Base field 4.4.8789.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 6 x^2 - 2 x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[29, 29, w^3 - 2 w^2 - 5 w]$ |
| Dimension: | $7$ |
| 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:
| \(x^7 + 6 x^6 - 50 x^4 - 43 x^3 + 119 x^2 + 81 x - 115\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^3 + 2 w^2 + 3 w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 1]$ | $-e^6 - 5 e^5 + 2 e^4 + 34 e^3 + 20 e^2 - 40 e - 17$ |
| 11 | $[11, 11, -w^3 + 2 w^2 + 4 w]$ | $-2 e^6 - 8 e^5 + 14 e^4 + 63 e^3 - 32 e^2 - 110 e + 70$ |
| 13 | $[13, 13, -2 w^3 + 3 w^2 + 10 w - 2]$ | $-e^6 - 3 e^5 + 13 e^4 + 31 e^3 - 61 e^2 - 80 e + 104$ |
| 16 | $[16, 2, 2]$ | $-e^5 - 4 e^4 + 5 e^3 + 26 e^2 - 29$ |
| 17 | $[17, 17, -w^3 + 2 w^2 + 5 w - 3]$ | $\phantom{-}e^6 + 4 e^5 - 7 e^4 - 31 e^3 + 17 e^2 + 51 e - 38$ |
| 17 | $[17, 17, -w^3 + w^2 + 5 w]$ | $\phantom{-}e^6 + 5 e^5 - 2 e^4 - 34 e^3 - 20 e^2 + 40 e + 15$ |
| 17 | $[17, 17, -w^2 + 2 w + 1]$ | $\phantom{-}e^6 + 4 e^5 - 7 e^4 - 32 e^3 + 16 e^2 + 59 e - 37$ |
| 19 | $[19, 19, w^2 - w - 2]$ | $-2 e^6 - 6 e^5 + 24 e^4 + 57 e^3 - 105 e^2 - 133 e + 175$ |
| 29 | $[29, 29, w^3 - 2 w^2 - 5 w]$ | $\phantom{-}1$ |
| 29 | $[29, 29, w^2 - w - 3]$ | $\phantom{-}4 e^6 + 17 e^5 - 24 e^4 - 131 e^3 + 37 e^2 + 218 e - 110$ |
| 31 | $[31, 31, -w^3 + 2 w^2 + 3 w - 2]$ | $\phantom{-}3 e^6 + 12 e^5 - 23 e^4 - 99 e^3 + 66 e^2 + 186 e - 147$ |
| 43 | $[43, 43, 2 w^3 - 3 w^2 - 11 w]$ | $\phantom{-}e^6 + 4 e^5 - 9 e^4 - 36 e^3 + 36 e^2 + 80 e - 83$ |
| 47 | $[47, 47, w^3 - 7 w - 4]$ | $-2 e^6 - 7 e^5 + 19 e^4 + 60 e^3 - 67 e^2 - 118 e + 118$ |
| 53 | $[53, 53, -2 w^3 + 3 w^2 + 9 w - 1]$ | $\phantom{-}e^6 + 3 e^5 - 12 e^4 - 28 e^3 + 50 e^2 + 61 e - 72$ |
| 61 | $[61, 61, -w - 3]$ | $-7 e^6 - 25 e^5 + 65 e^4 + 214 e^3 - 227 e^2 - 430 e + 408$ |
| 73 | $[73, 73, -w^3 + 2 w^2 + 3 w - 3]$ | $\phantom{-}2 e^6 + 6 e^5 - 23 e^4 - 54 e^3 + 97 e^2 + 119 e - 163$ |
| 73 | $[73, 73, w^3 - w^2 - 7 w - 1]$ | $\phantom{-}2 e^6 + 7 e^5 - 18 e^4 - 57 e^3 + 60 e^2 + 105 e - 105$ |
| 81 | $[81, 3, -3]$ | $-e^6 - 3 e^5 + 13 e^4 + 31 e^3 - 63 e^2 - 82 e + 109$ |
| 83 | $[83, 83, -2 w^3 + 3 w^2 + 9 w + 1]$ | $\phantom{-}4 e^6 + 10 e^5 - 59 e^4 - 111 e^3 + 287 e^2 + 301 e - 457$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, w^3 - 2 w^2 - 5 w]$ | $-1$ |