Base field \(\Q(\zeta_{9})^+\)
Generator \(w\), with minimal polynomial \(x^{3} - 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[107,107,-4w^{2} + 2w + 7]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 2x^{3} - 9x^{2} + 18x - 3\) |
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Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w + 1]$ | $\phantom{-}e$ |
8 | $[8, 2, 2]$ | $-\frac{1}{2}e^{3} + 4e - \frac{3}{2}$ |
17 | $[17, 17, -2w^{2} + w + 3]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - \frac{11}{2}e$ |
17 | $[17, 17, -w^{2} - w + 3]$ | $\phantom{-}e^{3} - e^{2} - 9e + 6$ |
17 | $[17, 17, -w^{2} + 2w + 3]$ | $-\frac{1}{2}e^{2} - \frac{1}{2}e + \frac{3}{2}$ |
19 | $[19, 19, -2w^{2} + 2w + 5]$ | $\phantom{-}e^{3} - e^{2} - 9e + 8$ |
19 | $[19, 19, -2w^{2} + 3]$ | $-\frac{1}{2}e^{2} - \frac{1}{2}e + \frac{7}{2}$ |
19 | $[19, 19, -2w + 1]$ | $-e^{3} + 8e - 1$ |
37 | $[37, 37, -w^{2} + 3w + 3]$ | $\phantom{-}\frac{3}{2}e^{3} - \frac{1}{2}e^{2} - \frac{29}{2}e + 8$ |
37 | $[37, 37, 2w^{2} + w - 5]$ | $-e^{3} + e^{2} + 10e - 7$ |
37 | $[37, 37, 3w^{2} - 2w - 5]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{5}{2}e - 1$ |
53 | $[53, 53, -w - 4]$ | $-2e^{3} + e^{2} + 18e - 12$ |
53 | $[53, 53, -w^{2} + w - 2]$ | $-e^{3} + 2e^{2} + 12e - 15$ |
53 | $[53, 53, w^{2} - 6]$ | $\phantom{-}e^{3} - 2e^{2} - 10e + 9$ |
71 | $[71, 71, w^{2} + w - 7]$ | $-e^{3} - e^{2} + 10e + 6$ |
71 | $[71, 71, w^{2} - 2w - 7]$ | $\phantom{-}2e^{2} - e - 9$ |
71 | $[71, 71, -2w^{2} + w - 1]$ | $-e^{3} + e^{2} + 5e - 6$ |
73 | $[73, 73, 3w^{2} - 3w - 8]$ | $\phantom{-}e^{3} - 12e + 5$ |
73 | $[73, 73, 2w^{2} - 3w - 7]$ | $\phantom{-}e^{2} + 5$ |
73 | $[73, 73, w^{2} + 2w - 5]$ | $\phantom{-}e^{2} + 3e - 7$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$107$ | $[107,107,-4w^{2} + 2w + 7]$ | $-1$ |