Base field 3.3.733.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 8\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[16, 4, w^{2} - w - 3]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} + x^{7} - 13x^{6} - 9x^{5} + 50x^{4} + 17x^{3} - 47x^{2} + 3x + 1\) |
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Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 2]$ | $\phantom{-}e$ |
4 | $[4, 2, -w^{2} - w + 5]$ | $\phantom{-}0$ |
5 | $[5, 5, -w + 3]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{11}{2}e^{5} + 16e^{3} + \frac{3}{2}e^{2} - 9e + \frac{1}{2}$ |
7 | $[7, 7, -w^{2} - 2w + 3]$ | $\phantom{-}e^{6} - e^{5} - 9e^{4} + 9e^{3} + 16e^{2} - 12e$ |
11 | $[11, 11, -w^{2} + 5]$ | $-e^{5} + 8e^{3} - e^{2} - 11e + 1$ |
13 | $[13, 13, w + 1]$ | $\phantom{-}\frac{1}{2}e^{7} + e^{6} - \frac{13}{2}e^{5} - 10e^{4} + 25e^{3} + \frac{47}{2}e^{2} - 21e - \frac{5}{2}$ |
23 | $[23, 23, w^{2} - 3]$ | $\phantom{-}2e^{6} - 3e^{5} - 19e^{4} + 25e^{3} + 37e^{2} - 30e - 4$ |
25 | $[25, 5, w^{2} + 2w - 1]$ | $-\frac{1}{2}e^{7} - e^{6} + \frac{15}{2}e^{5} + 9e^{4} - 34e^{3} - \frac{33}{2}e^{2} + 37e + \frac{5}{2}$ |
27 | $[27, 3, -3]$ | $-e^{6} + e^{5} + 9e^{4} - 9e^{3} - 17e^{2} + 12e + 5$ |
29 | $[29, 29, -3w + 7]$ | $\phantom{-}\frac{3}{2}e^{7} - \frac{35}{2}e^{5} + 58e^{3} + \frac{5}{2}e^{2} - 50e + \frac{7}{2}$ |
43 | $[43, 43, -3w^{2} - 2w + 17]$ | $-e^{7} + 11e^{5} + e^{4} - 31e^{3} - 8e^{2} + 15e + 1$ |
49 | $[49, 7, -2w^{2} + w + 11]$ | $\phantom{-}e^{7} - 12e^{5} + 40e^{3} + e^{2} - 31e + 3$ |
67 | $[67, 67, -2w^{2} - 4w + 3]$ | $-2e^{5} + e^{4} + 16e^{3} - 10e^{2} - 20e + 11$ |
71 | $[71, 71, -2w^{2} + w + 9]$ | $-e^{7} - 3e^{6} + 16e^{5} + 26e^{4} - 75e^{3} - 42e^{2} + 72e - 1$ |
73 | $[73, 73, w^{2} + 2w - 7]$ | $-\frac{1}{2}e^{7} + e^{6} + \frac{5}{2}e^{5} - 7e^{4} + 8e^{3} - \frac{5}{2}e^{2} - 18e + \frac{17}{2}$ |
73 | $[73, 73, -2w^{2} - 2w + 11]$ | $-\frac{1}{2}e^{7} + \frac{13}{2}e^{5} - e^{4} - 25e^{3} + \frac{15}{2}e^{2} + 21e - \frac{13}{2}$ |
73 | $[73, 73, w - 5]$ | $\phantom{-}e^{7} - 2e^{6} - 8e^{5} + 17e^{4} + 6e^{3} - 22e^{2} + 15e + 3$ |
89 | $[89, 89, 2w^{2} + w - 9]$ | $-\frac{5}{2}e^{7} - e^{6} + \frac{61}{2}e^{5} + 11e^{4} - 105e^{3} - \frac{63}{2}e^{2} + 81e - \frac{1}{2}$ |
89 | $[89, 89, -w^{2} - 2w + 9]$ | $\phantom{-}2e^{7} + 2e^{6} - 24e^{5} - 19e^{4} + 81e^{3} + 42e^{2} - 59e + 1$ |
89 | $[89, 89, -2w - 1]$ | $\phantom{-}\frac{1}{2}e^{7} + e^{6} - \frac{9}{2}e^{5} - 9e^{4} + 8e^{3} + \frac{41}{2}e^{2} + 4e - \frac{5}{2}$ |
Atkin-Lehner eigenvalues
The Atkin-Lehner eigenvalues for this form are not in the database.