# Properties

 Label 99.9.c Level $99$ Weight $9$ Character orbit 99.c Rep. character $\chi_{99}(10,\cdot)$ Character field $\Q$ Dimension $39$ Newform subspaces $4$ Sturm bound $108$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$99 = 3^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 99.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$108$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(99, [\chi])$$.

Total New Old
Modular forms 100 41 59
Cusp forms 92 39 53
Eisenstein series 8 2 6

## Trace form

 $$39 q - 5052 q^{4} + 413 q^{5} + O(q^{10})$$ $$39 q - 5052 q^{4} + 413 q^{5} + 1441 q^{11} - 34788 q^{14} + 531456 q^{16} - 188560 q^{20} + 257664 q^{22} - 368167 q^{23} + 1515150 q^{25} - 290292 q^{26} + 1502595 q^{31} + 4360224 q^{34} + 2110647 q^{37} + 10619424 q^{38} + 792352 q^{44} + 12988814 q^{47} - 26029665 q^{49} + 8209814 q^{53} - 14792613 q^{55} - 58650972 q^{56} + 5179056 q^{58} - 19228051 q^{59} - 6824592 q^{64} + 7233723 q^{67} - 37796832 q^{70} + 9388121 q^{71} + 73289172 q^{77} - 201976252 q^{80} - 36451488 q^{82} - 164131752 q^{86} - 120346512 q^{88} + 134407289 q^{89} + 139038384 q^{91} + 408006104 q^{92} + 248832519 q^{97} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(99, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
99.9.c.a $1$ $40.330$ $$\Q$$ $$\Q(\sqrt{-11})$$ $$0$$ $$0$$ $$-1151$$ $$0$$ $$q+2^{8}q^{4}-1151q^{5}-11^{4}q^{11}+2^{16}q^{16}+\cdots$$
99.9.c.b $6$ $40.330$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$0$$ $$0$$ $$448$$ $$0$$ $$q+\beta _{1}q^{2}+(-203+3\beta _{3}-2\beta _{4})q^{4}+\cdots$$
99.9.c.c $16$ $40.330$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(-151-\beta _{1})q^{4}+\beta _{3}q^{5}+\cdots$$
99.9.c.d $16$ $40.330$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$1116$$ $$0$$ $$q+\beta _{1}q^{2}+(-105+\beta _{2})q^{4}+(70-\beta _{4}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{9}^{\mathrm{old}}(99, [\chi])$$ into lower level spaces

$$S_{9}^{\mathrm{old}}(99, [\chi]) \cong$$ $$S_{9}^{\mathrm{new}}(11, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 2}$$