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: | $[25, 5, -\frac{1}{5}w^{3} + \frac{12}{5}w + \frac{4}{5}]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - x^{4} - 13x^{3} + 8x^{2} + 41x - 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -w + 2]$ | $\phantom{-}0$ |
5 | $[5, 5, -\frac{3}{5}w^{3} - w^{2} + \frac{26}{5}w + \frac{42}{5}]$ | $\phantom{-}e$ |
9 | $[9, 3, \frac{2}{5}w^{3} - \frac{19}{5}w - \frac{3}{5}]$ | $\phantom{-}\frac{3}{5}e^{4} + \frac{4}{5}e^{3} - \frac{23}{5}e^{2} - \frac{33}{5}e + \frac{11}{5}$ |
9 | $[9, 3, -\frac{1}{5}w^{3} + \frac{2}{5}w + \frac{4}{5}]$ | $-\frac{4}{5}e^{4} - \frac{7}{5}e^{3} + \frac{29}{5}e^{2} + \frac{59}{5}e + \frac{7}{5}$ |
11 | $[11, 11, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{28}{5}]$ | $-\frac{2}{5}e^{4} - \frac{1}{5}e^{3} + \frac{12}{5}e^{2} + \frac{12}{5}e + \frac{21}{5}$ |
11 | $[11, 11, \frac{1}{5}w^{3} - w^{2} - \frac{7}{5}w + \frac{36}{5}]$ | $-e^{4} - 2e^{3} + 8e^{2} + 15e$ |
16 | $[16, 2, 2]$ | $-\frac{1}{5}e^{4} + \frac{2}{5}e^{3} + \frac{11}{5}e^{2} - \frac{9}{5}e - \frac{22}{5}$ |
29 | $[29, 29, -w]$ | $\phantom{-}\frac{3}{5}e^{4} + \frac{9}{5}e^{3} - \frac{23}{5}e^{2} - \frac{68}{5}e + \frac{21}{5}$ |
29 | $[29, 29, \frac{1}{5}w^{3} - \frac{12}{5}w + \frac{1}{5}]$ | $-e^{4} + 8e^{2} + e - 6$ |
41 | $[41, 41, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{38}{5}]$ | $\phantom{-}\frac{8}{5}e^{4} + \frac{19}{5}e^{3} - \frac{63}{5}e^{2} - \frac{143}{5}e - \frac{9}{5}$ |
41 | $[41, 41, -w^{2} + 10]$ | $\phantom{-}e^{3} - 2e^{2} - 7e + 12$ |
41 | $[41, 41, \frac{11}{5}w^{3} + 3w^{2} - \frac{102}{5}w - \frac{149}{5}]$ | $\phantom{-}2e^{4} + e^{3} - 16e^{2} - 11e + 9$ |
41 | $[41, 41, -\frac{1}{5}w^{3} + w^{2} + \frac{7}{5}w - \frac{26}{5}]$ | $\phantom{-}\frac{1}{5}e^{4} - \frac{7}{5}e^{3} - \frac{16}{5}e^{2} + \frac{44}{5}e + \frac{57}{5}$ |
49 | $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{19}{5}]$ | $-\frac{2}{5}e^{4} - \frac{1}{5}e^{3} + \frac{22}{5}e^{2} + \frac{7}{5}e - \frac{34}{5}$ |
49 | $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{44}{5}]$ | $-e^{3} + 9e + 2$ |
59 | $[59, 59, -\frac{4}{5}w^{3} - w^{2} + \frac{33}{5}w + \frac{36}{5}]$ | $\phantom{-}\frac{7}{5}e^{4} + \frac{11}{5}e^{3} - \frac{67}{5}e^{2} - \frac{92}{5}e + \frac{69}{5}$ |
59 | $[59, 59, -2w^{3} - 3w^{2} + 17w + 26]$ | $-\frac{11}{5}e^{4} - \frac{28}{5}e^{3} + \frac{81}{5}e^{2} + \frac{216}{5}e + \frac{48}{5}$ |
61 | $[61, 61, -\frac{1}{5}w^{3} + w^{2} + \frac{12}{5}w - \frac{51}{5}]$ | $-\frac{12}{5}e^{4} - \frac{11}{5}e^{3} + \frac{97}{5}e^{2} + \frac{87}{5}e - \frac{59}{5}$ |
61 | $[61, 61, \frac{4}{5}w^{3} + w^{2} - \frac{28}{5}w - \frac{41}{5}]$ | $\phantom{-}\frac{1}{5}e^{4} - \frac{7}{5}e^{3} - \frac{11}{5}e^{2} + \frac{69}{5}e + \frac{37}{5}$ |
71 | $[71, 71, \frac{1}{5}w^{3} + w^{2} - \frac{7}{5}w - \frac{49}{5}]$ | $-\frac{4}{5}e^{4} - \frac{2}{5}e^{3} + \frac{34}{5}e^{2} + \frac{14}{5}e - \frac{18}{5}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, -w + 2]$ | $1$ |