# Properties

 Label 1859.1.c Level $1859$ Weight $1$ Character orbit 1859.c Rep. character $\chi_{1859}(846,\cdot)$ Character field $\Q$ Dimension $10$ Newform subspaces $3$ Sturm bound $182$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1859 = 11 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1859.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$182$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1859, [\chi])$$.

Total New Old
Modular forms 24 21 3
Cusp forms 10 10 0
Eisenstein series 14 11 3

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 10 0 0 0

## Trace form

 $$10 q - 4 q^{3} + 4 q^{4} + 6 q^{9} + O(q^{10})$$ $$10 q - 4 q^{3} + 4 q^{4} + 6 q^{9} + 4 q^{12} - 4 q^{14} + 6 q^{16} - 2 q^{22} - 8 q^{27} - 2 q^{36} - 6 q^{38} + 2 q^{42} - 2 q^{48} + 4 q^{49} - 4 q^{53} - 2 q^{55} - 2 q^{56} + 8 q^{64} + 6 q^{66} - 4 q^{75} + 2 q^{77} + 2 q^{81} + 4 q^{82} + 4 q^{88} + 2 q^{92} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1859, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1859.1.c.a $3$ $0.928$ $$\Q(\zeta_{14})^+$$ $D_{7}$ $$\Q(\sqrt{-11})$$ None $$0$$ $$-1$$ $$-1$$ $$0$$ $$q+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots$$
1859.1.c.b $3$ $0.928$ $$\Q(\zeta_{14})^+$$ $D_{7}$ $$\Q(\sqrt{-11})$$ None $$0$$ $$-1$$ $$1$$ $$0$$ $$q+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}+\beta _{1}q^{5}+\cdots$$
1859.1.c.c $4$ $0.928$ $$\Q(i, \sqrt{5})$$ $D_{5}$ $$\Q(\sqrt{-143})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(\beta _{1}-\beta _{3})q^{6}+\cdots$$