# Properties

 Label 145.1.f Level $145$ Weight $1$ Character orbit 145.f Rep. character $\chi_{145}(99,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $2$ Newform subspaces $1$ Sturm bound $15$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$145 = 5 \cdot 29$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 145.f (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$145$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$15$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(145, [\chi])$$.

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

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

 $$2q + O(q^{10})$$ $$2q - 2q^{11} - 2q^{16} - 2q^{19} + 2q^{20} - 2q^{25} + 2q^{31} - 2q^{36} + 2q^{41} + 2q^{44} + 2q^{45} + 2q^{49} - 2q^{55} + 2q^{61} + 2q^{76} - 2q^{79} - 2q^{81} - 2q^{89} - 2q^{95} + 2q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(145, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
145.1.f.a $$2$$ $$0.072$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ None $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{4}-iq^{5}+iq^{9}+(-1-i)q^{11}+\cdots$$