Properties

Label 3.3.785.1-5.2-a
Base field 3.3.785.1
Weight $[2, 2, 2]$
Level norm $5$
Level $[5, 5, -w + 3]$
Dimension $2$
CM no
Base change no

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Base field 3.3.785.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 5\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[5, 5, -w + 3]$
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:

\(x^{2} - 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w - 2]$ $\phantom{-}e$
5 $[5, 5, w]$ $-\frac{1}{2}e + \frac{5}{2}$
5 $[5, 5, -w + 3]$ $\phantom{-}1$
8 $[8, 2, 2]$ $\phantom{-}\frac{1}{2}e + \frac{3}{2}$
9 $[9, 3, w^{2} + w - 4]$ $-1$
13 $[13, 13, w + 3]$ $-\frac{3}{2}e + \frac{7}{2}$
17 $[17, 17, -w^{2} + w + 3]$ $\phantom{-}\frac{3}{2}e - \frac{9}{2}$
23 $[23, 23, w^{2} - 2]$ $-2e - 1$
23 $[23, 23, w^{2} - 3]$ $-2e - 1$
23 $[23, 23, -w^{2} + 8]$ $\phantom{-}e - 2$
29 $[29, 29, w - 4]$ $\phantom{-}\frac{1}{2}e + \frac{1}{2}$
37 $[37, 37, w^{2} + w - 8]$ $-2e + 2$
41 $[41, 41, w^{2} + 2w - 4]$ $\phantom{-}e - 6$
47 $[47, 47, 2w^{2} + w - 8]$ $\phantom{-}4e - 1$
59 $[59, 59, -2w^{2} - 3w + 6]$ $-3e + 6$
61 $[61, 61, -2w - 1]$ $-\frac{3}{2}e + \frac{15}{2}$
67 $[67, 67, -2w - 3]$ $\phantom{-}\frac{1}{2}e + \frac{11}{2}$
79 $[79, 79, 2w^{2} - 9]$ $-\frac{3}{2}e + \frac{7}{2}$
109 $[109, 109, w^{2} + 2w - 6]$ $\phantom{-}\frac{9}{2}e - \frac{3}{2}$
109 $[109, 109, 2w^{2} + w - 14]$ $-\frac{5}{2}e - \frac{13}{2}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -w + 3]$ $-1$