# Properties

 Label 405.2.b Level $405$ Weight $2$ Character orbit 405.b Rep. character $\chi_{405}(244,\cdot)$ Character field $\Q$ Dimension $20$ Newform subspaces $5$ Sturm bound $108$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$405 = 3^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 405.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$108$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$2$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(405, [\chi])$$.

Total New Old
Modular forms 66 28 38
Cusp forms 42 20 22
Eisenstein series 24 8 16

## Trace form

 $$20 q - 12 q^{4} + O(q^{10})$$ $$20 q - 12 q^{4} - 2 q^{10} + 4 q^{16} - 8 q^{19} + 14 q^{25} - 8 q^{31} - 28 q^{34} - 10 q^{40} + 8 q^{46} - 28 q^{49} + 12 q^{55} + 52 q^{61} - 4 q^{64} - 84 q^{70} + 120 q^{76} + 16 q^{79} - 26 q^{85} - 48 q^{91} + 80 q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(405, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
405.2.b.a $4$ $3.234$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$0$$ $$-3$$ $$0$$ $$q-\beta _{2}q^{2}+(-2+\beta _{1}+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$$
405.2.b.b $4$ $3.234$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$0$$ $$3$$ $$0$$ $$q-\beta _{2}q^{2}+(-2+\beta _{1}+\beta _{3})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$$
405.2.b.c $4$ $3.234$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots$$
405.2.b.d $4$ $3.234$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots$$
405.2.b.e $4$ $3.234$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}-2\beta _{1}q^{8}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(405, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(405, [\chi]) \cong$$