Base field 6.6.592661.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 5x^{4} + 4x^{3} + 5x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[49, 7, -w^{4} + 4w^{2} + w - 3]$ |
Dimension: | $5$ |
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:
\(x^{5} + 3x^{4} - 60x^{3} - 112x^{2} + 720x - 336\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
7 | $[7, 7, w^{5} - 5w^{3} + 4w]$ | $\phantom{-}2$ |
13 | $[13, 13, -w^{3} + 3w]$ | $\phantom{-}e$ |
25 | $[25, 5, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ | $-\frac{1}{48}e^{4} - \frac{1}{48}e^{3} + \frac{19}{24}e^{2} + \frac{1}{4}e + \frac{3}{2}$ |
31 | $[31, 31, -w^{5} + 5w^{3} - 5w + 1]$ | $\phantom{-}\frac{5}{144}e^{4} + \frac{17}{144}e^{3} - \frac{125}{72}e^{2} - \frac{49}{12}e + \frac{67}{6}$ |
31 | $[31, 31, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $-\frac{1}{48}e^{4} + \frac{1}{16}e^{3} + \frac{29}{24}e^{2} - \frac{9}{4}e - \frac{17}{2}$ |
37 | $[37, 37, w^{4} - 5w^{2} + w + 3]$ | $\phantom{-}\frac{1}{144}e^{4} + \frac{1}{144}e^{3} - \frac{31}{72}e^{2} + \frac{13}{12}e + \frac{35}{6}$ |
43 | $[43, 43, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 6w]$ | $-\frac{1}{12}e^{3} + \frac{1}{12}e^{2} + 3e - 1$ |
47 | $[47, 47, w^{5} - w^{4} - 4w^{3} + 4w^{2} - 2]$ | $-\frac{1}{48}e^{4} - \frac{1}{48}e^{3} + \frac{31}{24}e^{2} + \frac{3}{4}e - \frac{23}{2}$ |
49 | $[49, 7, -w^{4} + 4w^{2} + w - 3]$ | $-1$ |
53 | $[53, 53, -w^{4} + w^{3} + 4w^{2} - 3w - 4]$ | $\phantom{-}\frac{1}{144}e^{4} - \frac{11}{144}e^{3} - \frac{25}{72}e^{2} + \frac{49}{12}e + \frac{17}{6}$ |
59 | $[59, 59, w^{4} - 5w^{2} - w + 5]$ | $-\frac{5}{144}e^{4} - \frac{5}{144}e^{3} + \frac{119}{72}e^{2} + \frac{13}{12}e - \frac{73}{6}$ |
61 | $[61, 61, w^{3} - w^{2} - 3w]$ | $\phantom{-}\frac{1}{16}e^{4} + \frac{7}{48}e^{3} - \frac{71}{24}e^{2} - \frac{21}{4}e + \frac{31}{2}$ |
64 | $[64, 2, -2]$ | $-\frac{1}{12}e^{3} + \frac{1}{12}e^{2} + 3e - 2$ |
67 | $[67, 67, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 7w]$ | $-\frac{1}{36}e^{4} - \frac{7}{36}e^{3} + \frac{17}{9}e^{2} + \frac{26}{3}e - \frac{58}{3}$ |
67 | $[67, 67, 2w^{5} - w^{4} - 10w^{3} + 4w^{2} + 9w - 1]$ | $\phantom{-}\frac{5}{144}e^{4} + \frac{17}{144}e^{3} - \frac{125}{72}e^{2} - \frac{61}{12}e + \frac{43}{6}$ |
73 | $[73, 73, w^{5} - w^{4} - 4w^{3} + 5w^{2} + w - 3]$ | $-e + 4$ |
73 | $[73, 73, 3w^{5} - 3w^{4} - 13w^{3} + 11w^{2} + 7w - 3]$ | $-\frac{1}{144}e^{4} - \frac{13}{144}e^{3} + \frac{1}{72}e^{2} + \frac{29}{12}e + \frac{25}{6}$ |
83 | $[83, 83, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 2]$ | $-\frac{1}{24}e^{4} - \frac{1}{24}e^{3} + \frac{19}{12}e^{2} + \frac{1}{2}e + 1$ |
97 | $[97, 97, -2w^{4} + w^{3} + 9w^{2} - 3w - 4]$ | $-\frac{1}{48}e^{4} - \frac{3}{16}e^{3} + \frac{35}{24}e^{2} + \frac{35}{4}e - \frac{39}{2}$ |
101 | $[101, 101, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 4]$ | $\phantom{-}\frac{1}{72}e^{4} + \frac{7}{72}e^{3} - \frac{17}{18}e^{2} - \frac{23}{6}e + \frac{44}{3}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$49$ | $[49, 7, -w^{4} + 4w^{2} + w - 3]$ | $1$ |