Base field 4.4.15529.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - x^{7} - 29x^{6} + 22x^{5} + 216x^{4} - 68x^{3} - 324x^{2} + 248x - 48\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}e$ |
| 8 | $[8, 2, -w^{3} + w^{2} + 6w + 1]$ | $\phantom{-}1$ |
| 9 | $[9, 3, -w^{3} + w^{2} + 5w + 1]$ | $-\frac{3}{16}e^{7} + \frac{1}{16}e^{6} + \frac{87}{16}e^{5} - \frac{3}{8}e^{4} - \frac{319}{8}e^{3} - \frac{65}{4}e^{2} + \frac{95}{2}e - 10$ |
| 9 | $[9, 3, -w^{3} + 2w^{2} + 3w - 1]$ | $\phantom{-}\frac{1}{16}e^{7} + \frac{1}{16}e^{6} - \frac{33}{16}e^{5} - \frac{13}{8}e^{4} + \frac{153}{8}e^{3} + \frac{37}{4}e^{2} - \frac{73}{2}e + 14$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ | $\phantom{-}\frac{9}{16}e^{7} - \frac{3}{16}e^{6} - \frac{269}{16}e^{5} + \frac{17}{8}e^{4} + \frac{1053}{8}e^{3} + \frac{113}{4}e^{2} - \frac{395}{2}e + 70$ |
| 23 | $[23, 23, w^{2} - 2w - 1]$ | $-\frac{1}{2}e^{7} + \frac{3}{8}e^{6} + \frac{115}{8}e^{5} - \frac{55}{8}e^{4} - \frac{419}{4}e^{3} - \frac{17}{4}e^{2} + \frac{285}{2}e - 51$ |
| 29 | $[29, 29, w^{2} - 3w - 1]$ | $-\frac{1}{2}e^{7} + \frac{3}{8}e^{6} + \frac{115}{8}e^{5} - \frac{55}{8}e^{4} - \frac{419}{4}e^{3} - \frac{17}{4}e^{2} + \frac{287}{2}e - 51$ |
| 29 | $[29, 29, -w^{2} + w + 3]$ | $-\frac{1}{2}e^{7} + \frac{3}{8}e^{6} + \frac{115}{8}e^{5} - \frac{55}{8}e^{4} - \frac{419}{4}e^{3} - \frac{17}{4}e^{2} + \frac{287}{2}e - 51$ |
| 37 | $[37, 37, w^{3} - w^{2} - 5w + 1]$ | $-\frac{5}{8}e^{7} + \frac{1}{2}e^{6} + \frac{71}{4}e^{5} - \frac{71}{8}e^{4} - \frac{251}{2}e^{3} - \frac{45}{4}e^{2} + \frac{305}{2}e - 47$ |
| 43 | $[43, 43, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}\frac{9}{16}e^{7} - \frac{9}{16}e^{6} - \frac{251}{16}e^{5} + 11e^{4} + \frac{855}{8}e^{3} - \frac{15}{2}e^{2} - 124e + 53$ |
| 47 | $[47, 47, -w^{2} + 2w + 5]$ | $-\frac{1}{4}e^{7} + \frac{3}{8}e^{6} + \frac{55}{8}e^{5} - \frac{65}{8}e^{4} - \frac{183}{4}e^{3} + \frac{89}{4}e^{2} + \frac{115}{2}e - 33$ |
| 47 | $[47, 47, 2w^{3} - 2w^{2} - 11w - 5]$ | $-\frac{1}{8}e^{7} + \frac{15}{4}e^{5} + \frac{5}{8}e^{4} - 29e^{3} - \frac{53}{4}e^{2} + \frac{69}{2}e - 9$ |
| 53 | $[53, 53, -w^{3} + 2w^{2} + 2w + 1]$ | $-\frac{3}{8}e^{7} + \frac{45}{4}e^{5} + \frac{15}{8}e^{4} - 88e^{3} - \frac{155}{4}e^{2} + \frac{239}{2}e - 33$ |
| 59 | $[59, 59, -w - 3]$ | $\phantom{-}\frac{9}{16}e^{7} - \frac{1}{16}e^{6} - \frac{275}{16}e^{5} - e^{4} + \frac{1115}{8}e^{3} + 43e^{2} - 215e + 75$ |
| 73 | $[73, 73, w^{2} - w + 1]$ | $\phantom{-}\frac{13}{16}e^{7} - \frac{9}{16}e^{6} - \frac{371}{16}e^{5} + \frac{39}{4}e^{4} + \frac{1327}{8}e^{3} + 19e^{2} - 208e + 71$ |
| 73 | $[73, 73, 2w^{3} - 2w^{2} - 12w - 5]$ | $\phantom{-}\frac{5}{16}e^{7} + \frac{3}{16}e^{6} - \frac{159}{16}e^{5} - 6e^{4} + \frac{687}{8}e^{3} + \frac{101}{2}e^{2} - 139e + 37$ |
| 79 | $[79, 79, 4w^{3} - 4w^{2} - 22w - 7]$ | $\phantom{-}\frac{7}{8}e^{7} - \frac{1}{2}e^{6} - \frac{103}{4}e^{5} + \frac{65}{8}e^{4} + 196e^{3} + \frac{99}{4}e^{2} - \frac{571}{2}e + 103$ |
| 97 | $[97, 97, 2w^{3} - 3w^{2} - 9w + 1]$ | $\phantom{-}\frac{17}{16}e^{7} - \frac{11}{16}e^{6} - \frac{493}{16}e^{5} + \frac{93}{8}e^{4} + \frac{1817}{8}e^{3} + \frac{105}{4}e^{2} - \frac{601}{2}e + 106$ |
| 101 | $[101, 101, 2w^{2} - 2w - 9]$ | $\phantom{-}\frac{3}{4}e^{7} - \frac{1}{2}e^{6} - \frac{43}{2}e^{5} + \frac{33}{4}e^{4} + \frac{309}{2}e^{3} + \frac{49}{2}e^{2} - 188e + 54$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |
| $8$ | $[8, 2, -w^{3} + w^{2} + 6w + 1]$ | $-1$ |