Properties

Label 4.4.16357.1-25.2-l
Base field 4.4.16357.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 5, w^{2} + w - 2]$
Dimension $6$
CM no
Base change no

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Base field 4.4.16357.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[25, 5, w^{2} + w - 2]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $38$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 12x^{4} + 33x^{2} - 3x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
5 $[5, 5, -w^{3} + 5w + 2]$ $\phantom{-}1$
5 $[5, 5, w - 1]$ $-1$
11 $[11, 11, -w^{3} + 5w]$ $\phantom{-}\frac{1}{3}e^{5} + \frac{1}{3}e^{4} - \frac{14}{3}e^{3} - \frac{8}{3}e^{2} + \frac{43}{3}e - \frac{2}{3}$
13 $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $-e^{2} + 2$
16 $[16, 2, 2]$ $-\frac{1}{3}e^{5} - \frac{1}{3}e^{4} + \frac{11}{3}e^{3} + \frac{8}{3}e^{2} - \frac{28}{3}e + \frac{2}{3}$
19 $[19, 19, 2w^{3} - w^{2} - 11w + 2]$ $\phantom{-}\frac{1}{3}e^{5} + \frac{1}{3}e^{4} - \frac{11}{3}e^{3} - \frac{8}{3}e^{2} + \frac{28}{3}e - \frac{2}{3}$
25 $[25, 5, -w^{2} + w + 3]$ $\phantom{-}\frac{1}{3}e^{5} + \frac{1}{3}e^{4} - \frac{14}{3}e^{3} - \frac{5}{3}e^{2} + \frac{43}{3}e - \frac{11}{3}$
27 $[27, 3, w^{3} - w^{2} - 5w + 4]$ $\phantom{-}e^{2} + e - 4$
31 $[31, 31, -w - 3]$ $-\frac{4}{3}e^{5} - \frac{1}{3}e^{4} + \frac{44}{3}e^{3} + \frac{8}{3}e^{2} - \frac{103}{3}e + \frac{2}{3}$
37 $[37, 37, -w^{3} - w^{2} + 6w + 4]$ $-\frac{2}{3}e^{5} + \frac{1}{3}e^{4} + \frac{25}{3}e^{3} - \frac{11}{3}e^{2} - \frac{74}{3}e + \frac{13}{3}$
41 $[41, 41, w^{3} + w^{2} - 6w - 5]$ $\phantom{-}\frac{1}{3}e^{5} + \frac{1}{3}e^{4} - \frac{14}{3}e^{3} - \frac{8}{3}e^{2} + \frac{43}{3}e + \frac{7}{3}$
43 $[43, 43, w^{3} - 7w - 2]$ $-\frac{4}{3}e^{5} - \frac{1}{3}e^{4} + \frac{53}{3}e^{3} + \frac{8}{3}e^{2} - \frac{160}{3}e + \frac{8}{3}$
47 $[47, 47, -2w^{3} + 11w + 2]$ $\phantom{-}e^{5} - e^{4} - 11e^{3} + 7e^{2} + 28e - 6$
61 $[61, 61, w^{2} - 3]$ $\phantom{-}\frac{5}{3}e^{5} - \frac{1}{3}e^{4} - \frac{55}{3}e^{3} + \frac{2}{3}e^{2} + \frac{125}{3}e + \frac{8}{3}$
67 $[67, 67, w^{2} + w - 4]$ $-\frac{1}{3}e^{5} + \frac{2}{3}e^{4} + \frac{14}{3}e^{3} - \frac{10}{3}e^{2} - \frac{49}{3}e - \frac{19}{3}$
79 $[79, 79, -4w^{3} + 2w^{2} + 22w - 9]$ $-\frac{1}{3}e^{5} - \frac{1}{3}e^{4} + \frac{11}{3}e^{3} + \frac{5}{3}e^{2} - \frac{25}{3}e - \frac{4}{3}$
97 $[97, 97, -3w^{3} + 2w^{2} + 19w - 6]$ $-2e^{5} + 26e^{3} - 80e + 3$
97 $[97, 97, -w^{3} + 6w - 3]$ $\phantom{-}\frac{2}{3}e^{5} - \frac{1}{3}e^{4} - \frac{22}{3}e^{3} + \frac{8}{3}e^{2} + \frac{65}{3}e - \frac{16}{3}$
97 $[97, 97, -3w^{3} + 16w]$ $\phantom{-}e^{5} + e^{4} - 11e^{3} - 8e^{2} + 28e - 1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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