Base field 4.4.11525.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} + 5x + 25\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[25,5,\frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 2x^{3} - 10x^{2} + 15x - 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ | $\phantom{-}e$ |
5 | $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ | $\phantom{-}0$ |
11 | $[11, 11, w + 1]$ | $\phantom{-}\frac{2}{5}e^{3} - \frac{1}{5}e^{2} - \frac{19}{5}e - \frac{6}{5}$ |
11 | $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ | $-\frac{3}{5}e^{3} + \frac{4}{5}e^{2} + \frac{31}{5}e - \frac{36}{5}$ |
16 | $[16, 2, 2]$ | $\phantom{-}\frac{2}{5}e^{3} - \frac{6}{5}e^{2} - \frac{24}{5}e + \frac{34}{5}$ |
19 | $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ | $\phantom{-}\frac{6}{5}e^{3} - \frac{8}{5}e^{2} - \frac{67}{5}e + \frac{52}{5}$ |
19 | $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ | $\phantom{-}\frac{3}{5}e^{3} - \frac{4}{5}e^{2} - \frac{31}{5}e + \frac{1}{5}$ |
19 | $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ | $-\frac{3}{5}e^{3} + \frac{4}{5}e^{2} + \frac{26}{5}e - \frac{26}{5}$ |
19 | $[19, 19, w - 1]$ | $-\frac{3}{5}e^{3} + \frac{4}{5}e^{2} + \frac{31}{5}e - \frac{26}{5}$ |
29 | $[29, 29, w^{2} - w - 8]$ | $-\frac{8}{5}e^{3} + \frac{9}{5}e^{2} + \frac{96}{5}e - \frac{66}{5}$ |
29 | $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ | $-\frac{3}{5}e^{3} - \frac{1}{5}e^{2} + \frac{31}{5}e + \frac{24}{5}$ |
31 | $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ | $\phantom{-}\frac{2}{5}e^{3} - \frac{6}{5}e^{2} - \frac{14}{5}e + \frac{34}{5}$ |
31 | $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ | $-\frac{2}{5}e^{3} + \frac{6}{5}e^{2} + \frac{14}{5}e - \frac{29}{5}$ |
61 | $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ | $\phantom{-}\frac{4}{5}e^{3} - \frac{2}{5}e^{2} - \frac{63}{5}e + \frac{13}{5}$ |
61 | $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ | $\phantom{-}\frac{3}{5}e^{3} - \frac{9}{5}e^{2} - \frac{16}{5}e + \frac{46}{5}$ |
61 | $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ | $\phantom{-}2e^{3} - 2e^{2} - 21e + 14$ |
61 | $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ | $-\frac{11}{5}e^{3} + \frac{13}{5}e^{2} + \frac{102}{5}e - \frac{47}{5}$ |
71 | $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ | $\phantom{-}\frac{12}{5}e^{3} - \frac{16}{5}e^{2} - \frac{139}{5}e + \frac{99}{5}$ |
71 | $[71, 71, w^{2} - 8]$ | $\phantom{-}e^{3} - e^{2} - 10e$ |
79 | $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ | $\phantom{-}\frac{1}{5}e^{3} + \frac{2}{5}e^{2} - \frac{32}{5}e - \frac{38}{5}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5,5,\frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ | $-1$ |