# 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 Newform subspaces 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: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ 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

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

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

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 $$0$$ $$0$$ $$0$$ $$2$$ $$q+\beta _{7}q^{2}+(-\beta _{3}-\beta _{6}-\beta _{7})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$( 1 - T )^{2}( 1 + T )^{2}$$)($$( 1 + T^{4} )^{2}$$)($$( 1 - T^{2} + T^{4} )^{4}$$)
$3$ ()()()
$5$ ($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$1 - T^{4} + T^{8}$$)($$1 + T^{2} - T^{6} - T^{8} - T^{10} + T^{14} + T^{16}$$)
$7$ ($$( 1 + T + T^{2} )^{2}$$)($$( 1 - T^{2} + T^{4} )^{2}$$)($$( 1 - T + T^{3} - T^{4} + T^{5} - T^{7} + T^{8} )^{2}$$)
$11$ ($$( 1 - T )^{2}( 1 + T )^{2}$$)($$( 1 - T )^{4}( 1 + T )^{4}$$)($$( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2}$$)
$13$ ($$( 1 - T )^{2}( 1 + T + T^{2} )$$)($$( 1 + T )^{4}( 1 - T + T^{2} )^{2}$$)($$( 1 - T + T^{3} - T^{4} + T^{5} - T^{7} + T^{8} )^{2}$$)
$17$ ($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2}$$)($$1 + T^{2} - T^{6} - T^{8} - T^{10} + T^{14} + T^{16}$$)
$19$ ($$( 1 - T )^{2}( 1 + T + T^{2} )$$)($$( 1 + T )^{4}( 1 - T + T^{2} )^{2}$$)($$( 1 - T + T^{3} - T^{4} + T^{5} - T^{7} + T^{8} )^{2}$$)
$23$ ($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$1 - T^{4} + T^{8}$$)($$1 + T^{2} - T^{6} - T^{8} - T^{10} + T^{14} + T^{16}$$)
$29$ ($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2}$$)($$( 1 - T + T^{2} )^{4}( 1 + T + T^{2} )^{4}$$)
$31$ ($$( 1 - T )^{2}( 1 + T + T^{2} )$$)($$( 1 - T )^{4}( 1 + T + T^{2} )^{2}$$)($$( 1 - T^{2} + T^{4} )^{4}$$)
$37$ ($$( 1 + T + T^{2} )^{2}$$)($$( 1 - T^{2} + T^{4} )^{2}$$)($$( 1 - T^{2} + T^{4} )^{4}$$)
$41$ ($$( 1 - T )^{2}( 1 + T )^{2}$$)($$( 1 + T^{4} )^{2}$$)($$( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2}$$)
$43$ ($$( 1 - T )^{2}$$)($$( 1 + T )^{4}$$)($$( 1 + T + T^{2} )^{4}$$)
$47$ ($$( 1 - T )^{2}( 1 + T )^{2}$$)($$( 1 + T^{4} )^{2}$$)($$( 1 - T )^{8}( 1 + T )^{8}$$)
$53$ ($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$1 - T^{4} + T^{8}$$)($$1 + T^{2} - T^{6} - T^{8} - T^{10} + T^{14} + T^{16}$$)
$59$ ($$( 1 - T )^{2}( 1 + T )^{2}$$)($$( 1 - T )^{4}( 1 + T )^{4}$$)($$( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2}$$)
$61$ ($$( 1 - T )^{2}( 1 + T + T^{2} )$$)($$( 1 - T )^{4}( 1 + T + T^{2} )^{2}$$)($$( 1 + T )^{8}( 1 - T + T^{2} )^{4}$$)
$67$ ($$( 1 + T + T^{2} )^{2}$$)($$( 1 - T^{2} + T^{4} )^{2}$$)($$( 1 + T )^{8}( 1 - T + T^{2} )^{4}$$)
$71$ ($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$1 - T^{4} + T^{8}$$)($$( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} )^{2}$$)
$73$ ($$( 1 + T + T^{2} )^{2}$$)($$( 1 + T + T^{2} )^{4}$$)($$( 1 - T^{2} + T^{4} )^{4}$$)
$79$ ($$( 1 - T )^{2}( 1 + T + T^{2} )$$)($$( 1 + T )^{4}( 1 - T + T^{2} )^{2}$$)($$( 1 + T - T^{3} - T^{4} - T^{5} + T^{7} + T^{8} )^{2}$$)
$83$ ($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2}$$)($$( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} )^{2}$$)
$89$ ($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$1 - T^{4} + T^{8}$$)($$( 1 - T + T^{2} )^{4}( 1 + T + T^{2} )^{4}$$)
$97$ ($$( 1 + T + T^{2} )^{2}$$)($$( 1 - T + T^{2} )^{4}$$)($$( 1 - T + T^{2} - T^{3} + T^{4} )^{4}$$)