Properties

Label 4.4.11197.1-11.2-c
Base field 4.4.11197.1
Weight $[2, 2, 2, 2]$
Level norm $11$
Level $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$
Dimension $4$
CM no
Base change no

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Base field 4.4.11197.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 9x^{3} + 22x^{2} + 6x - 9\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $-\frac{1}{3}e^{3} - 2e^{2} - \frac{7}{3}e - 1$
7 $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ $\phantom{-}e$
11 $[11, 11, -w - 2]$ $-\frac{1}{3}e^{3} - e^{2} + \frac{5}{3}e + 1$
11 $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}1$
13 $[13, 13, -w^{2} + 2w + 2]$ $\phantom{-}\frac{2}{3}e^{3} + 4e^{2} + \frac{8}{3}e - 7$
16 $[16, 2, 2]$ $\phantom{-}e^{3} + 4e^{2} - 2e - 2$
19 $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ $-\frac{2}{3}e^{3} - 4e^{2} - \frac{11}{3}e + 1$
23 $[23, 23, -w^{2} + w + 3]$ $-e^{3} - 5e^{2} - 3e - 2$
23 $[23, 23, -w^{2} + 3]$ $-e^{3} - 7e^{2} - 10e + 4$
27 $[27, 3, w^{3} - 3w^{2} - w + 4]$ $-e^{2} - 3e + 5$
29 $[29, 29, -w^{3} + 3w^{2} + 3w - 5]$ $\phantom{-}e^{3} + 5e^{2} + e - 7$
29 $[29, 29, w^{3} - 2w^{2} - 4w]$ $\phantom{-}\frac{2}{3}e^{3} + 5e^{2} + \frac{26}{3}e - 3$
47 $[47, 47, -w^{3} + 2w^{2} + 3w - 5]$ $\phantom{-}\frac{1}{3}e^{3} + 6e^{2} + \frac{58}{3}e + 2$
47 $[47, 47, w^{2} - 3w - 2]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{14}{3}e + 2$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $-\frac{2}{3}e^{3} - 3e^{2} + \frac{10}{3}e + 8$
67 $[67, 67, -w^{3} + w^{2} + 5w - 1]$ $\phantom{-}3e^{2} + 12e - 6$
67 $[67, 67, -2w^{3} + 3w^{2} + 11w - 7]$ $-\frac{10}{3}e^{3} - 20e^{2} - \frac{67}{3}e + 8$
83 $[83, 83, -2w + 3]$ $\phantom{-}\frac{10}{3}e^{3} + 20e^{2} + \frac{67}{3}e - 4$
89 $[89, 89, 3w^{3} - 7w^{2} - 9w + 9]$ $\phantom{-}\frac{7}{3}e^{3} + 13e^{2} + \frac{40}{3}e - 3$
97 $[97, 97, w^{3} - w^{2} - 4w - 3]$ $-\frac{5}{3}e^{3} - 9e^{2} - \frac{29}{3}e - 1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$ $-1$