Base field \(\Q(\sqrt{221}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 55\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[5, 5, w]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} + 2x^{2} - x - 1\) |
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Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w]$ | $\phantom{-}1$ |
5 | $[5, 5, w + 4]$ | $\phantom{-}e + 2$ |
7 | $[7, 7, w + 2]$ | $\phantom{-}2e^{2} + 3e - 4$ |
7 | $[7, 7, w + 4]$ | $-2e^{2} - 5e + 1$ |
9 | $[9, 3, 3]$ | $-2e^{2} - 4e + 2$ |
11 | $[11, 11, w]$ | $-2e^{2} - 3e + 2$ |
11 | $[11, 11, w + 10]$ | $\phantom{-}4e^{2} + 4e - 5$ |
13 | $[13, 13, w + 6]$ | $\phantom{-}e^{2} + 3e - 2$ |
17 | $[17, 17, -w - 8]$ | $\phantom{-}e$ |
31 | $[31, 31, w + 14]$ | $-e - 2$ |
31 | $[31, 31, w + 16]$ | $-e^{2} - 4e$ |
37 | $[37, 37, w + 15]$ | $-e^{2} + 4e + 3$ |
37 | $[37, 37, w + 21]$ | $\phantom{-}5e^{2} + 6e - 10$ |
41 | $[41, 41, w + 18]$ | $-5e^{2} - 10e + 1$ |
41 | $[41, 41, w + 22]$ | $-3e^{2} - 5e + 1$ |
43 | $[43, 43, -w - 3]$ | $\phantom{-}e^{2} - e - 12$ |
43 | $[43, 43, w - 4]$ | $-2e^{2} + 6$ |
53 | $[53, 53, -w - 1]$ | $\phantom{-}e^{2} + 2e + 2$ |
53 | $[53, 53, w - 2]$ | $-2e^{2} + 3e + 7$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, w]$ | $-1$ |