# Properties

 Label 36.2.e Level $36$ Weight $2$ Character orbit 36.e Rep. character $\chi_{36}(13,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $2$ Newform subspaces $1$ Sturm bound $12$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$36 = 2^{2} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 36.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(36, [\chi])$$.

Total New Old
Modular forms 18 2 16
Cusp forms 6 2 4
Eisenstein series 12 0 12

## Trace form

 $$2 q - 3 q^{5} + q^{7} - 6 q^{9} + O(q^{10})$$ $$2 q - 3 q^{5} + q^{7} - 6 q^{9} - 3 q^{11} + q^{13} + 9 q^{15} + 12 q^{17} - 8 q^{19} + 3 q^{21} + 3 q^{23} - 4 q^{25} - 3 q^{29} - 5 q^{31} - 9 q^{33} - 6 q^{35} + 4 q^{37} - 3 q^{39} - 3 q^{41} + q^{43} + 9 q^{45} + 9 q^{47} + 6 q^{49} - 12 q^{53} + 18 q^{55} + 3 q^{59} + 13 q^{61} - 3 q^{63} + 3 q^{65} + 7 q^{67} - 9 q^{69} - 24 q^{71} - 20 q^{73} - 12 q^{75} + 3 q^{77} - 11 q^{79} + 18 q^{81} + 9 q^{83} - 18 q^{85} - 9 q^{87} + 12 q^{89} + 2 q^{91} + 15 q^{93} + 12 q^{95} - 11 q^{97} + 9 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(36, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
36.2.e.a $2$ $0.287$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$1$$ $$q+(1-2\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+\zeta_{6}q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(36, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(36, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 2}$$