# Properties

 Label 496.1.e Level $496$ Weight $1$ Character orbit 496.e Rep. character $\chi_{496}(433,\cdot)$ Character field $\Q$ Dimension $1$ Newform subspaces $1$ Sturm bound $64$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$496 = 2^{4} \cdot 31$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 496.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$31$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$64$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(496, [\chi])$$.

Total New Old
Modular forms 12 2 10
Cusp forms 6 1 5
Eisenstein series 6 1 5

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 1 0 0 0

## Trace form

 $$q - q^{5} + q^{7} + q^{9} + O(q^{10})$$ $$q - q^{5} + q^{7} + q^{9} + q^{19} - q^{31} - q^{35} - q^{41} - q^{45} - 2 q^{47} + q^{59} + q^{63} - 2 q^{67} + q^{71} + q^{81} - q^{95} - q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(496, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
496.1.e.a $1$ $0.248$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-31})$$ None $$0$$ $$0$$ $$-1$$ $$1$$ $$q-q^{5}+q^{7}+q^{9}+q^{19}-q^{31}-q^{35}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(496, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(496, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(31, [\chi])$$$$^{\oplus 5}$$