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: | $[16, 4, 2w]$ |
| 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:
| \(x^{10} + 27x^{8} + 267x^{6} + 1136x^{4} + 1729x^{2} + 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2}]$ | $\phantom{-}0$ |
| 4 | $[4, 2, w^{2} + w + 1]$ | $-\frac{2}{3}e^{9} - 13e^{7} - 81e^{5} - \frac{478}{3}e^{3} - \frac{44}{3}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 11 | $[11, 11, 10w + 4]$ | $-2e^{9} - 39e^{7} - 242e^{5} - 467e^{3} - 19e$ |
| 13 | $[13, 13, 12w^{2} + w + 7]$ | $\phantom{-}\frac{2}{15}e^{9} + \frac{14}{5}e^{7} + \frac{99}{5}e^{5} + \frac{161}{3}e^{3} + \frac{713}{15}e$ |
| 17 | $[17, 17, w + 1]$ | $\phantom{-}\frac{44}{5}e^{8} + \frac{854}{5}e^{6} + \frac{5264}{5}e^{4} + 2001e^{2} + \frac{51}{5}$ |
| 17 | $[17, 17, 16w^{2} + 16]$ | $-\frac{2}{5}e^{9} - \frac{37}{5}e^{7} - \frac{202}{5}e^{5} - 43e^{3} + \frac{457}{5}e$ |
| 17 | $[17, 17, 16w^{2} + 16w + 8]$ | $-\frac{1}{5}e^{9} - \frac{21}{5}e^{7} - \frac{146}{5}e^{5} - 73e^{3} - \frac{229}{5}e$ |
| 19 | $[19, 19, 18w^{2} + 18w + 1]$ | $-\frac{67}{15}e^{9} - \frac{434}{5}e^{7} - \frac{2684}{5}e^{5} - \frac{3097}{3}e^{3} - \frac{598}{15}e$ |
| 19 | $[19, 19, -w^{2} + 7]$ | $-\frac{9}{5}e^{8} - \frac{174}{5}e^{6} - \frac{1069}{5}e^{4} - 406e^{2} - \frac{16}{5}$ |
| 25 | $[25, 5, 4w^{2} + w + 4]$ | $-\frac{2}{3}e^{9} - 13e^{7} - 82e^{5} - \frac{514}{3}e^{3} - \frac{143}{3}e$ |
| 27 | $[27, 3, -3]$ | $\phantom{-}\frac{3}{5}e^{8} + \frac{58}{5}e^{6} + \frac{358}{5}e^{4} + 137e^{2} - \frac{13}{5}$ |
| 29 | $[29, 29, w + 7]$ | $-\frac{1}{5}e^{9} - \frac{21}{5}e^{7} - \frac{146}{5}e^{5} - 72e^{3} - \frac{189}{5}e$ |
| 41 | $[41, 41, 40w^{2} + 18]$ | $\phantom{-}\frac{22}{5}e^{9} + \frac{427}{5}e^{7} + \frac{2627}{5}e^{5} + 987e^{3} - \frac{192}{5}e$ |
| 43 | $[43, 43, w^{2} - 11]$ | $\phantom{-}\frac{27}{5}e^{8} + \frac{522}{5}e^{6} + \frac{3207}{5}e^{4} + 1216e^{2} + \frac{28}{5}$ |
| 47 | $[47, 47, 2w^{2} + 2w - 13]$ | $-\frac{13}{5}e^{8} - \frac{248}{5}e^{6} - \frac{1508}{5}e^{4} - 571e^{2} - \frac{42}{5}$ |
| 59 | $[59, 59, w^{2} - 3]$ | $-\frac{13}{5}e^{8} - \frac{248}{5}e^{6} - \frac{1508}{5}e^{4} - 572e^{2} - \frac{72}{5}$ |
| 73 | $[73, 73, w^{2} + 2w - 1]$ | $\phantom{-}6e^{8} + 117e^{6} + 725e^{4} + 1387e^{2} + 11$ |
| 79 | $[79, 79, w^{2} + 37]$ | $-\frac{32}{15}e^{9} - \frac{209}{5}e^{7} - \frac{1309}{5}e^{5} - \frac{1559}{3}e^{3} - \frac{908}{15}e$ |
| 97 | $[97, 97, w^{2} + 2w - 7]$ | $-\frac{18}{5}e^{8} - \frac{348}{5}e^{6} - \frac{2143}{5}e^{4} - 821e^{2} - \frac{97}{5}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w^{2}]$ | $1$ |
| $4$ | $[4, 2, w^{2} + w + 1]$ | $\frac{2}{3}e^{9} + 13e^{7} + 81e^{5} + \frac{478}{3}e^{3} + \frac{44}{3}e$ |