Properties

Label 3.3.985.1-5.1-a
Base field 3.3.985.1
Weight $[2, 2, 2]$
Level norm $5$
Level $[5, 5, w + 1]$
Dimension $2$
CM no
Base change no

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Base field 3.3.985.1

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

Form

Weight: $[2, 2, 2]$
Level: $[5, 5, w + 1]$
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:

\(x^{2} - 4x + 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $\phantom{-}1$
5 $[5, 5, w - 1]$ $\phantom{-}e$
7 $[7, 7, -w + 2]$ $-e$
8 $[8, 2, 2]$ $\phantom{-}2e - 3$
11 $[11, 11, -w^{2} + 2w + 2]$ $-e + 4$
17 $[17, 17, -w - 3]$ $\phantom{-}4$
17 $[17, 17, -w^{2} + 2w + 1]$ $\phantom{-}2e - 8$
17 $[17, 17, -w^{2} + w + 4]$ $-3e + 8$
23 $[23, 23, -w^{2} + 3]$ $-2e + 8$
27 $[27, 3, -3]$ $-4e + 10$
29 $[29, 29, w^{2} - w - 8]$ $\phantom{-}2$
29 $[29, 29, w^{2} - w - 3]$ $\phantom{-}e - 4$
29 $[29, 29, w^{2} - w - 1]$ $-2e$
31 $[31, 31, w^{2} - 2]$ $\phantom{-}5e - 12$
37 $[37, 37, 2w - 5]$ $\phantom{-}3e - 8$
43 $[43, 43, w^{2} - 2w - 5]$ $-4e + 12$
47 $[47, 47, w^{2} - 3w - 2]$ $\phantom{-}4e - 4$
49 $[49, 7, w^{2} + w - 4]$ $-3e + 12$
53 $[53, 53, w^{2} - 2w - 6]$ $-8e + 18$
71 $[71, 71, w - 5]$ $-4e - 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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