Base field \(\Q(\sqrt{109}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 27\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[1, 1, 1]$ |
Dimension: | $3$ |
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:
\(x^{3} + 2x^{2} - 3x - 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w + 6]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 5]$ | $\phantom{-}e$ |
4 | $[4, 2, 2]$ | $-e^{2} - 2e + 2$ |
5 | $[5, 5, -3w + 17]$ | $\phantom{-}e + 2$ |
5 | $[5, 5, -3w - 14]$ | $\phantom{-}e + 2$ |
7 | $[7, 7, w - 5]$ | $-e^{2} - e + 1$ |
7 | $[7, 7, w + 4]$ | $-e^{2} - e + 1$ |
29 | $[29, 29, -w - 7]$ | $\phantom{-}2e^{2} + e - 6$ |
29 | $[29, 29, -w + 8]$ | $\phantom{-}2e^{2} + e - 6$ |
31 | $[31, 31, -5w + 28]$ | $\phantom{-}e + 1$ |
31 | $[31, 31, -5w - 23]$ | $\phantom{-}e + 1$ |
43 | $[43, 43, 6w + 29]$ | $\phantom{-}e^{2} + 1$ |
43 | $[43, 43, -6w + 35]$ | $\phantom{-}e^{2} + 1$ |
61 | $[61, 61, 3w - 19]$ | $-2e^{2} - 4e + 2$ |
61 | $[61, 61, -3w - 16]$ | $-2e^{2} - 4e + 2$ |
71 | $[71, 71, -7w - 34]$ | $-5e^{2} - 5e + 10$ |
71 | $[71, 71, 7w - 41]$ | $-5e^{2} - 5e + 10$ |
73 | $[73, 73, 2w - 7]$ | $-3e^{2} + 14$ |
73 | $[73, 73, -2w - 5]$ | $-3e^{2} + 14$ |
83 | $[83, 83, -w - 10]$ | $\phantom{-}e^{2} - 13$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).