Base field \(\Q(\sqrt{113}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 28\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[1, 1, 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + x^{3} - 5x^{2} - 4x + 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 6]$ | $\phantom{-}e$ |
2 | $[2, 2, w + 5]$ | $\phantom{-}e$ |
7 | $[7, 7, 6w - 35]$ | $-e^{2} - e + 2$ |
7 | $[7, 7, -6w - 29]$ | $-e^{2} - e + 2$ |
9 | $[9, 3, 3]$ | $\phantom{-}e^{3} - e^{2} - 4e + 4$ |
11 | $[11, 11, 4w + 19]$ | $\phantom{-}e^{3} - e^{2} - 3e + 3$ |
11 | $[11, 11, 4w - 23]$ | $\phantom{-}e^{3} - e^{2} - 3e + 3$ |
13 | $[13, 13, -2w + 11]$ | $-e^{3} + e^{2} + 5e - 1$ |
13 | $[13, 13, 2w + 9]$ | $-e^{3} + e^{2} + 5e - 1$ |
25 | $[25, 5, -5]$ | $-3e^{3} + 11e + 2$ |
31 | $[31, 31, 2w - 13]$ | $\phantom{-}e^{3} + e^{2} - 6e - 4$ |
31 | $[31, 31, -2w - 11]$ | $\phantom{-}e^{3} + e^{2} - 6e - 4$ |
41 | $[41, 41, -8w - 39]$ | $\phantom{-}2e^{3} + 2e^{2} - 9e - 3$ |
41 | $[41, 41, 8w - 47]$ | $\phantom{-}2e^{3} + 2e^{2} - 9e - 3$ |
53 | $[53, 53, -26w - 125]$ | $-4e^{3} + 17e + 3$ |
53 | $[53, 53, 26w - 151]$ | $-4e^{3} + 17e + 3$ |
61 | $[61, 61, -14w + 81]$ | $-e^{2} - 2e + 5$ |
61 | $[61, 61, -14w - 67]$ | $-e^{2} - 2e + 5$ |
83 | $[83, 83, 2w - 15]$ | $-e^{3} + 6e^{2} + 6e - 15$ |
83 | $[83, 83, -2w - 13]$ | $-e^{3} + 6e^{2} + 6e - 15$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).