Properties

Base field \(\Q(\sqrt{5}, \sqrt{7})\)
Weight [2, 2, 2, 2]
Level norm 25
Level $[25, 5, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{40}{23}w - \frac{21}{23}]$
Label 4.4.19600.1-25.1-r
Dimension 4
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 $[25, 5, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{40}{23}w - \frac{21}{23}]$
Label 4.4.19600.1-25.1-r
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 62

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut -\mathstrut 12x^{3} \) \(\mathstrut +\mathstrut 14x^{2} \) \(\mathstrut +\mathstrut 232x \) \(\mathstrut -\mathstrut 604\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w + \frac{1}{23}]$ $-2$
9 $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w + \frac{24}{23}]$ $-\frac{1}{10}e^{3} + \frac{2}{5}e^{2} + \frac{14}{5}e - \frac{39}{5}$
9 $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w - \frac{68}{23}]$ $\phantom{-}\frac{1}{10}e^{3} - \frac{2}{5}e^{2} - \frac{14}{5}e + \frac{29}{5}$
19 $[19, 19, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w + \frac{24}{23}]$ $\phantom{-}e$
19 $[19, 19, -\frac{6}{23}w^{3} + \frac{9}{23}w^{2} + \frac{83}{23}w - \frac{20}{23}]$ $-\frac{4}{15}e^{3} + \frac{26}{15}e^{2} + \frac{29}{5}e - \frac{532}{15}$
19 $[19, 19, \frac{6}{23}w^{3} - \frac{9}{23}w^{2} - \frac{83}{23}w + \frac{66}{23}]$ $\phantom{-}\frac{1}{10}e^{3} - \frac{2}{5}e^{2} - \frac{9}{5}e + \frac{4}{5}$
19 $[19, 19, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w - \frac{22}{23}]$ $-\frac{1}{6}e^{3} + \frac{4}{3}e^{2} + 3e - \frac{68}{3}$
25 $[25, 5, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{40}{23}w - \frac{21}{23}]$ $\phantom{-}1$
29 $[29, 29, w]$ $-\frac{1}{30}e^{3} + \frac{1}{15}e^{2} + 2e - \frac{83}{15}$
29 $[29, 29, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{63}{23}w - \frac{21}{23}]$ $-\frac{1}{6}e^{3} + \frac{11}{15}e^{2} + \frac{18}{5}e - \frac{181}{15}$
29 $[29, 29, \frac{4}{23}w^{3} - \frac{6}{23}w^{2} - \frac{63}{23}w + \frac{44}{23}]$ $\phantom{-}\frac{3}{10}e^{3} - \frac{9}{5}e^{2} - \frac{34}{5}e + 31$
29 $[29, 29, -w + 1]$ $-\frac{1}{10}e^{3} + e^{2} + \frac{6}{5}e - \frac{107}{5}$
31 $[31, 31, w + 2]$ $\phantom{-}\frac{3}{10}e^{3} - \frac{11}{5}e^{2} - \frac{27}{5}e + \frac{192}{5}$
31 $[31, 31, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{63}{23}w + \frac{25}{23}]$ $\phantom{-}\frac{2}{5}e^{3} - \frac{13}{5}e^{2} - \frac{41}{5}e + \frac{246}{5}$
31 $[31, 31, \frac{4}{23}w^{3} - \frac{6}{23}w^{2} - \frac{63}{23}w + \frac{90}{23}]$ $-\frac{7}{30}e^{3} + \frac{19}{15}e^{2} + \frac{21}{5}e - \frac{248}{15}$
31 $[31, 31, -w + 3]$ $-\frac{2}{15}e^{3} + \frac{13}{15}e^{2} + \frac{7}{5}e - \frac{206}{15}$
49 $[49, 7, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w - \frac{22}{23}]$ $\phantom{-}6$
59 $[59, 59, -\frac{20}{23}w^{3} + \frac{30}{23}w^{2} + \frac{269}{23}w - \frac{128}{23}]$ $\phantom{-}\frac{3}{10}e^{3} - 2e^{2} - \frac{28}{5}e + \frac{216}{5}$
59 $[59, 59, -\frac{8}{23}w^{3} + \frac{12}{23}w^{2} + \frac{103}{23}w - \frac{88}{23}]$ $\phantom{-}\frac{3}{10}e^{3} - 2e^{2} - \frac{28}{5}e + \frac{136}{5}$
59 $[59, 59, -\frac{8}{23}w^{3} + \frac{12}{23}w^{2} + \frac{103}{23}w - \frac{19}{23}]$ $-\frac{7}{30}e^{3} + \frac{22}{15}e^{2} + 4e - \frac{476}{15}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
25 $[25,5,-\frac{4}{23}w^{3}+\frac{6}{23}w^{2}+\frac{40}{23}w-\frac{21}{23}]$ $-1$