Base field 3.3.1957.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 10\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[8, 2, 2]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} + x^{5} - 25x^{4} - 32x^{3} + 110x^{2} + 204x + 72\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w^{2}]$ | $-1$ |
4 | $[4, 2, w^{2} + w + 1]$ | $\phantom{-}1$ |
5 | $[5, 5, w]$ | $\phantom{-}e$ |
11 | $[11, 11, 10w + 4]$ | $\phantom{-}\frac{13}{36}e^{5} - \frac{11}{36}e^{4} - \frac{313}{36}e^{3} + \frac{37}{9}e^{2} + \frac{649}{18}e + \frac{37}{3}$ |
13 | $[13, 13, 12w^{2} + w + 7]$ | $\phantom{-}\frac{4}{9}e^{5} - \frac{2}{9}e^{4} - \frac{97}{9}e^{3} + \frac{13}{9}e^{2} + \frac{416}{9}e + \frac{82}{3}$ |
17 | $[17, 17, w + 1]$ | $-\frac{13}{36}e^{5} + \frac{11}{36}e^{4} + \frac{313}{36}e^{3} - \frac{37}{9}e^{2} - \frac{667}{18}e - \frac{37}{3}$ |
17 | $[17, 17, 16w^{2} + 16]$ | $\phantom{-}\frac{7}{36}e^{5} + \frac{1}{36}e^{4} - \frac{181}{36}e^{3} - \frac{37}{18}e^{2} + \frac{445}{18}e + \frac{58}{3}$ |
17 | $[17, 17, 16w^{2} + 16w + 8]$ | $-\frac{1}{4}e^{5} + \frac{1}{4}e^{4} + \frac{23}{4}e^{3} - \frac{7}{2}e^{2} - \frac{41}{2}e - 6$ |
19 | $[19, 19, 18w^{2} + 18w + 1]$ | $\phantom{-}\frac{13}{36}e^{5} - \frac{11}{36}e^{4} - \frac{313}{36}e^{3} + \frac{37}{9}e^{2} + \frac{649}{18}e + \frac{43}{3}$ |
19 | $[19, 19, -w^{2} + 7]$ | $\phantom{-}\frac{25}{36}e^{5} - \frac{17}{36}e^{4} - \frac{595}{36}e^{3} + \frac{107}{18}e^{2} + \frac{1183}{18}e + \frac{82}{3}$ |
25 | $[25, 5, 4w^{2} + w + 4]$ | $-\frac{1}{4}e^{5} + \frac{1}{4}e^{4} + \frac{23}{4}e^{3} - \frac{7}{2}e^{2} - \frac{41}{2}e - 4$ |
27 | $[27, 3, -3]$ | $\phantom{-}\frac{4}{9}e^{5} - \frac{2}{9}e^{4} - \frac{97}{9}e^{3} + \frac{13}{9}e^{2} + \frac{416}{9}e + \frac{88}{3}$ |
29 | $[29, 29, w + 7]$ | $-\frac{4}{9}e^{5} + \frac{2}{9}e^{4} + \frac{97}{9}e^{3} - \frac{22}{9}e^{2} - \frac{407}{9}e - \frac{58}{3}$ |
41 | $[41, 41, 40w^{2} + 18]$ | $-\frac{25}{36}e^{5} + \frac{17}{36}e^{4} + \frac{595}{36}e^{3} - \frac{89}{18}e^{2} - \frac{1219}{18}e - \frac{112}{3}$ |
43 | $[43, 43, w^{2} - 11]$ | $\phantom{-}\frac{19}{36}e^{5} - \frac{5}{36}e^{4} - \frac{463}{36}e^{3} - \frac{2}{9}e^{2} + \frac{979}{18}e + \frac{103}{3}$ |
47 | $[47, 47, 2w^{2} + 2w - 13]$ | $\phantom{-}2e$ |
59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}\frac{19}{36}e^{5} - \frac{5}{36}e^{4} - \frac{463}{36}e^{3} - \frac{2}{9}e^{2} + \frac{1015}{18}e + \frac{97}{3}$ |
73 | $[73, 73, w^{2} + 2w - 1]$ | $\phantom{-}\frac{5}{12}e^{5} - \frac{1}{12}e^{4} - \frac{119}{12}e^{3} + \frac{1}{6}e^{2} + \frac{233}{6}e + 22$ |
79 | $[79, 79, w^{2} + 37]$ | $\phantom{-}\frac{2}{3}e^{5} - \frac{1}{3}e^{4} - \frac{47}{3}e^{3} + \frac{8}{3}e^{2} + \frac{184}{3}e + 34$ |
97 | $[97, 97, w^{2} + 2w - 7]$ | $\phantom{-}\frac{25}{36}e^{5} - \frac{17}{36}e^{4} - \frac{595}{36}e^{3} + \frac{89}{18}e^{2} + \frac{1237}{18}e + \frac{118}{3}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w^{2}]$ | $1$ |
$4$ | $[4, 2, w^{2} + w + 1]$ | $-1$ |