Properties

Label 2.2.136.1-10.2-f
Base field \(\Q(\sqrt{34}) \)
Weight $[2, 2]$
Level norm $10$
Level $[10,10,-w + 2]$
Dimension $5$
CM no
Base change no

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Base field \(\Q(\sqrt{34}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 34\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[10,10,-w + 2]$
Dimension: $5$
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:

\(x^{5} + 3x^{4} - 9x^{3} - 23x^{2} + 16x + 20\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 6]$ $\phantom{-}1$
3 $[3, 3, w + 1]$ $-\frac{1}{4}e^{3} + \frac{7}{4}e - \frac{3}{2}$
3 $[3, 3, w + 2]$ $\phantom{-}e$
5 $[5, 5, w + 2]$ $-\frac{1}{4}e^{4} - \frac{1}{4}e^{3} + \frac{9}{4}e^{2} + \frac{3}{4}e - \frac{5}{2}$
5 $[5, 5, w + 3]$ $-1$
11 $[11, 11, w + 1]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{2}e^{3} - \frac{7}{4}e^{2} - 2e - 1$
11 $[11, 11, w + 10]$ $-\frac{1}{4}e^{3} - e^{2} + \frac{3}{4}e + \frac{5}{2}$
17 $[17, 17, -3w + 17]$ $-\frac{1}{2}e^{2} - \frac{1}{2}e + 1$
29 $[29, 29, w + 11]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{4}e^{3} - \frac{5}{4}e^{2} - \frac{3}{4}e - \frac{7}{2}$
29 $[29, 29, w + 18]$ $\phantom{-}\frac{1}{4}e^{4} + e^{3} - \frac{3}{4}e^{2} - \frac{15}{2}e - 2$
37 $[37, 37, w + 16]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{3}{4}e^{3} - \frac{11}{2}e^{2} - \frac{21}{4}e + \frac{13}{2}$
37 $[37, 37, w + 21]$ $-\frac{1}{4}e^{4} - \frac{1}{2}e^{3} + \frac{7}{4}e^{2} + 2e - 3$
47 $[47, 47, -w - 9]$ $\phantom{-}\frac{1}{4}e^{4} + 2e^{3} - \frac{1}{4}e^{2} - 12e - 1$
47 $[47, 47, w - 9]$ $-\frac{3}{4}e^{4} - \frac{3}{2}e^{3} + \frac{23}{4}e^{2} + \frac{17}{2}e - 6$
49 $[49, 7, -7]$ $\phantom{-}e^{2} + 2e - 4$
61 $[61, 61, w + 20]$ $-\frac{1}{2}e^{4} - \frac{5}{4}e^{3} + 2e^{2} + \frac{17}{4}e + \frac{11}{2}$
61 $[61, 61, w + 41]$ $-\frac{1}{2}e^{2} - \frac{7}{2}e + 1$
89 $[89, 89, 2w - 15]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{3}{2}e^{3} - 5e^{2} - 10e + 6$
89 $[89, 89, -2w - 15]$ $\phantom{-}\frac{1}{2}e^{4} - 8e^{2} - \frac{1}{2}e + 19$
103 $[103, 103, -14w + 81]$ $-\frac{1}{2}e^{4} - e^{3} + \frac{7}{2}e^{2} + 7e + 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2,2,-w - 6]$ $-1$
$5$ $[5,5,-w + 2]$ $1$