# Properties

 Label 99.8.g Level $99$ Weight $8$ Character orbit 99.g Rep. character $\chi_{99}(32,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $164$ Newform subspaces $2$ Sturm bound $96$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$99 = 3^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$8$$ Character orbit: $$[\chi]$$ $$=$$ 99.g (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$99$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(99, [\chi])$$.

Total New Old
Modular forms 172 172 0
Cusp forms 164 164 0
Eisenstein series 8 8 0

## Trace form

 $$164 q - 43 q^{3} - 5122 q^{4} + 207 q^{5} - 25 q^{9} + O(q^{10})$$ $$164 q - 43 q^{3} - 5122 q^{4} + 207 q^{5} - 25 q^{9} - 9408 q^{11} + 11282 q^{12} - 6 q^{14} - 14060 q^{15} - 311554 q^{16} - 53766 q^{20} + 35511 q^{22} + 140628 q^{23} + 1192245 q^{25} + 337178 q^{27} + 99325 q^{31} + 92354 q^{33} - 177714 q^{34} + 281648 q^{36} - 151790 q^{37} + 888852 q^{38} + 1782594 q^{42} + 38863 q^{45} - 986682 q^{47} + 4746920 q^{48} + 8235428 q^{49} - 1333586 q^{55} - 2569764 q^{56} - 691746 q^{58} + 12923613 q^{59} - 1601426 q^{60} + 35717624 q^{64} - 11217708 q^{66} + 699007 q^{67} - 3513479 q^{69} + 5740056 q^{70} - 14839869 q^{75} + 6403392 q^{77} - 20423958 q^{78} - 4629541 q^{81} - 3789672 q^{82} - 3411414 q^{86} + 12330003 q^{88} + 13655508 q^{91} - 39357234 q^{92} + 316801 q^{93} + 18791833 q^{97} + 3239687 q^{99} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(99, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
99.8.g.a $4$ $30.926$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ $$\Q(\sqrt{-11})$$ $$0$$ $$83$$ $$-1521$$ $$0$$ $$q+(48\beta _{2}+13\beta _{3})q^{3}+2^{7}\beta _{2}q^{4}+(-507+\cdots)q^{5}+\cdots$$
99.8.g.b $160$ $30.926$ None $$0$$ $$-126$$ $$1728$$ $$0$$