Base field 4.4.5125.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 6x^{2} + 7x + 11\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[49, 7, -2w^{2} + 3w + 8]$ |
Dimension: | $7$ |
CM: | no |
Base change: | no |
Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} + 3x^{6} - 8x^{5} - 21x^{4} + 19x^{3} + 31x^{2} - 5\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -w^{2} + 2w + 3]$ | $\phantom{-}e$ |
9 | $[9, 3, w^{3} - 3w^{2} - 2w + 9]$ | $-e^{6} - \frac{5}{2}e^{5} + \frac{19}{2}e^{4} + \frac{31}{2}e^{3} - 29e^{2} - 10e + \frac{15}{2}$ |
9 | $[9, 3, -w^{3} + 5w + 5]$ | $-\frac{1}{2}e^{6} - \frac{3}{2}e^{5} + \frac{7}{2}e^{4} + 9e^{3} - 7e^{2} - \frac{17}{2}e$ |
11 | $[11, 11, w]$ | $-\frac{1}{2}e^{5} - \frac{3}{2}e^{4} + \frac{7}{2}e^{3} + 8e^{2} - 8e - \frac{9}{2}$ |
11 | $[11, 11, w - 1]$ | $\phantom{-}\frac{1}{2}e^{5} + \frac{5}{2}e^{4} - \frac{3}{2}e^{3} - 13e^{2} + 3e + \frac{11}{2}$ |
16 | $[16, 2, 2]$ | $-\frac{3}{2}e^{6} - 4e^{5} + 13e^{4} + \frac{47}{2}e^{3} - 39e^{2} - \frac{31}{2}e + \frac{21}{2}$ |
19 | $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ | $-\frac{1}{2}e^{6} - e^{5} + 6e^{4} + \frac{17}{2}e^{3} - 20e^{2} - \frac{21}{2}e + \frac{15}{2}$ |
19 | $[19, 19, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}\frac{5}{2}e^{6} + 6e^{5} - 23e^{4} - \frac{75}{2}e^{3} + 66e^{2} + \frac{67}{2}e - \frac{25}{2}$ |
29 | $[29, 29, w^{3} - 4w^{2} - w + 10]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{1}{2}e^{5} - \frac{13}{2}e^{4} - 5e^{3} + 19e^{2} + \frac{13}{2}e$ |
29 | $[29, 29, -w^{3} + 3w^{2} + w - 7]$ | $-e^{6} - \frac{3}{2}e^{5} + \frac{25}{2}e^{4} + \frac{23}{2}e^{3} - 43e^{2} - 11e + \frac{35}{2}$ |
41 | $[41, 41, 3w^{2} - 2w - 10]$ | $-\frac{5}{2}e^{6} - 6e^{5} + 23e^{4} + \frac{73}{2}e^{3} - 67e^{2} - \frac{55}{2}e + \frac{31}{2}$ |
49 | $[49, 7, -2w^{2} + 3w + 8]$ | $-1$ |
49 | $[49, 7, w^{3} - 2w^{2} - 2w + 5]$ | $-\frac{3}{2}e^{6} - 3e^{5} + 15e^{4} + \frac{35}{2}e^{3} - 48e^{2} - \frac{25}{2}e + \frac{45}{2}$ |
71 | $[71, 71, -w - 3]$ | $\phantom{-}3e^{6} + \frac{13}{2}e^{5} - \frac{57}{2}e^{4} - \frac{75}{2}e^{3} + 87e^{2} + 22e - \frac{61}{2}$ |
71 | $[71, 71, w - 4]$ | $\phantom{-}\frac{1}{2}e^{6} + e^{5} - 7e^{4} - \frac{19}{2}e^{3} + 26e^{2} + \frac{23}{2}e - \frac{21}{2}$ |
79 | $[79, 79, -w^{3} + w^{2} + 3w + 3]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{1}{2}e^{5} - \frac{9}{2}e^{4} - e^{3} + 10e^{2} - \frac{11}{2}e$ |
79 | $[79, 79, -w^{3} + 2w^{2} + 2w - 6]$ | $\phantom{-}\frac{3}{2}e^{6} + \frac{7}{2}e^{5} - \frac{31}{2}e^{4} - 24e^{3} + 47e^{2} + \frac{45}{2}e$ |
89 | $[89, 89, w^{3} - 3w^{2} - 3w + 7]$ | $-\frac{1}{2}e^{6} - \frac{1}{2}e^{5} + \frac{15}{2}e^{4} + 7e^{3} - 25e^{2} - \frac{27}{2}e + 5$ |
89 | $[89, 89, w^{3} - 6w - 2]$ | $-2e^{6} - 6e^{5} + 16e^{4} + 35e^{3} - 47e^{2} - 21e + 15$ |
101 | $[101, 101, 2w^{3} - 5w^{2} - 3w + 9]$ | $\phantom{-}2e^{6} + 6e^{5} - 16e^{4} - 37e^{3} + 44e^{2} + 30e - 7$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$49$ | $[49, 7, -2w^{2} + 3w + 8]$ | $1$ |