Properties

Label 4.4.19821.1-25.2-c
Base field 4.4.19821.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 5, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 3]$
Dimension $35$
CM no
Base change no

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Base field 4.4.19821.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} + 6x + 3\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[25, 5, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 3]$
Dimension: $35$
CM: no
Base change: no
Newspace dimension: $67$

Hecke eigenvalues ($q$-expansion)

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

\(x^{35} - 7x^{34} - 49x^{33} + 438x^{32} + 873x^{31} - 12159x^{30} - 3795x^{29} + 198127x^{28} - 108631x^{27} - 2112297x^{26} + 2309881x^{25} + 15539422x^{24} - 23284783x^{23} - 81000905x^{22} + 149697296x^{21} + 301958442x^{20} - 665410338x^{19} - 799977672x^{18} + 2110382486x^{17} + 1464547490x^{16} - 4827132465x^{15} - 1713292096x^{14} + 7944938986x^{13} + 942191389x^{12} - 9279437589x^{11} + 477118093x^{10} + 7477617759x^{9} - 1321618554x^{8} - 3953154332x^{7} + 1070846692x^{6} + 1248226344x^{5} - 426807840x^{4} - 191392368x^{3} + 75079792x^{2} + 6754720x - 2652352\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 2w + 2]$ $...$
9 $[9, 3, w + 1]$ $...$
13 $[13, 13, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 5w]$ $...$
16 $[16, 2, 2]$ $...$
17 $[17, 17, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 3w + 5]$ $...$
19 $[19, 19, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w - 5]$ $...$
23 $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 2]$ $...$
25 $[25, 5, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w]$ $...$
25 $[25, 5, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 3]$ $-1$
29 $[29, 29, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 4w - 3]$ $...$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w]$ $...$
37 $[37, 37, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $...$
41 $[41, 41, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 4]$ $...$
43 $[43, 43, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w]$ $...$
47 $[47, 47, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w]$ $...$
59 $[59, 59, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 4]$ $...$
59 $[59, 59, \frac{4}{3}w^{3} - \frac{5}{3}w^{2} - 10w + 9]$ $...$
67 $[67, 67, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w]$ $...$
71 $[71, 71, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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