Properties

 Label 400.1.x Level $400$ Weight $1$ Character orbit 400.x Rep. character $\chi_{400}(79,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $4$ Newform subspaces $1$ Sturm bound $60$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$400 = 2^{4} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 400.x (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$100$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$1$$ Sturm bound: $$60$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(400, [\chi])$$.

Total New Old
Modular forms 28 4 24
Cusp forms 4 4 0
Eisenstein series 24 0 24

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

Trace form

 $$4 q + q^{5} + q^{9} + O(q^{10})$$ $$4 q + q^{5} + q^{9} - q^{25} - 2 q^{29} - 5 q^{37} + 2 q^{41} - q^{45} - 4 q^{49} - 5 q^{53} + 2 q^{61} - 5 q^{65} - q^{81} + 5 q^{85} + 3 q^{89} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(400, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
400.1.x.a $4$ $0.200$ $$\Q(\zeta_{10})$$ $D_{10}$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$1$$ $$0$$ $$q+\zeta_{10}^{3}q^{5}-\zeta_{10}^{4}q^{9}+(\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{13}+\cdots$$