116 q - 232 q^{4} + 4 q^{6} - 16 q^{9} + O(q^{10})$$ $$116 q - 232 q^{4} + 4 q^{6} - 16 q^{9} + 440 q^{16} - 108 q^{24} - 64 q^{25} + 124 q^{30} + 56 q^{34} + 12 q^{36} - 76 q^{45} - 316 q^{49} + 112 q^{51} - 164 q^{54} - 544 q^{64} - 168 q^{81} + 336 q^{91} - 176 q^{94} + 180 q^{96} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(435, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
435.3.b.a $1$ $11.853$ $$\Q$$ $$\Q(\sqrt{-435})$$ $$0$$ $$-3$$ $$-5$$ $$0$$ $$q-3q^{3}+4q^{4}-5q^{5}+9q^{9}-7q^{11}+\cdots$$
435.3.b.b $1$ $11.853$ $$\Q$$ $$\Q(\sqrt{-435})$$ $$0$$ $$-3$$ $$5$$ $$0$$ $$q-3q^{3}+4q^{4}+5q^{5}+9q^{9}+7q^{11}+\cdots$$
435.3.b.c $1$ $11.853$ $$\Q$$ $$\Q(\sqrt{-435})$$ $$0$$ $$3$$ $$-5$$ $$0$$ $$q+3q^{3}+4q^{4}-5q^{5}+9q^{9}+7q^{11}+\cdots$$
435.3.b.d $1$ $11.853$ $$\Q$$ $$\Q(\sqrt{-435})$$ $$0$$ $$3$$ $$5$$ $$0$$ $$q+3q^{3}+4q^{4}+5q^{5}+9q^{9}-7q^{11}+\cdots$$
435.3.b.e $112$ $11.853$ None $$0$$ $$0$$ $$0$$ $$0$$