Base field 4.4.13525.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 12x^{2} + 8x + 29\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[25, 5, \frac{2}{5}w^{3} - \frac{14}{5}w - \frac{3}{5}]$ |
Dimension: | $6$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $27$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 2x^{5} - 18x^{4} + 30x^{3} + 85x^{2} - 84x - 100\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -w + 2]$ | $-1$ |
5 | $[5, 5, -\frac{3}{5}w^{3} - w^{2} + \frac{26}{5}w + \frac{42}{5}]$ | $-1$ |
9 | $[9, 3, \frac{2}{5}w^{3} - \frac{19}{5}w - \frac{3}{5}]$ | $\phantom{-}e$ |
9 | $[9, 3, -\frac{1}{5}w^{3} + \frac{2}{5}w + \frac{4}{5}]$ | $\phantom{-}e$ |
11 | $[11, 11, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{28}{5}]$ | $\phantom{-}\frac{1}{4}e^{5} + \frac{1}{4}e^{4} - \frac{15}{4}e^{3} - \frac{11}{4}e^{2} + 12e + 5$ |
11 | $[11, 11, \frac{1}{5}w^{3} - w^{2} - \frac{7}{5}w + \frac{36}{5}]$ | $\phantom{-}\frac{1}{4}e^{5} + \frac{1}{4}e^{4} - \frac{15}{4}e^{3} - \frac{11}{4}e^{2} + 12e + 5$ |
16 | $[16, 2, 2]$ | $\phantom{-}\frac{3}{4}e^{5} + \frac{5}{4}e^{4} - \frac{43}{4}e^{3} - \frac{63}{4}e^{2} + \frac{57}{2}e + 35$ |
29 | $[29, 29, -w]$ | $-\frac{1}{4}e^{5} - \frac{1}{4}e^{4} + \frac{11}{4}e^{3} + \frac{11}{4}e^{2} - 2e - 5$ |
29 | $[29, 29, \frac{1}{5}w^{3} - \frac{12}{5}w + \frac{1}{5}]$ | $-\frac{1}{4}e^{5} - \frac{1}{4}e^{4} + \frac{11}{4}e^{3} + \frac{11}{4}e^{2} - 2e - 5$ |
41 | $[41, 41, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{38}{5}]$ | $-\frac{1}{4}e^{5} - \frac{3}{4}e^{4} + \frac{11}{4}e^{3} + \frac{37}{4}e^{2} - 3e - 15$ |
41 | $[41, 41, -w^{2} + 10]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} + 8$ |
41 | $[41, 41, \frac{11}{5}w^{3} + 3w^{2} - \frac{102}{5}w - \frac{149}{5}]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} + 8$ |
41 | $[41, 41, -\frac{1}{5}w^{3} + w^{2} + \frac{7}{5}w - \frac{26}{5}]$ | $-\frac{1}{4}e^{5} - \frac{3}{4}e^{4} + \frac{11}{4}e^{3} + \frac{37}{4}e^{2} - 3e - 15$ |
49 | $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{19}{5}]$ | $-e^{5} - e^{4} + 14e^{3} + 12e^{2} - 35e - 20$ |
49 | $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{44}{5}]$ | $-e^{5} - e^{4} + 14e^{3} + 12e^{2} - 35e - 20$ |
59 | $[59, 59, -\frac{4}{5}w^{3} - w^{2} + \frac{33}{5}w + \frac{36}{5}]$ | $-\frac{1}{2}e^{5} - e^{4} + \frac{15}{2}e^{3} + 15e^{2} - 24e - 40$ |
59 | $[59, 59, -2w^{3} - 3w^{2} + 17w + 26]$ | $-\frac{1}{2}e^{5} - e^{4} + \frac{15}{2}e^{3} + 15e^{2} - 24e - 40$ |
61 | $[61, 61, -\frac{1}{5}w^{3} + w^{2} + \frac{12}{5}w - \frac{51}{5}]$ | $\phantom{-}\frac{5}{4}e^{5} + \frac{5}{4}e^{4} - \frac{71}{4}e^{3} - \frac{59}{4}e^{2} + 45e + 25$ |
61 | $[61, 61, \frac{4}{5}w^{3} + w^{2} - \frac{28}{5}w - \frac{41}{5}]$ | $\phantom{-}\frac{5}{4}e^{5} + \frac{5}{4}e^{4} - \frac{71}{4}e^{3} - \frac{59}{4}e^{2} + 45e + 25$ |
71 | $[71, 71, \frac{1}{5}w^{3} + w^{2} - \frac{7}{5}w - \frac{49}{5}]$ | $\phantom{-}e^{2} - 10$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, -w + 2]$ | $1$ |
$5$ | $[5, 5, -\frac{3}{5}w^{3} - w^{2} + \frac{26}{5}w + \frac{42}{5}]$ | $1$ |