# Properties

 Label 175.1.d Level $175$ Weight $1$ Character orbit 175.d Rep. character $\chi_{175}(76,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $2$ Sturm bound $20$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$175 = 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 175.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$20$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(175, [\chi])$$.

Total New Old
Modular forms 8 5 3
Cusp forms 2 2 0
Eisenstein series 6 3 3

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2 q + 2 q^{9} + O(q^{10})$$ $$2 q + 2 q^{9} - 2 q^{11} - 2 q^{14} - 2 q^{16} - 2 q^{29} + 2 q^{46} + 2 q^{49} + 2 q^{56} + 2 q^{64} - 2 q^{71} + 2 q^{74} - 2 q^{79} + 2 q^{81} + 2 q^{86} - 2 q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(175, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.1.d.a $1$ $0.087$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-7})$$ None $$-1$$ $$0$$ $$0$$ $$1$$ $$q-q^{2}+q^{7}+q^{8}+q^{9}-q^{11}-q^{14}+\cdots$$
175.1.d.b $1$ $0.087$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-7})$$ None $$1$$ $$0$$ $$0$$ $$-1$$ $$q+q^{2}-q^{7}-q^{8}+q^{9}-q^{11}-q^{14}+\cdots$$