Base field 4.4.14725.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 13x^{2} + 11x + 31\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[19, 19, w + 2]$ |
| Dimension: | $5$ |
| 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:
| \(x^{5} + 7x^{4} - 64x^{2} - 93x - 19\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{11}{3}w + \frac{11}{3}]$ | $\phantom{-}\frac{1}{12}e^{4} + \frac{1}{2}e^{3} - \frac{1}{6}e^{2} - \frac{25}{6}e - \frac{21}{4}$ |
| 9 | $[9, 3, w - 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{5}{3}w + \frac{8}{3}]$ | $-\frac{1}{4}e^{4} - \frac{7}{6}e^{3} + \frac{5}{2}e^{2} + \frac{59}{6}e + \frac{37}{12}$ |
| 11 | $[11, 11, \frac{2}{3}w^{3} + \frac{2}{3}w^{2} - \frac{19}{3}w - \frac{13}{3}]$ | $\phantom{-}\frac{1}{12}e^{4} + \frac{1}{2}e^{3} - \frac{2}{3}e^{2} - \frac{31}{6}e - \frac{19}{4}$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{1}{6}e^{4} + \frac{5}{6}e^{3} - \frac{4}{3}e^{2} - \frac{15}{2}e - \frac{31}{6}$ |
| 19 | $[19, 19, w + 2]$ | $\phantom{-}1$ |
| 25 | $[25, 5, -\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{16}{3}w + \frac{13}{3}]$ | $\phantom{-}\frac{1}{6}e^{4} + \frac{5}{6}e^{3} - \frac{4}{3}e^{2} - \frac{13}{2}e - \frac{31}{6}$ |
| 29 | $[29, 29, -\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{19}{3}w + \frac{19}{3}]$ | $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{2}e^{2} - \frac{17}{6}e - \frac{17}{6}$ |
| 29 | $[29, 29, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{5}{3}w + \frac{14}{3}]$ | $-\frac{5}{12}e^{4} - \frac{13}{6}e^{3} + \frac{23}{6}e^{2} + \frac{115}{6}e + \frac{103}{12}$ |
| 29 | $[29, 29, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - \frac{8}{3}]$ | $\phantom{-}\frac{1}{12}e^{4} + \frac{1}{2}e^{3} - \frac{2}{3}e^{2} - \frac{37}{6}e - \frac{23}{4}$ |
| 29 | $[29, 29, w - 1]$ | $\phantom{-}\frac{1}{4}e^{4} + e^{3} - 3e^{2} - 7e + \frac{11}{4}$ |
| 31 | $[31, 31, w]$ | $-\frac{1}{6}e^{3} - e^{2} + \frac{5}{6}e + \frac{13}{3}$ |
| 31 | $[31, 31, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - \frac{8}{3}w + \frac{13}{3}]$ | $-\frac{5}{12}e^{4} - \frac{7}{3}e^{3} + \frac{17}{6}e^{2} + 21e + \frac{179}{12}$ |
| 31 | $[31, 31, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{11}{3}w + \frac{5}{3}]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{8}{3}e^{3} - 4e^{2} - \frac{70}{3}e - \frac{71}{6}$ |
| 41 | $[41, 41, \frac{1}{3}w^{3} + \frac{4}{3}w^{2} - \frac{8}{3}w - \frac{20}{3}]$ | $-\frac{1}{4}e^{4} - \frac{4}{3}e^{3} + \frac{3}{2}e^{2} + \frac{32}{3}e + \frac{101}{12}$ |
| 41 | $[41, 41, \frac{2}{3}w^{3} + \frac{5}{3}w^{2} - \frac{16}{3}w - \frac{40}{3}]$ | $\phantom{-}\frac{5}{12}e^{4} + \frac{13}{6}e^{3} - \frac{23}{6}e^{2} - \frac{127}{6}e - \frac{103}{12}$ |
| 49 | $[49, 7, -\frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{8}{3}w + \frac{38}{3}]$ | $\phantom{-}\frac{1}{6}e^{4} + e^{3} - \frac{4}{3}e^{2} - \frac{25}{3}e + \frac{7}{2}$ |
| 49 | $[49, 7, \frac{2}{3}w^{3} + \frac{5}{3}w^{2} - \frac{16}{3}w - \frac{43}{3}]$ | $-2e - 7$ |
| 59 | $[59, 59, \frac{5}{3}w^{3} + \frac{8}{3}w^{2} - \frac{40}{3}w - \frac{49}{3}]$ | $-\frac{1}{3}e^{4} - \frac{4}{3}e^{3} + \frac{14}{3}e^{2} + \frac{40}{3}e - \frac{13}{3}$ |
| 59 | $[59, 59, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - \frac{16}{3}w + \frac{11}{3}]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{5}{6}e^{3} - \frac{9}{2}e^{2} - \frac{43}{6}e + \frac{103}{12}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, w + 2]$ | $-1$ |