Properties

Label 4.4.12725.1-25.1-i
Base field 4.4.12725.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 5, -2w^{2} + 2w + 11]$
Dimension $4$
CM no
Base change no

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Base field 4.4.12725.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 10x^{2} + 11x + 29\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[25, 5, -2w^{2} + 2w + 11]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $29$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 44x^{2} + 32x + 292\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -w - 1]$ $\phantom{-}e$
11 $[11, 11, w^{2} - 5]$ $\phantom{-}\frac{1}{28}e^{3} + \frac{1}{14}e^{2} - \frac{13}{14}e + \frac{2}{7}$
11 $[11, 11, -w^{2} + 2w + 4]$ $\phantom{-}\frac{1}{28}e^{3} + \frac{1}{14}e^{2} - \frac{13}{14}e + \frac{2}{7}$
11 $[11, 11, w - 2]$ $\phantom{-}\frac{1}{14}e^{3} + \frac{1}{7}e^{2} - \frac{20}{7}e - \frac{10}{7}$
16 $[16, 2, 2]$ $-\frac{1}{14}e^{3} - \frac{1}{7}e^{2} + \frac{13}{7}e - \frac{4}{7}$
19 $[19, 19, w^{2} - 2w - 5]$ $-\frac{1}{56}e^{3} - \frac{1}{28}e^{2} + \frac{27}{28}e - \frac{37}{14}$
19 $[19, 19, -w^{2} + 6]$ $\phantom{-}\frac{1}{56}e^{3} + \frac{1}{28}e^{2} - \frac{27}{28}e - \frac{47}{14}$
25 $[25, 5, -2w^{2} + 2w + 11]$ $\phantom{-}1$
29 $[29, 29, w]$ $-\frac{3}{56}e^{3} - \frac{3}{28}e^{2} + \frac{25}{28}e + \frac{29}{14}$
29 $[29, 29, 2w^{2} - w - 10]$ $\phantom{-}\frac{1}{4}e^{2} - \frac{19}{2}$
29 $[29, 29, -2w^{2} + 3w + 9]$ $-\frac{1}{14}e^{3} - \frac{11}{28}e^{2} + \frac{13}{7}e + \frac{41}{14}$
29 $[29, 29, w - 1]$ $-\frac{5}{56}e^{3} - \frac{5}{28}e^{2} + \frac{79}{28}e + \frac{39}{14}$
31 $[31, 31, w^{3} - 6w - 6]$ $-\frac{1}{2}e^{2} - e + 8$
31 $[31, 31, -w^{3} + 3w^{2} + 3w - 11]$ $\phantom{-}\frac{1}{14}e^{3} + \frac{9}{14}e^{2} - \frac{6}{7}e - \frac{108}{7}$
41 $[41, 41, w^{3} - 4w^{2} - 2w + 16]$ $-\frac{3}{28}e^{3} - \frac{5}{7}e^{2} + \frac{39}{14}e + \frac{99}{7}$
41 $[41, 41, w^{3} - 5w^{2} - 2w + 24]$ $\phantom{-}\frac{1}{28}e^{3} + \frac{4}{7}e^{2} - \frac{13}{14}e - \frac{75}{7}$
59 $[59, 59, w^{3} - w^{2} - 5w - 2]$ $-\frac{3}{56}e^{3} + \frac{1}{7}e^{2} + \frac{25}{28}e - \frac{52}{7}$
59 $[59, 59, 2w^{2} - w - 13]$ $-\frac{9}{56}e^{3} - \frac{4}{7}e^{2} + \frac{131}{28}e + \frac{40}{7}$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $-\frac{1}{2}e^{2} + e + 13$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}\frac{3}{14}e^{3} + \frac{13}{14}e^{2} - \frac{46}{7}e - \frac{93}{7}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$25$ $[25, 5, -2w^{2} + 2w + 11]$ $-1$