Properties

 Label 145.1.h Level $145$ Weight $1$ Character orbit 145.h Rep. character $\chi_{145}(28,\cdot)$ 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.h (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

 $$2 q - 2 q^{7} + O(q^{10})$$ $$2 q - 2 q^{7} + 2 q^{13} - 2 q^{16} - 2 q^{20} - 2 q^{23} - 2 q^{25} + 2 q^{28} + 2 q^{35} + 2 q^{36} + 2 q^{45} + 2 q^{52} - 2 q^{53} - 2 q^{63} + 2 q^{65} + 2 q^{67} - 2 q^{81} + 2 q^{83} - 4 q^{91} - 2 q^{92} + O(q^{100})$$

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.h.a $2$ $0.072$ $$\Q(\sqrt{-1})$$ $D_{4}$ None $$\Q(\sqrt{29})$$ $$0$$ $$0$$ $$0$$ $$-2$$ $$q-iq^{4}-iq^{5}+(-1+i)q^{7}+iq^{9}+\cdots$$