Properties

Label 4.4.19821.1-21.1-c
Base field 4.4.19821.1
Weight $[2, 2, 2, 2]$
Level norm $21$
Level $[21, 21, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 5w - 1]$
Dimension $3$
CM no
Base change no

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Base field 4.4.19821.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} + 6x + 3\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[21, 21, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 5w - 1]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $37$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - 2x^{2} - 12x + 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-1$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 2w + 2]$ $\phantom{-}1$
9 $[9, 3, w + 1]$ $\phantom{-}e$
13 $[13, 13, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 5w]$ $-\frac{1}{4}e^{2} + e - 1$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{4}e^{2} - \frac{3}{2}e - 1$
17 $[17, 17, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 3w + 5]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 1$
19 $[19, 19, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w - 5]$ $\phantom{-}\frac{1}{2}e^{2} - 2e - 4$
23 $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 2]$ $-\frac{1}{4}e^{2} + \frac{1}{2}e$
25 $[25, 5, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w]$ $\phantom{-}\frac{1}{4}e^{2} + \frac{1}{2}e - 6$
25 $[25, 5, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 3]$ $\phantom{-}e^{2} - e - 8$
29 $[29, 29, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 4w - 3]$ $\phantom{-}\frac{3}{4}e^{2} - e - 5$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w]$ $-e^{2} + 10$
37 $[37, 37, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $-e^{2} + 8$
41 $[41, 41, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 4]$ $-\frac{1}{4}e^{2} + \frac{1}{2}e + 8$
43 $[43, 43, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w]$ $-\frac{1}{2}e^{2} + 2e - 2$
47 $[47, 47, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w]$ $-\frac{5}{4}e^{2} + \frac{3}{2}e + 8$
59 $[59, 59, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 4]$ $\phantom{-}\frac{1}{4}e^{2} - 2e - 3$
59 $[59, 59, \frac{4}{3}w^{3} - \frac{5}{3}w^{2} - 10w + 9]$ $\phantom{-}e - 10$
67 $[67, 67, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w]$ $-\frac{3}{2}e^{2} + e + 12$
71 $[71, 71, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $-e^{2} + \frac{5}{2}e + 5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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