Properties

Label 2.2.28.1-29.1-a
Base field \(\Q(\sqrt{7}) \)
Weight $[2, 2]$
Level norm $29$
Level $[29, 29, -w - 6]$
Dimension $8$
CM no
Base change no

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Base field \(\Q(\sqrt{7}) \)

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

Form

Weight: $[2, 2]$
Level: $[29, 29, -w - 6]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 22x^{6} + 162x^{4} - 464x^{2} + 448\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 3]$ $-\frac{1}{8}e^{6} + \frac{9}{4}e^{4} - \frac{49}{4}e^{2} + 20$
3 $[3, 3, w - 2]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $-\frac{1}{16}e^{7} + \frac{9}{8}e^{5} - \frac{45}{8}e^{3} + \frac{13}{2}e$
7 $[7, 7, w]$ $-\frac{1}{8}e^{7} + \frac{5}{2}e^{5} - \frac{59}{4}e^{3} + \frac{45}{2}e$
19 $[19, 19, 2w - 3]$ $\phantom{-}\frac{3}{16}e^{7} - \frac{31}{8}e^{5} + \frac{191}{8}e^{3} - \frac{81}{2}e$
19 $[19, 19, 2w + 3]$ $\phantom{-}\frac{1}{4}e^{7} - \frac{9}{2}e^{5} + \frac{47}{2}e^{3} - 33e$
25 $[25, 5, 5]$ $\phantom{-}\frac{1}{4}e^{6} - \frac{9}{2}e^{4} + \frac{47}{2}e^{2} - 32$
29 $[29, 29, -w - 6]$ $-1$
29 $[29, 29, w - 6]$ $\phantom{-}\frac{1}{8}e^{6} - \frac{11}{4}e^{4} + \frac{73}{4}e^{2} - 30$
31 $[31, 31, 4w + 9]$ $-\frac{1}{4}e^{7} + \frac{19}{4}e^{5} - 27e^{3} + \frac{91}{2}e$
31 $[31, 31, -4w + 9]$ $\phantom{-}\frac{1}{8}e^{7} - \frac{9}{4}e^{5} + \frac{45}{4}e^{3} - 13e$
37 $[37, 37, -3w + 10]$ $-e^{4} + 11e^{2} - 22$
37 $[37, 37, -6w + 17]$ $-\frac{3}{8}e^{6} + \frac{25}{4}e^{4} - \frac{115}{4}e^{2} + 34$
47 $[47, 47, -3w - 4]$ $\phantom{-}\frac{3}{8}e^{7} - \frac{27}{4}e^{5} + \frac{143}{4}e^{3} - 53e$
47 $[47, 47, 3w - 4]$ $-\frac{1}{16}e^{7} + \frac{9}{8}e^{5} - \frac{45}{8}e^{3} + \frac{15}{2}e$
53 $[53, 53, 2w - 9]$ $\phantom{-}\frac{1}{2}e^{6} - 10e^{4} + 60e^{2} - 94$
53 $[53, 53, 2w + 9]$ $-\frac{1}{2}e^{6} + 10e^{4} - 60e^{2} + 102$
59 $[59, 59, 3w - 2]$ $\phantom{-}\frac{5}{8}e^{7} - 12e^{5} + \frac{271}{4}e^{3} - \frac{209}{2}e$
59 $[59, 59, -3w - 2]$ $-\frac{1}{4}e^{7} + \frac{19}{4}e^{5} - 27e^{3} + \frac{85}{2}e$
83 $[83, 83, -6w - 13]$ $-\frac{3}{8}e^{7} + \frac{29}{4}e^{5} - \frac{171}{4}e^{3} + 75e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29, 29, -w - 6]$ $1$