Properties

Label 5.5.157457.1-21.1-k
Base field 5.5.157457.1
Weight $[2, 2, 2, 2, 2]$
Level norm $21$
Level $[21, 21, w^{4} - 3w^{3} - w^{2} + 6w - 3]$
Dimension $4$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 5.5.157457.1

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

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[21, 21, w^{4} - 3w^{3} - w^{2} + 6w - 3]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $15$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 2x^{3} - 13x^{2} + 18x + 32\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w - 1]$ $-1$
5 $[5, 5, w^{2} - w - 2]$ $\phantom{-}e$
7 $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ $\phantom{-}1$
13 $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e - 2$
29 $[29, 29, -w^{4} + 3w^{3} + 2w^{2} - 7w - 1]$ $-\frac{1}{2}e^{3} + \frac{9}{2}e + 2$
29 $[29, 29, -w^{2} + 2w + 3]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - \frac{13}{2}e - 8$
31 $[31, 31, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $-e^{2} + 2$
31 $[31, 31, w^{3} - 2w^{2} - 3w + 2]$ $-\frac{1}{2}e^{3} + \frac{13}{2}e$
32 $[32, 2, 2]$ $\phantom{-}e^{2} - e - 9$
43 $[43, 43, -w^{2} - w + 4]$ $-\frac{1}{2}e^{3} + \frac{9}{2}e + 6$
53 $[53, 53, -w^{4} + w^{3} + 6w^{2} - 2w - 5]$ $\phantom{-}e^{3} + 2e^{2} - 10e - 18$
53 $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e + 4$
73 $[73, 73, w^{4} - w^{3} - 6w^{2} + 2w + 6]$ $-\frac{1}{2}e^{3} + e^{2} + \frac{9}{2}e - 6$
73 $[73, 73, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}2e^{2} - 14$
81 $[81, 3, 2w^{4} - 5w^{3} - 4w^{2} + 9w + 2]$ $-2$
83 $[83, 83, w^{3} - w^{2} - 5w]$ $\phantom{-}\frac{1}{2}e^{3} + 2e^{2} - \frac{9}{2}e - 16$
89 $[89, 89, -w^{4} + 2w^{3} + 4w^{2} - 4w - 2]$ $-e^{3} + 9e + 2$
97 $[97, 97, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ $-2e^{2} + 12$
101 $[101, 101, -w^{4} + 3w^{3} + 3w^{2} - 7w - 3]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e - 2$
103 $[103, 103, -w^{4} + w^{3} + 6w^{2} - w - 7]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{17}{2}e + 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w - 1]$ $1$
$7$ $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ $-1$