Properties

Base field \(\Q(\sqrt{5}, \sqrt{7})\)
Weight [2, 2, 2, 2]
Level norm 9
Level $[9,3,\frac{2}{23}w^{3} - \frac{3}{23}w^{2} - \frac{43}{23}w + \frac{68}{23}]$
Label 4.4.19600.1-9.2-b
Dimension 6
CM no
Base change no

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Base field \(\Q(\sqrt{5}, \sqrt{7})\)

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 15x^{2} + 16x + 29\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[9,3,\frac{2}{23}w^{3} - \frac{3}{23}w^{2} - \frac{43}{23}w + \frac{68}{23}]$
Label 4.4.19600.1-9.2-b
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 18

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut -\mathstrut 17x^{4} \) \(\mathstrut +\mathstrut 40x^{2} \) \(\mathstrut -\mathstrut 21\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w + \frac{1}{23}]$ $\phantom{-}\frac{1}{11}e^{4} - \frac{12}{11}e^{2} + \frac{2}{11}$
9 $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w + \frac{24}{23}]$ $\phantom{-}\frac{2}{11}e^{4} - \frac{35}{11}e^{2} + \frac{26}{11}$
9 $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w - \frac{68}{23}]$ $\phantom{-}1$
19 $[19, 19, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w + \frac{24}{23}]$ $\phantom{-}\frac{1}{11}e^{5} - \frac{12}{11}e^{3} - \frac{31}{11}e$
19 $[19, 19, -\frac{6}{23}w^{3} + \frac{9}{23}w^{2} + \frac{83}{23}w - \frac{20}{23}]$ $-e$
19 $[19, 19, \frac{6}{23}w^{3} - \frac{9}{23}w^{2} - \frac{83}{23}w + \frac{66}{23}]$ $-\frac{1}{11}e^{5} + \frac{12}{11}e^{3} + \frac{31}{11}e$
19 $[19, 19, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w - \frac{22}{23}]$ $\phantom{-}e$
25 $[25, 5, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{40}{23}w - \frac{21}{23}]$ $-\frac{6}{11}e^{4} + \frac{94}{11}e^{2} - \frac{166}{11}$
29 $[29, 29, w]$ $-\frac{7}{11}e^{4} + \frac{106}{11}e^{2} - \frac{102}{11}$
29 $[29, 29, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{63}{23}w - \frac{21}{23}]$ $-\frac{7}{11}e^{4} + \frac{106}{11}e^{2} - \frac{102}{11}$
29 $[29, 29, \frac{4}{23}w^{3} - \frac{6}{23}w^{2} - \frac{63}{23}w + \frac{44}{23}]$ $\phantom{-}\frac{5}{11}e^{4} - \frac{82}{11}e^{2} + \frac{87}{11}$
29 $[29, 29, -w + 1]$ $\phantom{-}\frac{5}{11}e^{4} - \frac{82}{11}e^{2} + \frac{87}{11}$
31 $[31, 31, w + 2]$ $\phantom{-}\frac{1}{11}e^{5} - \frac{12}{11}e^{3} - \frac{9}{11}e$
31 $[31, 31, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{63}{23}w + \frac{25}{23}]$ $-\frac{1}{11}e^{5} + \frac{12}{11}e^{3} + \frac{9}{11}e$
31 $[31, 31, \frac{4}{23}w^{3} - \frac{6}{23}w^{2} - \frac{63}{23}w + \frac{90}{23}]$ $\phantom{-}\frac{7}{11}e^{5} - \frac{117}{11}e^{3} + \frac{223}{11}e$
31 $[31, 31, -w + 3]$ $-\frac{7}{11}e^{5} + \frac{117}{11}e^{3} - \frac{223}{11}e$
49 $[49, 7, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w - \frac{22}{23}]$ $-\frac{5}{11}e^{4} + \frac{71}{11}e^{2} - \frac{131}{11}$
59 $[59, 59, -\frac{20}{23}w^{3} + \frac{30}{23}w^{2} + \frac{269}{23}w - \frac{128}{23}]$ $-\frac{9}{11}e^{5} + \frac{141}{11}e^{3} - \frac{172}{11}e$
59 $[59, 59, -\frac{8}{23}w^{3} + \frac{12}{23}w^{2} + \frac{103}{23}w - \frac{88}{23}]$ $\phantom{-}\frac{9}{11}e^{5} - \frac{141}{11}e^{3} + \frac{172}{11}e$
59 $[59, 59, -\frac{8}{23}w^{3} + \frac{12}{23}w^{2} + \frac{103}{23}w - \frac{19}{23}]$ $-\frac{3}{11}e^{5} + \frac{47}{11}e^{3} - \frac{17}{11}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9,3,\frac{2}{23}w^{3} - \frac{3}{23}w^{2} - \frac{43}{23}w + \frac{68}{23}]$ $-1$