# Properties

 Label 36.9.g Level $36$ Weight $9$ Character orbit 36.g Rep. character $\chi_{36}(5,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $16$ Newform subspaces $1$ Sturm bound $54$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$36 = 2^{2} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 36.g (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$54$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(36, [\chi])$$.

Total New Old
Modular forms 102 16 86
Cusp forms 90 16 74
Eisenstein series 12 0 12

## Trace form

 $$16 q + 21 q^{3} + 441 q^{5} + 923 q^{7} + 9111 q^{9} + O(q^{10})$$ $$16 q + 21 q^{3} + 441 q^{5} + 923 q^{7} + 9111 q^{9} - 5490 q^{11} + 1685 q^{13} + 33975 q^{15} + 84518 q^{19} + 68391 q^{21} + 379071 q^{23} + 455803 q^{25} + 726408 q^{27} + 2421 q^{29} - 378307 q^{31} - 8622 q^{33} - 1671664 q^{37} + 695721 q^{39} - 6289236 q^{41} + 339512 q^{43} + 4706649 q^{45} - 2770281 q^{47} - 3026445 q^{49} + 5772195 q^{51} - 17497638 q^{55} + 4803009 q^{57} - 43273584 q^{59} + 17450705 q^{61} + 19287969 q^{63} + 29762595 q^{65} - 35026726 q^{67} + 70486947 q^{69} + 28071218 q^{73} - 17457507 q^{75} - 81778311 q^{77} + 30689459 q^{79} + 102173175 q^{81} + 52482087 q^{83} - 39893022 q^{85} + 149643225 q^{87} - 55534214 q^{91} - 227776119 q^{93} - 401097996 q^{95} - 33421078 q^{97} + 80448723 q^{99} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(36, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
36.9.g.a $16$ $14.666$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$21$$ $$441$$ $$923$$ $$q+(7+11\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(37+18\beta _{1}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{9}^{\mathrm{old}}(36, [\chi])$$ into lower level spaces

$$S_{9}^{\mathrm{old}}(36, [\chi]) \simeq$$ $$S_{9}^{\mathrm{new}}(9, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 2}$$