# Properties

 Label 36.3.d Level $36$ Weight $3$ Character orbit 36.d Rep. character $\chi_{36}(19,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $3$ Sturm bound $18$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$36 = 2^{2} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 36.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$18$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(36, [\chi])$$.

Total New Old
Modular forms 16 6 10
Cusp forms 8 4 4
Eisenstein series 8 2 6

## Trace form

 $$4 q + 2 q^{2} + 4 q^{4} + 4 q^{5} - 16 q^{8} + O(q^{10})$$ $$4 q + 2 q^{2} + 4 q^{4} + 4 q^{5} - 16 q^{8} - 28 q^{10} - 16 q^{13} + 24 q^{14} + 16 q^{16} - 20 q^{17} - 8 q^{20} + 24 q^{22} + 36 q^{25} + 4 q^{26} + 48 q^{28} + 52 q^{29} + 32 q^{32} + 44 q^{34} - 88 q^{37} - 72 q^{38} - 160 q^{40} - 116 q^{41} + 48 q^{44} - 96 q^{46} + 100 q^{49} - 42 q^{50} - 88 q^{52} + 148 q^{53} + 212 q^{58} + 8 q^{61} - 24 q^{62} + 256 q^{64} + 8 q^{65} + 40 q^{68} + 48 q^{70} + 128 q^{73} + 52 q^{74} - 144 q^{76} - 96 q^{77} - 32 q^{80} - 436 q^{82} - 296 q^{85} + 168 q^{86} - 164 q^{89} - 192 q^{92} + 240 q^{94} - 256 q^{97} + 2 q^{98} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(36, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
36.3.d.a $1$ $0.981$ $$\Q$$ $$\Q(\sqrt{-1})$$ $$-2$$ $$0$$ $$8$$ $$0$$ $$q-2q^{2}+4q^{4}+8q^{5}-8q^{8}-2^{4}q^{10}+\cdots$$
36.3.d.b $1$ $0.981$ $$\Q$$ $$\Q(\sqrt{-1})$$ $$2$$ $$0$$ $$-8$$ $$0$$ $$q+2q^{2}+4q^{4}-8q^{5}+8q^{8}-2^{4}q^{10}+\cdots$$
36.3.d.c $2$ $0.981$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$4$$ $$0$$ $$q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{4}+2q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(36, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(36, [\chi]) \simeq$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 2}$$