Properties

Label 5.5.89417.1-15.1-c
Base field 5.5.89417.1
Weight $[2, 2, 2, 2, 2]$
Level norm $15$
Level $[15, 15, w^{3} + w^{2} - 4w - 3]$
Dimension $2$
CM no
Base change no

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Base field 5.5.89417.1

Generator \(w\), with minimal polynomial \(x^{5} - 6x^{3} - x^{2} + 8x + 3\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[15, 15, w^{3} + w^{2} - 4w - 3]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 4x - 76\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w^{2} - 3]$ $-1$
5 $[5, 5, w^{4} - 5w^{2} + 4]$ $\phantom{-}1$
11 $[11, 11, -w^{4} + w^{3} + 5w^{2} - 3w - 4]$ $\phantom{-}4$
17 $[17, 17, w^{4} - 4w^{2} + 2]$ $\phantom{-}2$
32 $[32, 2, 2]$ $\phantom{-}1$
37 $[37, 37, -w^{4} + 2w^{3} + 5w^{2} - 7w - 5]$ $\phantom{-}e$
37 $[37, 37, -w^{3} + 4w - 1]$ $-e + 4$
41 $[41, 41, w^{3} + w^{2} - 4w - 1]$ $\phantom{-}2$
41 $[41, 41, -w^{3} + 2w + 2]$ $-e$
43 $[43, 43, w^{2} - w - 4]$ $-4$
49 $[49, 7, w^{4} - 5w^{2} + 2]$ $\phantom{-}e - 4$
53 $[53, 53, w^{4} - w^{3} - 5w^{2} + 2w + 5]$ $\phantom{-}6$
59 $[59, 59, w^{4} - w^{3} - 4w^{2} + 3w - 1]$ $-e + 2$
67 $[67, 67, -w^{4} + 3w^{2} + 2w + 2]$ $\phantom{-}e - 2$
79 $[79, 79, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}e - 6$
81 $[81, 3, -w^{4} + 6w^{2} + w - 8]$ $\phantom{-}2$
83 $[83, 83, w^{4} + w^{3} - 5w^{2} - 4w + 1]$ $\phantom{-}e + 6$
89 $[89, 89, -w^{4} + 5w^{2} + w - 1]$ $-e$
97 $[97, 97, -w^{4} + 2w^{3} + 5w^{2} - 5w - 5]$ $\phantom{-}e + 4$
101 $[101, 101, 2w^{2} - w - 2]$ $-e + 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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