# Properties

 Label 43.9.b Level $43$ Weight $9$ Character orbit 43.b Rep. character $\chi_{43}(42,\cdot)$ Character field $\Q$ Dimension $29$ Newform subspaces $2$ Sturm bound $33$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$43$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 43.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$43$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$33$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(43, [\chi])$$.

Total New Old
Modular forms 31 31 0
Cusp forms 29 29 0
Eisenstein series 2 2 0

## Trace form

 $$29 q - 4028 q^{4} - 1794 q^{6} - 74193 q^{9} + O(q^{10})$$ $$29 q - 4028 q^{4} - 1794 q^{6} - 74193 q^{9} + 24982 q^{10} + 14857 q^{11} - 32635 q^{13} + 24732 q^{14} + 15388 q^{15} + 591348 q^{16} - 55169 q^{17} - 261352 q^{21} + 356287 q^{23} + 1770326 q^{24} - 2249809 q^{25} + 479407 q^{31} + 10947816 q^{35} + 13281682 q^{36} - 7189158 q^{38} - 21389338 q^{40} - 960905 q^{41} + 5892221 q^{43} - 6176816 q^{44} - 5000240 q^{47} - 9796135 q^{49} - 1080700 q^{52} + 10880833 q^{53} - 13757972 q^{54} + 34967256 q^{56} + 35225148 q^{57} + 22565734 q^{58} - 13418942 q^{59} - 44902072 q^{60} - 153667356 q^{64} - 48457584 q^{66} - 170770235 q^{67} + 170492674 q^{68} + 205870278 q^{74} + 267860612 q^{78} + 80425884 q^{79} - 14554283 q^{81} - 135695411 q^{83} + 251931292 q^{84} - 45482652 q^{86} - 106687410 q^{87} - 255044692 q^{90} - 271107950 q^{92} + 123322986 q^{95} - 692987086 q^{96} - 156101641 q^{97} - 542004247 q^{99} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(43, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
43.9.b.a $$1$$ $$17.517$$ $$\Q$$ $$\Q(\sqrt{-43})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+2^{8}q^{4}+3^{8}q^{9}+10319q^{11}-54721q^{13}+\cdots$$
43.9.b.b $$28$$ $$17.517$$ None $$0$$ $$0$$ $$0$$ $$0$$