Properties

Label 5.5.65657.1-15.1-b
Base field 5.5.65657.1
Weight $[2, 2, 2, 2, 2]$
Level norm $15$
Level $[15, 15, w^{4} - w^{3} - 5w^{2} + 2w + 3]$
Dimension $2$
CM no
Base change no

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Base field 5.5.65657.1

Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 2x^{2} + 5x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[15, 15, w^{4} - w^{3} - 5w^{2} + 2w + 3]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $3$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 4x - 24\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ $-1$
5 $[5, 5, w^{2} - w - 2]$ $\phantom{-}1$
19 $[19, 19, w^{4} - 2w^{3} - 4w^{2} + 5w + 4]$ $\phantom{-}e$
23 $[23, 23, -w^{3} + w^{2} + 3w - 1]$ $-e + 4$
29 $[29, 29, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 4]$ $\phantom{-}6$
32 $[32, 2, 2]$ $-e + 1$
37 $[37, 37, w^{3} - 2w^{2} - 2w + 2]$ $-2$
41 $[41, 41, -2w^{4} + 3w^{3} + 9w^{2} - 8w - 6]$ $-e - 2$
43 $[43, 43, -2w^{4} + 3w^{3} + 8w^{2} - 8w - 6]$ $\phantom{-}e$
47 $[47, 47, w^{4} - 2w^{3} - 5w^{2} + 6w + 5]$ $\phantom{-}0$
53 $[53, 53, -w^{4} + w^{3} + 4w^{2} - w - 4]$ $\phantom{-}2e - 2$
61 $[61, 61, w^{2} - 2w - 3]$ $-e + 2$
67 $[67, 67, w^{4} - w^{3} - 4w^{2} + 3w]$ $\phantom{-}2e - 4$
67 $[67, 67, -w^{4} + w^{3} + 5w^{2} - 2w - 2]$ $\phantom{-}2e - 4$
71 $[71, 71, w^{4} - w^{3} - 4w^{2} + 5]$ $-2e + 8$
71 $[71, 71, w^{4} - 2w^{3} - 3w^{2} + 5w + 3]$ $-e + 4$
71 $[71, 71, 2w^{4} - 2w^{3} - 8w^{2} + 5w + 4]$ $-e + 4$
73 $[73, 73, -2w^{4} + 2w^{3} + 9w^{2} - 5w - 6]$ $\phantom{-}2$
81 $[81, 3, -2w^{4} + 3w^{3} + 10w^{2} - 9w - 10]$ $\phantom{-}2$
97 $[97, 97, -2w^{4} + 3w^{3} + 7w^{2} - 5w - 4]$ $\phantom{-}2e + 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ $1$
$5$ $[5, 5, w^{2} - w - 2]$ $-1$