# Properties

 Label 176.9.h Level $176$ Weight $9$ Character orbit 176.h Rep. character $\chi_{176}(65,\cdot)$ Character field $\Q$ Dimension $47$ Newform subspaces $6$ Sturm bound $216$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$176 = 2^{4} \cdot 11$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 176.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$216$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(176, [\chi])$$.

Total New Old
Modular forms 198 49 149
Cusp forms 186 47 139
Eisenstein series 12 2 10

## Trace form

 $$47 q + 2 q^{3} - 2 q^{5} + 102221 q^{9} + O(q^{10})$$ $$47 q + 2 q^{3} - 2 q^{5} + 102221 q^{9} + 9889 q^{11} + 98468 q^{15} + 650306 q^{23} + 2721997 q^{25} + 664964 q^{27} + 2 q^{31} - 644930 q^{33} + 2360254 q^{37} - 794374 q^{45} - 667294 q^{47} - 30146577 q^{49} + 5131390 q^{53} + 13359874 q^{55} - 9739774 q^{59} + 101498562 q^{67} - 36178116 q^{69} + 4502402 q^{71} - 12266618 q^{75} + 21892992 q^{77} + 188723691 q^{81} + 6166270 q^{89} - 241880448 q^{91} - 211173444 q^{93} + 36754046 q^{97} + 206261891 q^{99} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(176, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
176.9.h.a $1$ $71.699$ $$\Q$$ $$\Q(\sqrt{-11})$$ $$0$$ $$113$$ $$1151$$ $$0$$ $$q+113q^{3}+1151q^{5}+6208q^{9}-11^{4}q^{11}+\cdots$$
176.9.h.b $2$ $71.699$ $$\Q(\sqrt{33})$$ $$\Q(\sqrt{-11})$$ $$0$$ $$-113$$ $$-1151$$ $$0$$ $$q+(-59-5\beta )q^{3}+(-565+21\beta )q^{5}+\cdots$$
176.9.h.c $6$ $71.699$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$0$$ $$36$$ $$-448$$ $$0$$ $$q+(6+\beta _{5})q^{3}+(-73-5\beta _{4}-3\beta _{5})q^{5}+\cdots$$
176.9.h.d $6$ $71.699$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$0$$ $$36$$ $$1856$$ $$0$$ $$q+(6+\beta _{2})q^{3}+(309+\beta _{5})q^{5}+\beta _{1}q^{7}+\cdots$$
176.9.h.e $8$ $71.699$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$-182$$ $$-1410$$ $$0$$ $$q+(-23-\beta _{1})q^{3}+(-176+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
176.9.h.f $24$ $71.699$ None $$0$$ $$112$$ $$0$$ $$0$$

## Decomposition of $$S_{9}^{\mathrm{old}}(176, [\chi])$$ into lower level spaces

$$S_{9}^{\mathrm{old}}(176, [\chi]) \cong$$ $$S_{9}^{\mathrm{new}}(11, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(22, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(44, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(88, [\chi])$$$$^{\oplus 2}$$