Base field 4.4.2624.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 3x^{2} + 2x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[49, 7, w^{2} - 4w - 1]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 3x^{4} - 14x^{3} + 38x^{2} + 17x - 35\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{3} - 2w^{2} - 2w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{3} + 3w^{2} + w - 3]$ | $\phantom{-}\frac{1}{11}e^{4} - \frac{5}{22}e^{3} - \frac{25}{22}e^{2} + \frac{47}{22}e + \frac{41}{22}$ |
| 7 | $[7, 7, -w^{2} + w + 2]$ | $\phantom{-}\frac{1}{11}e^{4} - \frac{5}{22}e^{3} - \frac{25}{22}e^{2} + \frac{47}{22}e + \frac{41}{22}$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} - 3]$ | $-\frac{1}{11}e^{4} - \frac{3}{11}e^{3} + \frac{18}{11}e^{2} + \frac{37}{11}e - \frac{37}{11}$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 4w]$ | $-\frac{1}{11}e^{4} - \frac{3}{11}e^{3} + \frac{18}{11}e^{2} + \frac{37}{11}e - \frac{37}{11}$ |
| 25 | $[25, 5, -w^{3} + 3w^{2} + 2w - 2]$ | $-\frac{1}{22}e^{4} + \frac{4}{11}e^{3} - \frac{2}{11}e^{2} - \frac{42}{11}e + \frac{117}{22}$ |
| 25 | $[25, 5, -2w^{3} + 4w^{2} + 5w - 1]$ | $-\frac{1}{22}e^{4} + \frac{4}{11}e^{3} - \frac{2}{11}e^{2} - \frac{42}{11}e + \frac{117}{22}$ |
| 41 | $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ | $\phantom{-}\frac{5}{11}e^{4} - \frac{7}{11}e^{3} - \frac{79}{11}e^{2} + \frac{57}{11}e + \frac{152}{11}$ |
| 47 | $[47, 47, -2w^{3} + 5w^{2} + 4w - 4]$ | $\phantom{-}\frac{3}{11}e^{4} - \frac{2}{11}e^{3} - \frac{43}{11}e^{2} + \frac{21}{11}e + \frac{23}{11}$ |
| 47 | $[47, 47, 2w^{3} - 4w^{2} - 5w]$ | $\phantom{-}\frac{3}{11}e^{4} - \frac{2}{11}e^{3} - \frac{43}{11}e^{2} + \frac{21}{11}e + \frac{23}{11}$ |
| 49 | $[49, 7, w^{2} - 4w - 1]$ | $-1$ |
| 71 | $[71, 71, 2w - 3]$ | $-\frac{5}{11}e^{4} + \frac{7}{11}e^{3} + \frac{57}{11}e^{2} - \frac{57}{11}e + \frac{2}{11}$ |
| 71 | $[71, 71, -w^{3} + w^{2} + 6w - 2]$ | $-\frac{5}{11}e^{4} + \frac{7}{11}e^{3} + \frac{57}{11}e^{2} - \frac{57}{11}e + \frac{2}{11}$ |
| 73 | $[73, 73, -w^{3} + 3w^{2} + 3w - 5]$ | $-\frac{4}{11}e^{4} + \frac{10}{11}e^{3} + \frac{61}{11}e^{2} - \frac{138}{11}e - \frac{71}{11}$ |
| 73 | $[73, 73, 2w^{3} - 5w^{2} - 5w + 4]$ | $-\frac{4}{11}e^{4} + \frac{10}{11}e^{3} + \frac{61}{11}e^{2} - \frac{138}{11}e - \frac{71}{11}$ |
| 73 | $[73, 73, -w^{3} + 3w^{2} - 5]$ | $\phantom{-}\frac{3}{22}e^{4} + \frac{9}{22}e^{3} - \frac{43}{22}e^{2} - \frac{155}{22}e + \frac{39}{11}$ |
| 73 | $[73, 73, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}\frac{3}{22}e^{4} + \frac{9}{22}e^{3} - \frac{43}{22}e^{2} - \frac{155}{22}e + \frac{39}{11}$ |
| 79 | $[79, 79, 2w^{3} - 3w^{2} - 6w + 2]$ | $-\frac{9}{22}e^{4} + \frac{3}{11}e^{3} + \frac{81}{11}e^{2} - \frac{15}{11}e - \frac{465}{22}$ |
| 79 | $[79, 79, 2w^{3} - 3w^{2} - 5w]$ | $-\frac{9}{22}e^{4} + \frac{3}{11}e^{3} + \frac{81}{11}e^{2} - \frac{15}{11}e - \frac{465}{22}$ |
| 81 | $[81, 3, -3]$ | $-\frac{6}{11}e^{4} + \frac{15}{11}e^{3} + \frac{86}{11}e^{2} - \frac{141}{11}e - \frac{68}{11}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $49$ | $[49, 7, w^{2} - 4w - 1]$ | $1$ |