# Properties

 Label 16.3.c Level $16$ Weight $3$ Character orbit 16.c Rep. character $\chi_{16}(15,\cdot)$ Character field $\Q$ Dimension $1$ Newform subspaces $1$ Sturm bound $6$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$16 = 2^{4}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 16.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$6$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(16, [\chi])$$.

Total New Old
Modular forms 7 1 6
Cusp forms 1 1 0
Eisenstein series 6 0 6

## Trace form

 $$q - 6q^{5} + 9q^{9} + O(q^{10})$$ $$q - 6q^{5} + 9q^{9} + 10q^{13} - 30q^{17} + 11q^{25} + 42q^{29} - 70q^{37} + 18q^{41} - 54q^{45} + 49q^{49} + 90q^{53} - 22q^{61} - 60q^{65} - 110q^{73} + 81q^{81} + 180q^{85} - 78q^{89} + 130q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(16, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
16.3.c.a $$1$$ $$0.436$$ $$\Q$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$-6$$ $$0$$ $$q-6q^{5}+9q^{9}+10q^{13}-30q^{17}+\cdots$$