Properties

Label 4.4.19525.1-25.1-f
Base field 4.4.19525.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 5, -\frac{2}{3}w^{2} + \frac{5}{3}w + 5]$
Dimension $8$
CM no
Base change no

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Base field 4.4.19525.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 14x^{2} + 15x + 45\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[25, 5, -\frac{2}{3}w^{2} + \frac{5}{3}w + 5]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $44$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 28x^{6} + 168x^{4} - 344x^{2} + 196\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ $\phantom{-}0$
5 $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ $-\frac{5}{56}e^{7} + \frac{9}{4}e^{5} - \frac{35}{4}e^{3} + \frac{47}{7}e$
9 $[9, 3, -w + 3]$ $-\frac{5}{56}e^{7} + \frac{9}{4}e^{5} - \frac{35}{4}e^{3} + \frac{54}{7}e$
9 $[9, 3, w + 2]$ $-2$
11 $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ $-\frac{1}{8}e^{6} + 3e^{4} - \frac{35}{4}e^{2} + \frac{5}{2}$
16 $[16, 2, 2]$ $-\frac{3}{56}e^{7} + \frac{11}{8}e^{5} - 6e^{3} + \frac{243}{28}e$
19 $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ $\phantom{-}\frac{3}{14}e^{7} - \frac{21}{4}e^{5} + \frac{35}{2}e^{3} - \frac{115}{14}e$
19 $[19, 19, \frac{1}{3}w^{3} - w^{2} - \frac{7}{3}w + 6]$ $-\frac{1}{8}e^{6} + 3e^{4} - \frac{35}{4}e^{2} + \frac{5}{2}$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 2]$ $-\frac{1}{8}e^{7} + 3e^{5} - \frac{35}{4}e^{3} + \frac{3}{2}e$
29 $[29, 29, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $\phantom{-}\frac{3}{8}e^{6} - 9e^{4} + \frac{105}{4}e^{2} - \frac{15}{2}$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w + 1]$ $\phantom{-}\frac{1}{8}e^{6} - \frac{13}{4}e^{4} + \frac{57}{4}e^{2} - 13$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 4]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{11}{2}e^{2} + \frac{21}{2}$
49 $[49, 7, \frac{1}{3}w^{3} - \frac{10}{3}w - 1]$ $\phantom{-}\frac{5}{28}e^{7} - \frac{9}{2}e^{5} + \frac{35}{2}e^{3} - \frac{94}{7}e$
49 $[49, 7, -\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 4]$ $-\frac{3}{8}e^{6} + \frac{19}{2}e^{4} - \frac{149}{4}e^{2} + \frac{57}{2}$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{5}{3}w - 11]$ $\phantom{-}\frac{11}{56}e^{7} - 5e^{5} + \frac{83}{4}e^{3} - \frac{351}{14}e$
59 $[59, 59, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 5w - 13]$ $-e^{6} + 25e^{4} - 94e^{2} + 76$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{2}{3}w - 9]$ $-\frac{5}{56}e^{7} + \frac{9}{4}e^{5} - \frac{35}{4}e^{3} + \frac{54}{7}e$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 4w + 2]$ $\phantom{-}\frac{3}{7}e^{7} - \frac{21}{2}e^{5} + 35e^{3} - \frac{115}{7}e$
61 $[61, 61, \frac{2}{3}w^{2} - \frac{5}{3}w - 1]$ $\phantom{-}\frac{3}{56}e^{7} - \frac{3}{2}e^{5} + \frac{35}{4}e^{3} - \frac{167}{14}e$
61 $[61, 61, -\frac{1}{3}w^{2} + \frac{4}{3}w + 6]$ $-\frac{29}{56}e^{7} + 13e^{5} - \frac{197}{4}e^{3} + \frac{513}{14}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ $-1$