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: | $[8, 8, w^{2} + w + 6]$ |
| Dimension: | $10$ |
| 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:
| \(x^{10} + 25x^{8} + 222x^{6} + 862x^{4} + 1441x^{2} + 841\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2}]$ | $\phantom{-}0$ |
| 4 | $[4, 2, w^{2} + w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $-\frac{23}{464}e^{9} - \frac{273}{232}e^{7} - \frac{272}{29}e^{5} - \frac{6607}{232}e^{3} - \frac{11625}{464}e$ |
| 11 | $[11, 11, 10w + 4]$ | $-\frac{21}{464}e^{9} - \frac{31}{29}e^{7} - \frac{1983}{232}e^{5} - \frac{787}{29}e^{3} - \frac{13325}{464}e$ |
| 13 | $[13, 13, 12w^{2} + w + 7]$ | $\phantom{-}\frac{13}{464}e^{9} + \frac{37}{58}e^{7} + \frac{1095}{232}e^{5} + \frac{741}{58}e^{3} + \frac{5045}{464}e$ |
| 17 | $[17, 17, w + 1]$ | $-\frac{1}{8}e^{6} - \frac{15}{8}e^{4} - \frac{55}{8}e^{2} - \frac{25}{8}$ |
| 17 | $[17, 17, 16w^{2} + 16]$ | $\phantom{-}\frac{19}{464}e^{9} + \frac{97}{116}e^{7} + \frac{1239}{232}e^{5} + \frac{1383}{116}e^{3} + \frac{3135}{464}e$ |
| 17 | $[17, 17, 16w^{2} + 16w + 8]$ | $-\frac{25}{232}e^{9} - \frac{567}{232}e^{7} - \frac{4303}{232}e^{5} - \frac{12705}{232}e^{3} - \frac{1498}{29}e$ |
| 19 | $[19, 19, 18w^{2} + 18w + 1]$ | $\phantom{-}\frac{17}{232}e^{9} + \frac{99}{58}e^{7} + \frac{1539}{116}e^{5} + \frac{2257}{58}e^{3} + \frac{7561}{232}e$ |
| 19 | $[19, 19, -w^{2} + 7]$ | $\phantom{-}\frac{1}{16}e^{8} + \frac{5}{4}e^{6} + \frac{61}{8}e^{4} + \frac{63}{4}e^{2} + \frac{149}{16}$ |
| 25 | $[25, 5, 4w^{2} + w + 4]$ | $\phantom{-}\frac{1}{16}e^{9} + \frac{11}{8}e^{7} + 10e^{5} + \frac{221}{8}e^{3} + \frac{335}{16}e$ |
| 27 | $[27, 3, -3]$ | $-\frac{3}{16}e^{8} - \frac{17}{4}e^{6} - \frac{259}{8}e^{4} - \frac{387}{4}e^{2} - \frac{1415}{16}$ |
| 29 | $[29, 29, w + 7]$ | $-\frac{9}{116}e^{9} - \frac{421}{232}e^{7} - \frac{3271}{232}e^{5} - \frac{9571}{232}e^{3} - \frac{8335}{232}e$ |
| 41 | $[41, 41, 40w^{2} + 18]$ | $-\frac{5}{116}e^{9} - \frac{125}{116}e^{7} - \frac{1081}{116}e^{5} - \frac{3759}{116}e^{3} - \frac{2051}{58}e$ |
| 43 | $[43, 43, w^{2} - 11]$ | $\phantom{-}\frac{1}{4}e^{8} + \frac{11}{2}e^{6} + 40e^{4} + \frac{225}{2}e^{2} + \frac{407}{4}$ |
| 47 | $[47, 47, 2w^{2} + 2w - 13]$ | $-\frac{1}{8}e^{8} - \frac{11}{4}e^{6} - \frac{39}{2}e^{4} - \frac{201}{4}e^{2} - \frac{283}{8}$ |
| 59 | $[59, 59, w^{2} - 3]$ | $-\frac{1}{16}e^{8} - \frac{3}{2}e^{6} - \frac{91}{8}e^{4} - \frac{55}{2}e^{2} - \frac{217}{16}$ |
| 73 | $[73, 73, w^{2} + 2w - 1]$ | $\phantom{-}\frac{3}{16}e^{8} + \frac{35}{8}e^{6} + \frac{137}{4}e^{4} + \frac{845}{8}e^{2} + \frac{1689}{16}$ |
| 79 | $[79, 79, w^{2} + 37]$ | $-\frac{91}{464}e^{9} - \frac{259}{58}e^{7} - \frac{7781}{232}e^{5} - \frac{5477}{58}e^{3} - \frac{35547}{464}e$ |
| 97 | $[97, 97, w^{2} + 2w - 7]$ | $-\frac{3}{16}e^{8} - \frac{35}{8}e^{6} - \frac{135}{4}e^{4} - \frac{789}{8}e^{2} - \frac{1425}{16}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w^{2}]$ | $\frac{3}{232}e^{9} + \frac{75}{232}e^{7} + \frac{637}{232}e^{5} + \frac{2093}{232}e^{3} + \frac{254}{29}e$ |