Properties

Label 2.2.120.1-5.1-c
Base field \(\Q(\sqrt{30}) \)
Weight $[2, 2]$
Level norm $5$
Level $[5, 5, -w + 5]$
Dimension $8$
CM no
Base change yes

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Base field \(\Q(\sqrt{30}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 30\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[5, 5, -w + 5]$
Dimension: $8$
CM: no
Base change: yes
Newspace dimension: $20$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} + 15x^{6} + 72x^{4} + 112x^{2} + 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
3 $[3, 3, w]$ $\phantom{-}\frac{1}{2}e^{5} + \frac{9}{2}e^{3} + 9e$
5 $[5, 5, -w + 5]$ $-1$
7 $[7, 7, w + 3]$ $-e^{3} - 5e$
7 $[7, 7, w + 4]$ $-e^{3} - 5e$
13 $[13, 13, w + 2]$ $-\frac{1}{4}e^{7} - \frac{13}{4}e^{5} - \frac{25}{2}e^{3} - 14e$
13 $[13, 13, w + 11]$ $-\frac{1}{4}e^{7} - \frac{13}{4}e^{5} - \frac{25}{2}e^{3} - 14e$
17 $[17, 17, w + 8]$ $-\frac{1}{2}e^{5} - \frac{11}{2}e^{3} - 14e$
17 $[17, 17, w + 9]$ $-\frac{1}{2}e^{5} - \frac{11}{2}e^{3} - 14e$
19 $[19, 19, w + 7]$ $-\frac{1}{2}e^{6} - \frac{9}{2}e^{4} - 9e^{2} - 2$
19 $[19, 19, -w + 7]$ $-\frac{1}{2}e^{6} - \frac{9}{2}e^{4} - 9e^{2} - 2$
29 $[29, 29, -w - 1]$ $\phantom{-}\frac{1}{2}e^{6} + \frac{9}{2}e^{4} + 7e^{2} - 6$
29 $[29, 29, w - 1]$ $\phantom{-}\frac{1}{2}e^{6} + \frac{9}{2}e^{4} + 7e^{2} - 6$
37 $[37, 37, w + 17]$ $\phantom{-}\frac{1}{4}e^{7} + \frac{17}{4}e^{5} + \frac{43}{2}e^{3} + 28e$
37 $[37, 37, w + 20]$ $\phantom{-}\frac{1}{4}e^{7} + \frac{17}{4}e^{5} + \frac{43}{2}e^{3} + 28e$
71 $[71, 71, 2w - 7]$ $\phantom{-}\frac{1}{2}e^{6} + \frac{11}{2}e^{4} + 18e^{2} + 12$
71 $[71, 71, -2w - 7]$ $\phantom{-}\frac{1}{2}e^{6} + \frac{11}{2}e^{4} + 18e^{2} + 12$
83 $[83, 83, w + 14]$ $-\frac{1}{2}e^{5} - \frac{13}{2}e^{3} - 19e$
83 $[83, 83, w + 69]$ $-\frac{1}{2}e^{5} - \frac{13}{2}e^{3} - 19e$
101 $[101, 101, -7w + 37]$ $-\frac{3}{2}e^{6} - \frac{31}{2}e^{4} - 39e^{2} - 10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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