Properties

Label 4.4.15188.1-11.1-c
Base field 4.4.15188.1
Weight $[2, 2, 2, 2]$
Level norm $11$
Level $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$
Dimension $8$
CM no
Base change no

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Base field 4.4.15188.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 2\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $26$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 9x^{6} + 24x^{4} - 19x^{2} + 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $-\frac{1}{2}e^{7} + \frac{9}{2}e^{5} - 11e^{3} + \frac{9}{2}e$
2 $[2, 2, -\frac{1}{2}w^{3} + w^{2} + \frac{3}{2}w]$ $\phantom{-}e$
11 $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$ $\phantom{-}1$
11 $[11, 11, -w^{3} + w^{2} + 6w + 1]$ $-e^{3} + 2e$
13 $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $\phantom{-}e^{7} - 10e^{5} + 29e^{3} - 20e$
19 $[19, 19, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w]$ $-2e^{7} + 16e^{5} - 33e^{3} + 12e$
23 $[23, 23, -\frac{1}{2}w^{3} + 2w^{2} - \frac{1}{2}w - 2]$ $-e^{6} + 9e^{4} - 22e^{2} + 4$
31 $[31, 31, -w^{3} + w^{2} + 6w - 1]$ $\phantom{-}4e^{7} - 32e^{5} + 68e^{3} - 27e$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ $-e^{7} + 9e^{5} - 25e^{3} + 19e$
43 $[43, 43, \frac{1}{2}w^{3} - w^{2} - \frac{9}{2}w + 2]$ $-e^{7} + 10e^{5} - 26e^{3} + 9e$
67 $[67, 67, w^{2} - w - 5]$ $\phantom{-}3e^{6} - 23e^{4} + 42e^{2} - 12$
67 $[67, 67, -\frac{1}{2}w^{3} + \frac{11}{2}w + 2]$ $-2e^{7} + 17e^{5} - 40e^{3} + 20e$
73 $[73, 73, w^{2} + w + 1]$ $-4e^{6} + 30e^{4} - 55e^{2} + 14$
79 $[79, 79, \frac{1}{2}w^{3} + w^{2} - \frac{5}{2}w - 2]$ $\phantom{-}6e^{6} - 49e^{4} + 108e^{2} - 48$
81 $[81, 3, -3]$ $-5e^{6} + 45e^{4} - 110e^{2} + 46$
83 $[83, 83, 2w^{3} - 2w^{2} - 12w + 5]$ $-2e^{7} + 17e^{5} - 42e^{3} + 27e$
83 $[83, 83, -\frac{1}{2}w^{3} - w^{2} + \frac{1}{2}w + 2]$ $\phantom{-}e^{4} - 6e^{2} - 4$
89 $[89, 89, -\frac{3}{2}w^{3} + 2w^{2} + \frac{17}{2}w - 2]$ $-5e^{7} + 45e^{5} - 111e^{3} + 56e$
89 $[89, 89, \frac{3}{2}w^{3} - 2w^{2} - \frac{21}{2}w + 2]$ $\phantom{-}9e^{7} - 76e^{5} + 174e^{3} - 77e$
97 $[97, 97, \frac{1}{2}w^{3} - w^{2} - \frac{1}{2}w - 2]$ $\phantom{-}5e^{6} - 44e^{4} + 104e^{2} - 42$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$ $-1$