Properties

Label 4.4.12197.1-25.2-c
Base field 4.4.12197.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 5, -w^{2} + w + 2]$
Dimension $6$
CM no
Base change no

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Base field 4.4.12197.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[25, 5, -w^{2} + w + 2]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $23$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} + 4x^{5} - 31x^{4} - 128x^{3} + 126x^{2} + 918x + 864\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $-1$
5 $[5, 5, -w + 2]$ $-1$
11 $[11, 11, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}e$
13 $[13, 13, w^{3} - w^{2} - 4w]$ $-\frac{19}{54}e^{5} - \frac{17}{27}e^{4} + \frac{667}{54}e^{3} + \frac{493}{27}e^{2} - \frac{767}{9}e - \frac{431}{3}$
16 $[16, 2, 2]$ $-\frac{25}{27}e^{5} - \frac{40}{27}e^{4} + \frac{871}{27}e^{3} + \frac{1115}{27}e^{2} - \frac{1933}{9}e - \frac{1003}{3}$
17 $[17, 17, -w^{2} + w + 3]$ $\phantom{-}\frac{17}{54}e^{5} + \frac{10}{27}e^{4} - \frac{593}{54}e^{3} - \frac{254}{27}e^{2} + \frac{640}{9}e + \frac{271}{3}$
19 $[19, 19, w^{3} - 5w]$ $-2e^{5} - \frac{10}{3}e^{4} + \frac{209}{3}e^{3} + \frac{280}{3}e^{2} - \frac{1399}{3}e - 744$
19 $[19, 19, -w + 3]$ $-\frac{37}{18}e^{5} - \frac{29}{9}e^{4} + \frac{1291}{18}e^{3} + \frac{802}{9}e^{2} - 479e - 731$
23 $[23, 23, 2w^{3} - 2w^{2} - 9w + 4]$ $-\frac{22}{27}e^{5} - \frac{37}{27}e^{4} + \frac{769}{27}e^{3} + \frac{1037}{27}e^{2} - \frac{1729}{9}e - \frac{910}{3}$
23 $[23, 23, w^{2} - 2]$ $-\frac{89}{54}e^{5} - \frac{73}{27}e^{4} + \frac{3095}{54}e^{3} + \frac{2027}{27}e^{2} - \frac{3439}{9}e - \frac{1801}{3}$
25 $[25, 5, w^{2} - 3]$ $-\frac{25}{27}e^{5} - \frac{40}{27}e^{4} + \frac{871}{27}e^{3} + \frac{1115}{27}e^{2} - \frac{1942}{9}e - \frac{1012}{3}$
37 $[37, 37, -w^{3} + 2w^{2} + 4w - 6]$ $-\frac{3}{2}e^{5} - \frac{7}{3}e^{4} + \frac{313}{6}e^{3} + \frac{193}{3}e^{2} - \frac{1036}{3}e - 525$
37 $[37, 37, -w^{3} + w^{2} + 6w - 4]$ $\phantom{-}\frac{61}{54}e^{5} + \frac{47}{27}e^{4} - \frac{2131}{54}e^{3} - \frac{1291}{27}e^{2} + \frac{2387}{9}e + \frac{1187}{3}$
41 $[41, 41, w^{2} - w - 5]$ $-\frac{68}{27}e^{5} - \frac{107}{27}e^{4} + \frac{2372}{27}e^{3} + \frac{2977}{27}e^{2} - \frac{5282}{9}e - \frac{2708}{3}$
47 $[47, 47, w^{3} - 6w + 1]$ $-\frac{5}{6}e^{5} - \frac{4}{3}e^{4} + \frac{173}{6}e^{3} + \frac{110}{3}e^{2} - 190e - 297$
61 $[61, 61, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}\frac{31}{27}e^{5} + \frac{46}{27}e^{4} - \frac{1075}{27}e^{3} - \frac{1244}{27}e^{2} + \frac{2350}{9}e + \frac{1150}{3}$
67 $[67, 67, 2w^{3} - w^{2} - 9w + 2]$ $\phantom{-}\frac{47}{18}e^{5} + \frac{40}{9}e^{4} - \frac{1637}{18}e^{3} - \frac{1118}{9}e^{2} + 611e + 979$
67 $[67, 67, w^{3} - 7w + 3]$ $\phantom{-}\frac{29}{18}e^{5} + \frac{22}{9}e^{4} - \frac{1007}{18}e^{3} - \frac{596}{9}e^{2} + 369e + 541$
73 $[73, 73, 2w^{3} - w^{2} - 9w]$ $-\frac{17}{27}e^{5} - \frac{29}{27}e^{4} + \frac{584}{27}e^{3} + \frac{787}{27}e^{2} - \frac{1274}{9}e - \frac{668}{3}$
81 $[81, 3, -3]$ $-\frac{1}{18}e^{5} + \frac{1}{9}e^{4} + \frac{37}{18}e^{3} - \frac{29}{9}e^{2} - \frac{41}{3}e - 1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w + 1]$ $1$
$5$ $[5, 5, -w + 2]$ $1$