# Properties

 Label 99.8.d Level $99$ Weight $8$ Character orbit 99.d Rep. character $\chi_{99}(98,\cdot)$ Character field $\Q$ Dimension $28$ Newform subspaces $1$ Sturm bound $96$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$99 = 3^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$8$$ Character orbit: $$[\chi]$$ $$=$$ 99.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$33$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$96$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 88 28 60
Cusp forms 80 28 52
Eisenstein series 8 0 8

## Trace form

 $$28 q + 1792 q^{4} + O(q^{10})$$ $$28 q + 1792 q^{4} + 136936 q^{16} + 69696 q^{22} - 877308 q^{25} - 21616 q^{31} + 161304 q^{34} + 408464 q^{37} - 5023892 q^{49} + 439472 q^{55} + 2851344 q^{58} - 15376208 q^{64} - 17729872 q^{67} + 3438408 q^{70} + 54779784 q^{82} + 26540976 q^{88} - 19094256 q^{91} + 10561400 q^{97} + O(q^{100})$$

## 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.d.a $28$ $30.926$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{8}^{\mathrm{old}}(99, [\chi])$$ into lower level spaces

$$S_{8}^{\mathrm{old}}(99, [\chi]) \cong$$ $$S_{8}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 2}$$