Properties

Label 4.4.17069.1-16.1-e
Base field 4.4.17069.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $4$
CM no
Base change no

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Base field 4.4.17069.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $36$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 2x^{3} - 9x^{2} + 10x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}\frac{2}{5}e^{3} - \frac{3}{5}e^{2} - \frac{17}{5}e + \frac{9}{5}$
3 $[3, 3, w^{3} - 2w^{2} - 6w + 1]$ $-\frac{2}{5}e^{3} + \frac{3}{5}e^{2} + \frac{17}{5}e - \frac{9}{5}$
9 $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ $\phantom{-}\frac{2}{5}e^{3} - \frac{3}{5}e^{2} - \frac{22}{5}e + \frac{9}{5}$
16 $[16, 2, 2]$ $\phantom{-}1$
17 $[17, 17, w^{3} - w^{2} - 8w - 5]$ $-e + 1$
17 $[17, 17, -2w^{3} + 4w^{2} + 11w - 2]$ $-\frac{3}{5}e^{3} + \frac{7}{5}e^{2} + \frac{28}{5}e - \frac{36}{5}$
17 $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ $\phantom{-}\frac{4}{5}e^{3} - \frac{6}{5}e^{2} - \frac{39}{5}e + \frac{23}{5}$
17 $[17, 17, w^{3} - 2w^{2} - 4w + 1]$ $-\frac{1}{5}e^{3} - \frac{1}{5}e^{2} + \frac{16}{5}e - \frac{2}{5}$
25 $[25, 5, w^{3} - 3w^{2} - 3w + 1]$ $\phantom{-}\frac{2}{5}e^{3} - \frac{3}{5}e^{2} - \frac{12}{5}e + \frac{19}{5}$
25 $[25, 5, w^{2} - 2w - 7]$ $-\frac{6}{5}e^{3} + \frac{9}{5}e^{2} + \frac{56}{5}e - \frac{17}{5}$
29 $[29, 29, w^{3} - 2w^{2} - 6w - 1]$ $\phantom{-}\frac{9}{5}e^{3} - \frac{16}{5}e^{2} - \frac{79}{5}e + \frac{38}{5}$
29 $[29, 29, w - 2]$ $-e^{3} + 2e^{2} + 7e - 10$
53 $[53, 53, w^{3} - 3w^{2} - 4w + 4]$ $\phantom{-}e^{3} - 3e^{2} - 8e + 15$
53 $[53, 53, -w^{3} + 3w^{2} + 4w - 5]$ $-\frac{1}{5}e^{3} + \frac{9}{5}e^{2} - \frac{4}{5}e - \frac{27}{5}$
61 $[61, 61, -w^{3} + 2w^{2} + 7w - 4]$ $-\frac{11}{5}e^{3} + \frac{19}{5}e^{2} + \frac{106}{5}e - \frac{77}{5}$
61 $[61, 61, -4w^{3} + 11w^{2} + 14w - 8]$ $-\frac{1}{5}e^{3} - \frac{1}{5}e^{2} + \frac{26}{5}e - \frac{7}{5}$
101 $[101, 101, -w^{3} + 2w^{2} + 7w - 1]$ $-6$
103 $[103, 103, -w^{3} + 3w^{2} + 2w - 5]$ $-\frac{7}{5}e^{3} + \frac{13}{5}e^{2} + \frac{57}{5}e - \frac{54}{5}$
103 $[103, 103, -w^{3} + w^{2} + 8w + 2]$ $\phantom{-}\frac{7}{5}e^{3} - \frac{13}{5}e^{2} - \frac{57}{5}e + \frac{34}{5}$
113 $[113, 113, w^{3} - 3w^{2} - 3w + 7]$ $\phantom{-}\frac{11}{5}e^{3} - \frac{9}{5}e^{2} - \frac{96}{5}e - \frac{8}{5}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$16$ $[16, 2, 2]$ $-1$