# Properties

 Label 405.2.j Level $405$ Weight $2$ Character orbit 405.j Rep. character $\chi_{405}(109,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $44$ Newform subspaces $8$ Sturm bound $108$ Trace bound $10$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$405 = 3^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 405.j (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$45$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$8$$ Sturm bound: $$108$$ Trace bound: $$10$$ Distinguishing $$T_p$$: $$2$$, $$7$$

## Dimensions

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

Total New Old
Modular forms 132 52 80
Cusp forms 84 44 40
Eisenstein series 48 8 40

## Trace form

 $$44 q + 24 q^{4} + O(q^{10})$$ $$44 q + 24 q^{4} + 4 q^{10} - 20 q^{16} - 8 q^{19} + 8 q^{25} - 8 q^{31} + 26 q^{34} - 4 q^{40} + 44 q^{46} + 2 q^{49} - 96 q^{55} + 16 q^{61} - 100 q^{64} + 24 q^{70} - 18 q^{76} - 68 q^{79} - 14 q^{85} + 24 q^{91} - 136 q^{94} + O(q^{100})$$

## 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.j.a $4$ $3.234$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$-3$$ $$0$$ $$-6$$ $$-12$$ $$q+(-1-\beta _{3})q^{2}+(2-\beta _{1}-\beta _{2}+2\beta _{3})q^{4}+\cdots$$
405.2.j.b $4$ $3.234$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$-3$$ $$0$$ $$-3$$ $$12$$ $$q+(-1-\beta _{3})q^{2}+(2-\beta _{1}-\beta _{2}+2\beta _{3})q^{4}+\cdots$$
405.2.j.c $4$ $3.234$ $$\Q(\sqrt{-3}, \sqrt{-5})$$ $$\Q(\sqrt{-15})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(\beta _{1}-\beta _{3})q^{5}+\beta _{3}q^{8}+\cdots$$
405.2.j.d $4$ $3.234$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$3$$ $$0$$ $$3$$ $$12$$ $$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$$
405.2.j.e $4$ $3.234$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$3$$ $$0$$ $$6$$ $$-12$$ $$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$$
405.2.j.f $8$ $3.234$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}^{6}q^{2}-\zeta_{24}^{4}q^{5}-\zeta_{24}q^{7}+(2\zeta_{24}^{5}+\cdots)q^{8}+\cdots$$
405.2.j.g $8$ $3.234$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}^{5}q^{2}+(\zeta_{24}^{2}+\zeta_{24}^{3})q^{5}+\zeta_{24}^{6}q^{7}+\cdots$$
405.2.j.h $8$ $3.234$ 8.0.12960000.1 $$\Q(\sqrt{-15})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+(2-\beta _{3}+2\beta _{5}+\beta _{6})q^{4}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(405, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(135, [\chi])$$$$^{\oplus 2}$$