# Properties

 Label 95.1.d Level $95$ Weight $1$ Character orbit 95.d Rep. character $\chi_{95}(94,\cdot)$ Character field $\Q$ Dimension $3$ Newform subspaces $2$ Sturm bound $10$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$95 = 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 95.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$10$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(95, [\chi])$$.

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 3 0 0 0

## Trace form

 $$3 q + q^{4} - q^{5} - 4 q^{6} + q^{9} + O(q^{10})$$ $$3 q + q^{4} - q^{5} - 4 q^{6} + q^{9} - 2 q^{11} - q^{16} - q^{19} - 3 q^{20} + 3 q^{25} + 4 q^{26} + 4 q^{30} + 3 q^{36} - 4 q^{39} + 2 q^{44} - 3 q^{45} + 3 q^{49} - 2 q^{55} - 2 q^{61} - 3 q^{64} - 4 q^{74} - 3 q^{76} + 3 q^{80} - q^{81} + 3 q^{95} + 4 q^{96} + 2 q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(95, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
95.1.d.a $1$ $0.047$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-19})$$, $$\Q(\sqrt{-95})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$1$$ $$0$$ $$q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\cdots$$
95.1.d.b $2$ $0.047$ $$\Q(\sqrt{2})$$ $D_{4}$ $$\Q(\sqrt{-95})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots$$