Base field 5.5.170701.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 4x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[28, 14, w^{4} - 2w^{3} - 5w^{2} + 4w + 3]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $29$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - x^{6} - 25x^{5} - x^{4} + 131x^{3} + 97x^{2} + 21x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{4} + w^{3} + 6w^{2} - w - 3]$ | $-1$ |
| 7 | $[7, 7, w^{4} - w^{3} - 6w^{2} + w + 2]$ | $-1$ |
| 8 | $[8, 2, -2w^{4} + 3w^{3} + 10w^{2} - 5w - 3]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{4} - w^{3} - 6w^{2} + 2]$ | $\phantom{-}\frac{7}{2}e^{6} - \frac{19}{4}e^{5} - \frac{343}{4}e^{4} + 27e^{3} + 448e^{2} + \frac{723}{4}e + \frac{37}{4}$ |
| 13 | $[13, 13, -w^{4} + 2w^{3} + 5w^{2} - 5w - 3]$ | $\phantom{-}\frac{13}{4}e^{6} - \frac{17}{4}e^{5} - 80e^{4} + \frac{43}{2}e^{3} + \frac{1679}{4}e^{2} + \frac{743}{4}e + 12$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $-\frac{11}{4}e^{6} + \frac{7}{2}e^{5} + \frac{271}{4}e^{4} - \frac{31}{2}e^{3} - \frac{1423}{4}e^{2} - 172e - \frac{45}{4}$ |
| 23 | $[23, 23, -w + 2]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{3}{4}e^{5} - \frac{49}{4}e^{4} + 6e^{3} + 65e^{2} + \frac{47}{4}e - \frac{25}{4}$ |
| 31 | $[31, 31, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ | $-\frac{15}{4}e^{6} + \frac{11}{2}e^{5} + \frac{365}{4}e^{4} - \frac{77}{2}e^{3} - \frac{1903}{4}e^{2} - 147e + \frac{9}{4}$ |
| 43 | $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ | $-10e^{6} + \frac{53}{4}e^{5} + \frac{983}{4}e^{4} - 70e^{3} - \frac{2575}{2}e^{2} - \frac{2201}{4}e - \frac{157}{4}$ |
| 47 | $[47, 47, -w^{4} + 2w^{3} + 5w^{2} - 4w - 4]$ | $-\frac{5}{2}e^{6} + \frac{7}{2}e^{5} + 61e^{4} - 22e^{3} - \frac{633}{2}e^{2} - \frac{227}{2}e - 10$ |
| 53 | $[53, 53, w^{2} - w - 4]$ | $\phantom{-}4e^{6} - \frac{11}{2}e^{5} - 98e^{4} + 33e^{3} + 513e^{2} + \frac{381}{2}e + 5$ |
| 53 | $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 4w - 3]$ | $-8e^{6} + \frac{21}{2}e^{5} + \frac{393}{2}e^{4} - 53e^{3} - 1027e^{2} - \frac{915}{2}e - \frac{79}{2}$ |
| 53 | $[53, 53, -w^{3} + w^{2} + 4w - 1]$ | $\phantom{-}2e^{6} - \frac{5}{2}e^{5} - \frac{99}{2}e^{4} + 11e^{3} + 260e^{2} + \frac{243}{2}e + \frac{31}{2}$ |
| 71 | $[71, 71, w^{4} - w^{3} - 7w^{2} + 3w + 6]$ | $-e^{6} + e^{5} + 25e^{4} + e^{3} - 131e^{2} - 98e - 21$ |
| 71 | $[71, 71, -2w^{4} + 2w^{3} + 11w^{2} - 2]$ | $-e^{6} + \frac{3}{2}e^{5} + \frac{49}{2}e^{4} - 12e^{3} - 129e^{2} - \frac{51}{2}e + \frac{7}{2}$ |
| 71 | $[71, 71, -w^{4} + 3w^{3} + 3w^{2} - 9w - 1]$ | $\phantom{-}\frac{15}{4}e^{6} - \frac{21}{4}e^{5} - \frac{183}{2}e^{4} + \frac{65}{2}e^{3} + \frac{1901}{4}e^{2} + \frac{703}{4}e + \frac{19}{2}$ |
| 73 | $[73, 73, 2w^{4} - 4w^{3} - 9w^{2} + 10w + 5]$ | $-\frac{15}{4}e^{6} + \frac{23}{4}e^{5} + 91e^{4} - \frac{91}{2}e^{3} - \frac{1897}{4}e^{2} - \frac{421}{4}e + 10$ |
| 79 | $[79, 79, 2w^{4} - 3w^{3} - 11w^{2} + 4w + 8]$ | $\phantom{-}\frac{41}{4}e^{6} - \frac{27}{2}e^{5} - \frac{1007}{4}e^{4} + \frac{137}{2}e^{3} + \frac{5269}{4}e^{2} + 589e + \frac{193}{4}$ |
| 83 | $[83, 83, -3w^{4} + 5w^{3} + 15w^{2} - 9w - 10]$ | $\phantom{-}\frac{51}{4}e^{6} - \frac{33}{2}e^{5} - \frac{1255}{4}e^{4} + \frac{159}{2}e^{3} + \frac{6575}{4}e^{2} + 751e + \frac{237}{4}$ |
| 89 | $[89, 89, w^{3} - w^{2} - 5w + 1]$ | $\phantom{-}\frac{23}{4}e^{6} - 8e^{5} - \frac{563}{4}e^{4} + \frac{99}{2}e^{3} + \frac{2947}{4}e^{2} + \frac{537}{2}e + \frac{41}{4}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w^{4} + w^{3} + 6w^{2} - w - 3]$ | $1$ |
| $7$ | $[7, 7, w^{4} - w^{3} - 6w^{2} + w + 2]$ | $1$ |