Properties

Label 3.3.1304.1-8.2-a
Base field 3.3.1304.1
Weight $[2, 2, 2]$
Level norm $8$
Level $[8, 4, -\frac{1}{2}w^{2} + \frac{1}{2}w + 5]$
Dimension $2$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 3.3.1304.1

Generator \(w\), with minimal polynomial \(x^{3} - 11x - 2\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[8, 4, -\frac{1}{2}w^{2} + \frac{1}{2}w + 5]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{2} + x - 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}0$
2 $[2, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w]$ $\phantom{-}1$
3 $[3, 3, -w^{2} + 3w + 1]$ $\phantom{-}e$
9 $[9, 3, w^{2} + w - 7]$ $\phantom{-}e - 3$
11 $[11, 11, 2w^{2} - 21]$ $-2e - 2$
17 $[17, 17, -\frac{1}{2}w^{2} + \frac{5}{2}w]$ $-6$
19 $[19, 19, -\frac{1}{2}w^{2} + \frac{1}{2}w + 2]$ $-3e - 2$
37 $[37, 37, w^{2} - w - 13]$ $\phantom{-}3e - 4$
37 $[37, 37, -\frac{1}{2}w^{2} + \frac{1}{2}w + 8]$ $-2$
37 $[37, 37, \frac{5}{2}w^{2} - \frac{17}{2}w - 2]$ $\phantom{-}5e + 3$
47 $[47, 47, -\frac{3}{2}w^{2} + \frac{11}{2}w]$ $-7e - 4$
53 $[53, 53, w^{2} - w - 7]$ $\phantom{-}e + 1$
59 $[59, 59, 2w - 1]$ $\phantom{-}2e - 4$
61 $[61, 61, -\frac{3}{2}w^{2} + \frac{3}{2}w + 20]$ $-2e + 8$
67 $[67, 67, w^{2} - 3w - 3]$ $-6e - 2$
71 $[71, 71, w^{2} - w - 1]$ $-e + 5$
73 $[73, 73, 3w^{2} - w - 33]$ $\phantom{-}2e - 8$
79 $[79, 79, w^{2} - w - 11]$ $\phantom{-}4e + 8$
79 $[79, 79, w^{2} - 3w + 1]$ $\phantom{-}3e + 7$
79 $[79, 79, -2w - 5]$ $-4e - 8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w]$ $-1$
$2$ $[2, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w]$ $-1$