Properties

Base field 3.3.1101.1
Weight [2, 2, 2]
Level norm 9
Level $[9, 3, w^{2} + 2w - 3]$
Label 3.3.1101.1-9.2-e
Dimension 3
CM no
Base change no

Related objects

Downloads

Learn more about

Base field 3.3.1101.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 12\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2]
Level $[9, 3, w^{2} + 2w - 3]$
Label 3.3.1101.1-9.2-e
Dimension 3
Is CM no
Is base change no
Parent newspace dimension 7

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} \) \(\mathstrut -\mathstrut 7x \) \(\mathstrut -\mathstrut 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 2]$ $\phantom{-}e$
3 $[3, 3, -w + 3]$ $\phantom{-}1$
3 $[3, 3, w - 1]$ $-1$
4 $[4, 2, w^{2} + w - 7]$ $-e$
19 $[19, 19, w + 1]$ $\phantom{-}e^{2} - 2e - 3$
23 $[23, 23, w^{2} - 2w - 1]$ $\phantom{-}2e - 2$
31 $[31, 31, -2w^{2} + 19]$ $\phantom{-}e^{2} - 1$
31 $[31, 31, -w^{2} + 5]$ $-e^{2} + 2e + 7$
31 $[31, 31, -3w + 5]$ $-e^{2} - 2e + 3$
41 $[41, 41, w^{2} + 2w - 7]$ $\phantom{-}6$
43 $[43, 43, w^{2} - 11]$ $-e^{2} + 5$
47 $[47, 47, 3w - 7]$ $\phantom{-}8$
53 $[53, 53, -3w^{2} - 6w + 11]$ $-2e - 8$
59 $[59, 59, 2w - 1]$ $\phantom{-}2e^{2} - 4e - 10$
67 $[67, 67, 2w^{2} + w - 19]$ $\phantom{-}e^{2} + 2e - 15$
67 $[67, 67, 3w^{2} + 2w - 25]$ $-4e^{2} + 16$
67 $[67, 67, w - 5]$ $-e^{2} - 2e + 7$
73 $[73, 73, -4w^{2} - 3w + 29]$ $\phantom{-}3e^{2} - 2e - 7$
73 $[73, 73, 2w^{2} - w - 11]$ $-4e + 2$
73 $[73, 73, w^{2} + 2w - 11]$ $-3e^{2} + 4e + 13$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 3]$ $-1$
3 $[3, 3, w - 1]$ $1$