# Properties

 Label 32.3.d Level $32$ Weight $3$ Character orbit 32.d Rep. character $\chi_{32}(15,\cdot)$ Character field $\Q$ Dimension $1$ Newform subspaces $1$ Sturm bound $12$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$32 = 2^{5}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 32.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(32, [\chi])$$.

Total New Old
Modular forms 12 3 9
Cusp forms 4 1 3
Eisenstein series 8 2 6

## Trace form

 $$q + 2q^{3} - 5q^{9} + O(q^{10})$$ $$q + 2q^{3} - 5q^{9} - 14q^{11} + 2q^{17} + 34q^{19} + 25q^{25} - 28q^{27} - 28q^{33} - 46q^{41} - 14q^{43} + 49q^{49} + 4q^{51} + 68q^{57} + 82q^{59} - 62q^{67} - 142q^{73} + 50q^{75} - 11q^{81} - 158q^{83} + 146q^{89} - 94q^{97} + 70q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(32, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
32.3.d.a $$1$$ $$0.872$$ $$\Q$$ $$\Q(\sqrt{-2})$$ $$0$$ $$2$$ $$0$$ $$0$$ $$q+2q^{3}-5q^{9}-14q^{11}+2q^{17}+34q^{19}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(32, [\chi])$$ into lower level spaces

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