# Properties

 Label 12.9.c Level $12$ Weight $9$ Character orbit 12.c Rep. character $\chi_{12}(5,\cdot)$ Character field $\Q$ Dimension $3$ Newform subspaces $2$ Sturm bound $18$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$12 = 2^{2} \cdot 3$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 12.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$18$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(12, [\chi])$$.

Total New Old
Modular forms 19 3 16
Cusp forms 13 3 10
Eisenstein series 6 0 6

## Trace form

 $$3 q - 21 q^{3} - 2154 q^{7} + 3843 q^{9} + O(q^{10})$$ $$3 q - 21 q^{3} - 2154 q^{7} + 3843 q^{9} - 50394 q^{13} + 142560 q^{15} - 419178 q^{19} + 642342 q^{21} - 1394205 q^{25} + 1477899 q^{27} - 937578 q^{31} + 142560 q^{33} + 2822118 q^{37} - 2156298 q^{39} + 5472726 q^{43} - 14541120 q^{45} + 18124425 q^{49} - 7413120 q^{51} - 2566080 q^{55} - 12747354 q^{57} + 14911782 q^{61} + 34876566 q^{63} - 61469994 q^{67} + 12260160 q^{69} - 34291002 q^{73} + 122666955 q^{75} - 145689834 q^{79} - 35659197 q^{81} + 133436160 q^{85} + 108773280 q^{87} - 99306132 q^{91} - 191025114 q^{93} + 216008646 q^{97} - 14541120 q^{99} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(12, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
12.9.c.a $1$ $4.889$ $$\Q$$ $$\Q(\sqrt{-3})$$ $$0$$ $$81$$ $$0$$ $$4034$$ $$q+3^{4}q^{3}+4034q^{7}+3^{8}q^{9}-35806q^{13}+\cdots$$
12.9.c.b $2$ $4.889$ $$\Q(\sqrt{-110})$$ None $$0$$ $$-102$$ $$0$$ $$-6188$$ $$q+(-51+\beta )q^{3}-18\beta q^{5}-3094q^{7}+\cdots$$

## Decomposition of $$S_{9}^{\mathrm{old}}(12, [\chi])$$ into lower level spaces

$$S_{9}^{\mathrm{old}}(12, [\chi]) \simeq$$ $$S_{9}^{\mathrm{new}}(3, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(6, [\chi])$$$$^{\oplus 2}$$