Properties

 Label 1375.1.ch Level $1375$ Weight $1$ Character orbit 1375.ch Rep. character $\chi_{1375}(21,\cdot)$ Character field $\Q(\zeta_{50})$ Dimension $20$ Newform subspaces $1$ Sturm bound $150$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1375 = 5^{3} \cdot 11$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1375.ch (of order $$50$$ and degree $$20$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1375$$ Character field: $$\Q(\zeta_{50})$$ Newform subspaces: $$1$$ Sturm bound: $$150$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1375, [\chi])$$.

Total New Old
Modular forms 60 60 0
Cusp forms 20 20 0
Eisenstein series 40 40 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 20 0 0 0

Trace form

 $$20q - 5q^{5} + O(q^{10})$$ $$20q - 5q^{5} + 20q^{12} - 5q^{25} - 5q^{27} - 5q^{48} - 5q^{49} - 5q^{59} - 5q^{60} - 5q^{67} - 5q^{69} - 5q^{81} - 5q^{92} - 10q^{93} - 5q^{99} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(1375, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1375.1.ch.a $$20$$ $$0.686$$ $$\Q(\zeta_{50})$$ $$D_{25}$$ $$\Q(\sqrt{-11})$$ None $$0$$ $$0$$ $$-5$$ $$0$$ $$q+(\zeta_{50}^{4}+\zeta_{50}^{18})q^{3}-\zeta_{50}^{21}q^{4}+\cdots$$