Base field \(\Q(\sqrt{401}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 100\); narrow class number \(5\) and class number \(5\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $120$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 3x^{7} - 10x^{6} + 28x^{5} + 37x^{4} - 78x^{3} - 58x^{2} + 53x + 19\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $-\frac{1}{2}e^{6} + e^{5} + \frac{7}{2}e^{4} - \frac{9}{2}e^{3} - \frac{15}{2}e^{2} + e + \frac{7}{2}$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{1}{2}e^{7} - e^{6} - \frac{7}{2}e^{5} + \frac{11}{2}e^{4} + \frac{13}{2}e^{3} - 7e^{2} - \frac{1}{2}e + 3$ |
| 5 | $[5, 5, w + 4]$ | $-e^{7} + \frac{5}{2}e^{6} + 6e^{5} - \frac{27}{2}e^{4} - \frac{17}{2}e^{3} + \frac{29}{2}e^{2} - 2e - \frac{3}{2}$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{3}{2}e^{6} - \frac{5}{2}e^{5} + 9e^{4} + 2e^{3} - \frac{29}{2}e^{2} + \frac{1}{2}e + \frac{13}{2}$ |
| 7 | $[7, 7, w + 5]$ | $-e^{7} + \frac{5}{2}e^{6} + 6e^{5} - \frac{27}{2}e^{4} - \frac{17}{2}e^{3} + \frac{29}{2}e^{2} - e - \frac{3}{2}$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}e^{7} - \frac{3}{2}e^{6} - 8e^{5} + \frac{11}{2}e^{4} + \frac{41}{2}e^{3} + \frac{9}{2}e^{2} - 13e - \frac{17}{2}$ |
| 11 | $[11, 11, w + 3]$ | $-\frac{5}{2}e^{6} + 6e^{5} + \frac{31}{2}e^{4} - \frac{61}{2}e^{3} - \frac{53}{2}e^{2} + 26e + \frac{11}{2}$ |
| 11 | $[11, 11, w + 7]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{13}{2}e^{5} - \frac{1}{2}e^{4} + \frac{47}{2}e^{3} + 4e^{2} - \frac{39}{2}e - 3$ |
| 29 | $[29, 29, w + 6]$ | $\phantom{-}\frac{3}{2}e^{6} - 4e^{5} - \frac{17}{2}e^{4} + \frac{39}{2}e^{3} + \frac{25}{2}e^{2} - 13e - \frac{3}{2}$ |
| 29 | $[29, 29, w + 22]$ | $-e^{7} + 12e^{5} + 3e^{4} - 42e^{3} - 15e^{2} + 34e + 3$ |
| 41 | $[41, 41, w + 13]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{3}{2}e^{6} - \frac{9}{2}e^{5} + 13e^{4} + 12e^{3} - \frac{57}{2}e^{2} - \frac{19}{2}e + \frac{19}{2}$ |
| 41 | $[41, 41, w + 27]$ | $-e^{7} - \frac{9}{2}e^{6} + 22e^{5} + \frac{63}{2}e^{4} - \frac{183}{2}e^{3} - \frac{133}{2}e^{2} + 77e + \frac{53}{2}$ |
| 43 | $[43, 43, w + 16]$ | $-\frac{1}{2}e^{7} + \frac{9}{2}e^{6} - \frac{9}{2}e^{5} - 29e^{4} + 36e^{3} + \frac{107}{2}e^{2} - \frac{81}{2}e - \frac{35}{2}$ |
| 43 | $[43, 43, w + 26]$ | $\phantom{-}\frac{5}{2}e^{7} - \frac{13}{2}e^{6} - \frac{27}{2}e^{5} + 33e^{4} + 15e^{3} - \frac{61}{2}e^{2} + \frac{13}{2}e + \frac{15}{2}$ |
| 47 | $[47, 47, w + 2]$ | $\phantom{-}2e^{7} - \frac{7}{2}e^{6} - 17e^{5} + \frac{39}{2}e^{4} + \frac{91}{2}e^{3} - \frac{39}{2}e^{2} - 30e - \frac{5}{2}$ |
| 47 | $[47, 47, w + 44]$ | $-6e^{6} + 14e^{5} + 37e^{4} - 70e^{3} - 62e^{2} + 58e + 14$ |
| 73 | $[73, 73, w + 33]$ | $\phantom{-}\frac{3}{2}e^{7} - 6e^{6} - \frac{9}{2}e^{5} + \frac{75}{2}e^{4} - \frac{27}{2}e^{3} - 60e^{2} + \frac{63}{2}e + 19$ |
| 73 | $[73, 73, w + 39]$ | $-3e^{7} + 6e^{6} + 21e^{5} - 30e^{4} - 45e^{3} + 27e^{2} + 27e - 5$ |
| 83 | $[83, 83, -4w - 37]$ | $-\frac{1}{2}e^{7} - 7e^{6} + \frac{45}{2}e^{5} + \frac{87}{2}e^{4} - \frac{207}{2}e^{3} - 74e^{2} + \frac{177}{2}e + 23$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).