Properties

Label 4.4.14725.1-25.1-e
Base field 4.4.14725.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 5, -\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{16}{3}w + \frac{13}{3}]$
Dimension $6$
CM no
Base change no

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Base field 4.4.14725.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 13x^{2} + 11x + 31\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[25, 5, -\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{16}{3}w + \frac{13}{3}]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $38$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 12x^{4} + 41x^{2} - 40\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{11}{3}w + \frac{11}{3}]$ $-\frac{1}{2}e^{5} + 4e^{3} - \frac{11}{2}e$
9 $[9, 3, w - 2]$ $\phantom{-}e$
11 $[11, 11, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{5}{3}w + \frac{8}{3}]$ $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + \frac{23}{2}e$
11 $[11, 11, \frac{2}{3}w^{3} + \frac{2}{3}w^{2} - \frac{19}{3}w - \frac{13}{3}]$ $\phantom{-}e^{3} - 5e$
16 $[16, 2, 2]$ $\phantom{-}e^{4} - 9e^{2} + 13$
19 $[19, 19, w + 2]$ $-\frac{1}{2}e^{5} + 4e^{3} - \frac{13}{2}e$
25 $[25, 5, -\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{16}{3}w + \frac{13}{3}]$ $\phantom{-}1$
29 $[29, 29, -\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{19}{3}w + \frac{19}{3}]$ $\phantom{-}2e^{4} - 17e^{2} + 30$
29 $[29, 29, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{5}{3}w + \frac{14}{3}]$ $\phantom{-}e^{2} - 10$
29 $[29, 29, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - \frac{8}{3}]$ $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + \frac{15}{2}e$
29 $[29, 29, w - 1]$ $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + \frac{23}{2}e$
31 $[31, 31, w]$ $\phantom{-}\frac{1}{2}e^{5} - 4e^{3} + \frac{5}{2}e$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - \frac{8}{3}w + \frac{13}{3}]$ $-2e^{4} + 18e^{2} - 32$
31 $[31, 31, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{11}{3}w + \frac{5}{3}]$ $-e^{5} + 10e^{3} - 19e$
41 $[41, 41, \frac{1}{3}w^{3} + \frac{4}{3}w^{2} - \frac{8}{3}w - \frac{20}{3}]$ $-e^{2} - 2$
41 $[41, 41, \frac{2}{3}w^{3} + \frac{5}{3}w^{2} - \frac{16}{3}w - \frac{40}{3}]$ $-2e^{4} + 19e^{2} - 32$
49 $[49, 7, -\frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{8}{3}w + \frac{38}{3}]$ $\phantom{-}2e^{4} - 21e^{2} + 40$
49 $[49, 7, \frac{2}{3}w^{3} + \frac{5}{3}w^{2} - \frac{16}{3}w - \frac{43}{3}]$ $-2e^{4} + 17e^{2} - 30$
59 $[59, 59, \frac{5}{3}w^{3} + \frac{8}{3}w^{2} - \frac{40}{3}w - \frac{49}{3}]$ $\phantom{-}e^{4} - 7e^{2}$
59 $[59, 59, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - \frac{16}{3}w + \frac{11}{3}]$ $-3e^{4} + 25e^{2} - 40$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$25$ $[25, 5, -\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{16}{3}w + \frac{13}{3}]$ $-1$