Properties

Label 4.4.15317.1-4.2-a
Base field 4.4.15317.1
Weight $[2, 2, 2, 2]$
Level norm $4$
Level $[4, 2, -w^{2} + w + 1]$
Dimension $4$
CM no
Base change no

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Base field 4.4.15317.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[4, 2, -w^{2} + w + 1]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $9$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - x^{3} - 7x^{2} + 3x + 9\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
2 $[2, 2, -w + 1]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{1}{3}e^{2} - \frac{7}{3}e + 1$
4 $[4, 2, -w^{2} + w + 1]$ $-1$
19 $[19, 19, -w^{3} + 5w + 3]$ $-\frac{2}{3}e^{3} + \frac{8}{3}e^{2} + \frac{2}{3}e - 8$
19 $[19, 19, w^{3} - 3w^{2} - 2w + 7]$ $-\frac{2}{3}e^{3} - \frac{4}{3}e^{2} + \frac{14}{3}e + 6$
43 $[43, 43, -w^{3} + 3w^{2} + 2w - 5]$ $\phantom{-}2e^{3} - 2e^{2} - 10e + 6$
43 $[43, 43, -w^{3} + w^{2} + 2w - 1]$ $-e^{3} - e^{2} + 8e + 6$
43 $[43, 43, w^{3} - 2w^{2} - w + 1]$ $-\frac{1}{3}e^{3} + \frac{7}{3}e^{2} - \frac{8}{3}e - 6$
43 $[43, 43, -w^{3} + 5w + 1]$ $\phantom{-}\frac{4}{3}e^{3} - \frac{4}{3}e^{2} - \frac{10}{3}e + 4$
47 $[47, 47, -w^{3} + w^{2} + 2w + 1]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{7}{3}e^{2} - \frac{10}{3}e + 10$
47 $[47, 47, w^{3} - 5w - 5]$ $-\frac{1}{3}e^{3} + \frac{13}{3}e^{2} - \frac{2}{3}e - 11$
47 $[47, 47, -w^{3} + 3w^{2} + 2w - 9]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{13}{3}e^{2} + \frac{2}{3}e + 19$
47 $[47, 47, w^{3} - 2w^{2} - w + 3]$ $-e^{3} + 3e^{2} + 6e - 8$
49 $[49, 7, -w^{3} + w^{2} + 6w + 1]$ $-\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{2}{3}e - 2$
49 $[49, 7, -w^{3} + 2w^{2} + 5w - 7]$ $-e^{3} + e^{2} + 6e - 4$
53 $[53, 53, 2w - 1]$ $-2e^{3} + 2e^{2} + 8e + 2$
67 $[67, 67, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}\frac{7}{3}e^{3} - \frac{13}{3}e^{2} - \frac{28}{3}e + 7$
67 $[67, 67, -w^{3} + 2w^{2} + 3w - 1]$ $\phantom{-}\frac{5}{3}e^{3} + \frac{1}{3}e^{2} - \frac{20}{3}e - 9$
81 $[81, 3, -3]$ $-\frac{7}{3}e^{3} + \frac{7}{3}e^{2} + \frac{28}{3}e - 1$
83 $[83, 83, 2w^{3} - 4w^{2} - 6w + 9]$ $-\frac{1}{3}e^{3} + \frac{13}{3}e^{2} - \frac{14}{3}e - 13$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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