Properties

Label 4.4.3600.1-49.2-b
Base field \(\Q(\sqrt{3}, \sqrt{5})\)
Weight $[2, 2, 2, 2]$
Level norm $49$
Level $[49,7,-w^{3} + 2w^{2} + 6w - 6]$
Dimension $4$
CM no
Base change no

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Base field \(\Q(\sqrt{3}, \sqrt{5})\)

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 8x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[49,7,-w^{3} + 2w^{2} + 6w - 6]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 44x^{2} + 92\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{2}{7}w^{3} + \frac{3}{7}w^{2} + \frac{19}{7}w - \frac{17}{7}]$ $-\frac{1}{14}e^{2} + \frac{18}{7}$
9 $[9, 3, -\frac{2}{7}w^{3} + \frac{3}{7}w^{2} + \frac{19}{7}w - \frac{10}{7}]$ $\phantom{-}4$
11 $[11, 11, -w - 1]$ $-\frac{1}{14}e^{3} + \frac{18}{7}e$
11 $[11, 11, \frac{4}{7}w^{3} - \frac{6}{7}w^{2} - \frac{31}{7}w + \frac{27}{7}]$ $-e$
11 $[11, 11, \frac{4}{7}w^{3} - \frac{6}{7}w^{2} - \frac{31}{7}w + \frac{6}{7}]$ $\phantom{-}e$
11 $[11, 11, -w + 2]$ $\phantom{-}\frac{1}{14}e^{3} - \frac{18}{7}e$
25 $[25, 5, \frac{4}{7}w^{3} - \frac{6}{7}w^{2} - \frac{24}{7}w + \frac{13}{7}]$ $-\frac{1}{7}e^{2} + \frac{22}{7}$
49 $[49, 7, \frac{5}{7}w^{3} - \frac{11}{7}w^{2} - \frac{23}{7}w + \frac{25}{7}]$ $\phantom{-}\frac{4}{7}e^{2} - \frac{74}{7}$
49 $[49, 7, w^{3} - w^{2} - 7w + 1]$ $-1$
59 $[59, 59, \frac{3}{7}w^{3} - \frac{1}{7}w^{2} - \frac{32}{7}w + \frac{15}{7}]$ $\phantom{-}\frac{1}{7}e^{3} - \frac{57}{7}e$
59 $[59, 59, -\frac{3}{7}w^{3} + \frac{8}{7}w^{2} + \frac{25}{7}w - \frac{43}{7}]$ $\phantom{-}\frac{1}{14}e^{3} - \frac{18}{7}e$
59 $[59, 59, -\frac{3}{7}w^{3} + \frac{1}{7}w^{2} + \frac{32}{7}w + \frac{13}{7}]$ $-\frac{1}{14}e^{3} + \frac{18}{7}e$
59 $[59, 59, \frac{3}{7}w^{3} - \frac{8}{7}w^{2} - \frac{25}{7}w + \frac{15}{7}]$ $-\frac{1}{7}e^{3} + \frac{57}{7}e$
61 $[61, 61, -\frac{8}{7}w^{3} + \frac{12}{7}w^{2} + \frac{55}{7}w - \frac{26}{7}]$ $\phantom{-}\frac{1}{7}e^{2} - \frac{36}{7}$
61 $[61, 61, -\frac{4}{7}w^{3} + \frac{6}{7}w^{2} + \frac{17}{7}w - \frac{6}{7}]$ $\phantom{-}8$
61 $[61, 61, \frac{6}{7}w^{3} - \frac{9}{7}w^{2} - \frac{50}{7}w + \frac{16}{7}]$ $\phantom{-}8$
61 $[61, 61, \frac{8}{7}w^{3} - \frac{12}{7}w^{2} - \frac{55}{7}w + \frac{33}{7}]$ $\phantom{-}\frac{1}{7}e^{2} - \frac{36}{7}$
71 $[71, 71, -\frac{3}{7}w^{3} + \frac{1}{7}w^{2} + \frac{25}{7}w - \frac{15}{7}]$ $\phantom{-}\frac{1}{14}e^{3} - \frac{25}{7}e$
71 $[71, 71, -w^{3} + w^{2} + 8w - 2]$ $-\frac{2}{7}e^{3} + \frac{72}{7}e$
71 $[71, 71, w^{3} - 2w^{2} - 7w + 6]$ $\phantom{-}\frac{2}{7}e^{3} - \frac{72}{7}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$49$ $[49,7,-w^{3} + 2w^{2} + 6w - 6]$ $1$