# Properties

 Label 12.9.d Level $12$ Weight $9$ Character orbit 12.d Rep. character $\chi_{12}(7,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $1$ Sturm bound $18$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$12 = 2^{2} \cdot 3$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 12.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$18$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 18 8 10
Cusp forms 14 8 6
Eisenstein series 4 0 4

## Trace form

 $$8 q + 6 q^{2} - 52 q^{4} - 336 q^{5} + 1134 q^{6} - 12960 q^{8} - 17496 q^{9} + O(q^{10})$$ $$8 q + 6 q^{2} - 52 q^{4} - 336 q^{5} + 1134 q^{6} - 12960 q^{8} - 17496 q^{9} + 36628 q^{10} - 11340 q^{12} - 2864 q^{13} + 52728 q^{14} + 99440 q^{16} - 193200 q^{17} - 13122 q^{18} + 335592 q^{20} + 121824 q^{21} - 556968 q^{22} + 221616 q^{24} - 579048 q^{25} + 21564 q^{26} - 594672 q^{28} + 2063472 q^{29} + 46980 q^{30} - 3602784 q^{32} - 920160 q^{33} + 1568476 q^{34} + 113724 q^{36} + 7470352 q^{37} + 3659400 q^{38} + 1749184 q^{40} - 8865456 q^{41} - 5288328 q^{42} + 2395920 q^{44} + 734832 q^{45} - 13649856 q^{46} + 10916208 q^{48} - 18923896 q^{49} + 14581842 q^{50} + 18592888 q^{52} + 8706672 q^{53} - 2480058 q^{54} - 45565632 q^{56} - 2325024 q^{57} - 8816444 q^{58} + 28348056 q^{60} + 13457296 q^{61} + 80783976 q^{62} + 1268864 q^{64} + 7293408 q^{65} - 51205608 q^{66} - 117288264 q^{68} - 8636544 q^{69} - 60373104 q^{70} + 28343520 q^{72} + 94738960 q^{73} + 119548428 q^{74} + 144621360 q^{76} - 56971392 q^{77} - 140630580 q^{78} - 163857888 q^{80} + 38263752 q^{81} - 188383460 q^{82} + 199712304 q^{84} - 201200416 q^{85} + 240327384 q^{86} + 156323520 q^{88} + 188992272 q^{89} - 80105436 q^{90} - 387657984 q^{92} - 54802656 q^{93} - 38749872 q^{94} + 246092256 q^{96} - 123291632 q^{97} + 691081830 q^{98} + O(q^{100})$$

## 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.d.a $8$ $4.889$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$6$$ $$0$$ $$-336$$ $$0$$ $$q+(1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-6+\cdots)q^{4}+\cdots$$

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

$$S_{9}^{\mathrm{old}}(12, [\chi]) \cong$$ $$S_{9}^{\mathrm{new}}(4, [\chi])$$$$^{\oplus 2}$$