# Properties

 Label 1161.1.i Level 1161 Weight 1 Character orbit i Rep. character $$\chi_{1161}(350,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 14 Newforms 3 Sturm bound 132 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$1161 = 3^{3} \cdot 43$$ Weight: $$k$$ = $$1$$ Character orbit: $$[\chi]$$ = 1161.i (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$129$$ Character field: $$\Q(\zeta_{6})$$ Newforms: $$3$$ Sturm bound: $$132$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1161, [\chi])$$.

Total New Old
Modular forms 26 14 12
Cusp forms 14 14 0
Eisenstein series 12 0 12

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 4 8

## Trace form

 $$14q$$ $$\mathstrut -\mathstrut 2q^{4}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$14q$$ $$\mathstrut -\mathstrut 2q^{4}$$ $$\mathstrut -\mathstrut 2q^{10}$$ $$\mathstrut +\mathstrut q^{13}$$ $$\mathstrut -\mathstrut 10q^{16}$$ $$\mathstrut +\mathstrut q^{19}$$ $$\mathstrut -\mathstrut 4q^{22}$$ $$\mathstrut +\mathstrut 3q^{25}$$ $$\mathstrut -\mathstrut 2q^{28}$$ $$\mathstrut +\mathstrut 3q^{31}$$ $$\mathstrut +\mathstrut 2q^{34}$$ $$\mathstrut -\mathstrut 2q^{37}$$ $$\mathstrut +\mathstrut 2q^{40}$$ $$\mathstrut -\mathstrut 6q^{43}$$ $$\mathstrut -\mathstrut 2q^{46}$$ $$\mathstrut -\mathstrut 3q^{49}$$ $$\mathstrut +\mathstrut 3q^{52}$$ $$\mathstrut +\mathstrut 6q^{55}$$ $$\mathstrut -\mathstrut q^{61}$$ $$\mathstrut -\mathstrut 2q^{64}$$ $$\mathstrut -\mathstrut 6q^{67}$$ $$\mathstrut -\mathstrut 8q^{70}$$ $$\mathstrut -\mathstrut 6q^{73}$$ $$\mathstrut +\mathstrut 3q^{76}$$ $$\mathstrut -\mathstrut 3q^{79}$$ $$\mathstrut +\mathstrut 12q^{82}$$ $$\mathstrut -\mathstrut 12q^{85}$$ $$\mathstrut -\mathstrut 4q^{88}$$ $$\mathstrut +\mathstrut 6q^{91}$$ $$\mathstrut -\mathstrut 8q^{94}$$ $$\mathstrut +\mathstrut 6q^{97}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1161, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1161.1.i.a $$2$$ $$0.579$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+q^{4}-\zeta_{6}q^{7}+\zeta_{6}q^{13}+q^{16}-\zeta_{6}^{2}q^{19}+\cdots$$
1161.1.i.b $$4$$ $$0.579$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ $$S_{4}$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}-q^{4}-\beta _{1}q^{5}+(-2+2\beta _{2}+\cdots)q^{10}+\cdots$$
1161.1.i.c $$8$$ $$0.579$$ 8.0.12960000.1 $$A_{5}$$ None None $$0$$ $$0$$ $$0$$ $$2$$ $$q+\beta _{7}q^{2}+(-\beta _{3}-\beta _{6}-\beta _{7})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$$