Base field 4.4.4525.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 3x + 9\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[61, 61, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{2}{3}w + 4]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 2x^{5} - 15x^{4} - 40x^{3} - 20x^{2} + 12x + 7\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{7}{3}w + 4]$ | $\phantom{-}e$ |
| 5 | $[5, 5, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{1}{3}w + 3]$ | $-\frac{1}{2}e^{5} + 8e^{3} + 4e^{2} - \frac{13}{2}e + \frac{1}{2}$ |
| 9 | $[9, 3, -w]$ | $\phantom{-}4e^{5} + 3e^{4} - \frac{127}{2}e^{3} - \frac{161}{2}e^{2} + 16e + \frac{43}{2}$ |
| 9 | $[9, 3, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w + 1]$ | $\phantom{-}\frac{3}{2}e^{5} + \frac{1}{2}e^{4} - 24e^{3} - \frac{41}{2}e^{2} + 15e + 4$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{3}{2}e^{5} + e^{4} - 24e^{3} - 28e^{2} + \frac{17}{2}e + \frac{13}{2}$ |
| 19 | $[19, 19, \frac{2}{3}w^{3} - \frac{2}{3}w^{2} - \frac{11}{3}w]$ | $-\frac{11}{2}e^{5} - \frac{9}{2}e^{4} + 87e^{3} + \frac{233}{2}e^{2} - 15e - 33$ |
| 19 | $[19, 19, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{1}{3}w + 1]$ | $-\frac{9}{2}e^{5} - \frac{7}{2}e^{4} + \frac{143}{2}e^{3} + 93e^{2} - 20e - \frac{61}{2}$ |
| 31 | $[31, 31, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - 2]$ | $-e^{5} - e^{4} + 16e^{3} + 24e^{2} - 5e - 11$ |
| 31 | $[31, 31, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{5}{3}w + 5]$ | $-\frac{1}{2}e^{5} + e^{4} + \frac{17}{2}e^{3} - \frac{23}{2}e^{2} - \frac{41}{2}e + 4$ |
| 41 | $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 6]$ | $-\frac{21}{2}e^{5} - 7e^{4} + 167e^{3} + 197e^{2} - \frac{111}{2}e - \frac{107}{2}$ |
| 41 | $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 3]$ | $\phantom{-}\frac{11}{2}e^{5} + \frac{5}{2}e^{4} - \frac{175}{2}e^{3} - 85e^{2} + 41e + \frac{39}{2}$ |
| 61 | $[61, 61, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{2}{3}w + 4]$ | $\phantom{-}1$ |
| 61 | $[61, 61, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{14}{3}w - 2]$ | $-\frac{1}{2}e^{5} - e^{4} + 8e^{3} + 20e^{2} + \frac{3}{2}e - \frac{33}{2}$ |
| 71 | $[71, 71, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{1}{3}w - 7]$ | $\phantom{-}2e^{5} + e^{4} - 31e^{3} - 33e^{2} + 3e + 4$ |
| 71 | $[71, 71, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w]$ | $-\frac{19}{2}e^{5} - 6e^{4} + \frac{303}{2}e^{3} + \frac{349}{2}e^{2} - \frac{121}{2}e - 57$ |
| 89 | $[89, 89, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{10}{3}w - 3]$ | $\phantom{-}e^{5} + \frac{1}{2}e^{4} - 15e^{3} - \frac{35}{2}e^{2} - \frac{11}{2}e + \frac{3}{2}$ |
| 89 | $[89, 89, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ | $\phantom{-}6e^{5} + 3e^{4} - \frac{191}{2}e^{3} - \frac{193}{2}e^{2} + 38e + \frac{35}{2}$ |
| 101 | $[101, 101, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w - 3]$ | $\phantom{-}13e^{5} + 10e^{4} - 207e^{3} - 265e^{2} + 61e + 82$ |
| 101 | $[101, 101, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + \frac{11}{3}w - 4]$ | $\phantom{-}\frac{11}{2}e^{5} + \frac{7}{2}e^{4} - 88e^{3} - \frac{201}{2}e^{2} + 40e + 31$ |
| 101 | $[101, 101, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{8}{3}w + 3]$ | $-3e^{5} - 3e^{4} + \frac{97}{2}e^{3} + \frac{143}{2}e^{2} - 19e - \frac{63}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $61$ | $[61, 61, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{2}{3}w + 4]$ | $-1$ |