Properties

Label 2.2.29.1-59.1-c
Base field \(\Q(\sqrt{29}) \)
Weight $[2, 2]$
Level norm $59$
Level $[59, 59, -3w - 1]$
Dimension $4$
CM no
Base change no

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Base field \(\Q(\sqrt{29}) \)

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

Form

Weight: $[2, 2]$
Level: $[59, 59, -3w - 1]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 4x^{3} - 4x^{2} - 21x - 9\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}e$
5 $[5, 5, w + 1]$ $-e - 1$
5 $[5, 5, w - 2]$ $\phantom{-}\frac{1}{9}e^{3} - \frac{2}{9}e^{2} - \frac{10}{9}e + \frac{1}{3}$
7 $[7, 7, w]$ $-\frac{1}{3}e^{3} - \frac{1}{3}e^{2} + \frac{7}{3}e - 1$
7 $[7, 7, -w + 1]$ $\phantom{-}\frac{4}{9}e^{3} + \frac{10}{9}e^{2} - \frac{31}{9}e - \frac{17}{3}$
9 $[9, 3, 3]$ $-\frac{4}{9}e^{3} - \frac{10}{9}e^{2} + \frac{31}{9}e + \frac{14}{3}$
13 $[13, 13, w + 4]$ $-\frac{1}{9}e^{3} + \frac{2}{9}e^{2} + \frac{19}{9}e + \frac{5}{3}$
13 $[13, 13, w - 5]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{7}{3}e$
23 $[23, 23, -w - 5]$ $-\frac{2}{3}e^{3} - \frac{8}{3}e^{2} + \frac{8}{3}e + 8$
23 $[23, 23, w - 6]$ $\phantom{-}\frac{2}{3}e^{3} + \frac{5}{3}e^{2} - \frac{14}{3}e - 10$
29 $[29, 29, 2w - 1]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{4}{3}e^{2} - \frac{7}{3}e - 6$
53 $[53, 53, 3w - 5]$ $\phantom{-}\frac{2}{9}e^{3} + \frac{5}{9}e^{2} - \frac{2}{9}e - \frac{22}{3}$
53 $[53, 53, -3w - 2]$ $-\frac{4}{3}e^{3} - \frac{13}{3}e^{2} + \frac{22}{3}e + 11$
59 $[59, 59, -3w - 1]$ $\phantom{-}1$
59 $[59, 59, 3w - 4]$ $-\frac{1}{9}e^{3} - \frac{7}{9}e^{2} + \frac{10}{9}e - \frac{10}{3}$
67 $[67, 67, 3w - 13]$ $-\frac{10}{9}e^{3} - \frac{7}{9}e^{2} + \frac{91}{9}e - \frac{1}{3}$
67 $[67, 67, -3w - 10]$ $\phantom{-}\frac{14}{9}e^{3} + \frac{35}{9}e^{2} - \frac{122}{9}e - \frac{55}{3}$
71 $[71, 71, 2w - 11]$ $-\frac{2}{9}e^{3} + \frac{4}{9}e^{2} + \frac{29}{9}e - \frac{26}{3}$
71 $[71, 71, -2w - 9]$ $-\frac{5}{3}e^{3} - \frac{17}{3}e^{2} + \frac{26}{3}e + 20$
83 $[83, 83, -w - 9]$ $\phantom{-}\frac{2}{3}e^{3} + \frac{5}{3}e^{2} - \frac{14}{3}e - 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$59$ $[59, 59, -3w - 1]$ $-1$