# Properties

 Label 32.8.b Level $32$ Weight $8$ Character orbit 32.b Rep. character $\chi_{32}(17,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $1$ Sturm bound $32$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$32 = 2^{5}$$ Weight: $$k$$ $$=$$ $$8$$ Character orbit: $$[\chi]$$ $$=$$ 32.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$32$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(32, [\chi])$$.

Total New Old
Modular forms 32 8 24
Cusp forms 24 6 18
Eisenstein series 8 2 6

## Trace form

 $$6 q + 688 q^{7} - 2918 q^{9} + O(q^{10})$$ $$6 q + 688 q^{7} - 2918 q^{9} - 17872 q^{15} + 1452 q^{17} + 1296 q^{23} - 39314 q^{25} + 89280 q^{31} + 53880 q^{33} + 328208 q^{39} + 521244 q^{41} - 1566432 q^{47} - 511050 q^{49} + 3270256 q^{55} - 1889896 q^{57} - 5776816 q^{63} + 1416480 q^{65} + 7597104 q^{71} + 2089564 q^{73} - 16015904 q^{79} - 723058 q^{81} + 37453776 q^{87} + 2169084 q^{89} - 48537936 q^{95} - 1088308 q^{97} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(32, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
32.8.b.a $6$ $9.996$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$688$$ $$q+\beta _{2}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(115+\beta _{1}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{8}^{\mathrm{old}}(32, [\chi])$$ into lower level spaces

$$S_{8}^{\mathrm{old}}(32, [\chi]) \cong$$ $$S_{8}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 3}$$