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: | $[10, 10, w]$ |
| Dimension: | $10$ |
| 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:
| \(x^{10} + 33x^{8} + 398x^{6} + 2078x^{4} + 3953x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2}]$ | $-\frac{1}{8}e^{7} - \frac{25}{8}e^{5} - \frac{199}{8}e^{3} - \frac{503}{8}e$ |
| 4 | $[4, 2, w^{2} + w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $-\frac{1}{8}e^{7} - \frac{25}{8}e^{5} - \frac{199}{8}e^{3} - \frac{503}{8}e$ |
| 11 | $[11, 11, 10w + 4]$ | $-\frac{1}{16}e^{9} - \frac{7}{4}e^{7} - \frac{135}{8}e^{5} - \frac{259}{4}e^{3} - \frac{1273}{16}e$ |
| 13 | $[13, 13, 12w^{2} + w + 7]$ | $-\frac{1}{16}e^{9} - \frac{7}{4}e^{7} - \frac{135}{8}e^{5} - \frac{259}{4}e^{3} - \frac{1273}{16}e$ |
| 17 | $[17, 17, w + 1]$ | $\phantom{-}\frac{3}{16}e^{8} + \frac{19}{4}e^{6} + \frac{307}{8}e^{4} + \frac{397}{4}e^{2} + \frac{119}{16}$ |
| 17 | $[17, 17, 16w^{2} + 16]$ | $\phantom{-}\frac{1}{8}e^{7} + \frac{27}{8}e^{5} + \frac{235}{8}e^{3} + \frac{657}{8}e$ |
| 17 | $[17, 17, 16w^{2} + 16w + 8]$ | $-\frac{1}{16}e^{9} - \frac{7}{4}e^{7} - \frac{137}{8}e^{5} - \frac{277}{4}e^{3} - \frac{1597}{16}e$ |
| 19 | $[19, 19, 18w^{2} + 18w + 1]$ | $-\frac{1}{16}e^{9} - \frac{5}{4}e^{7} - \frac{39}{8}e^{5} + \frac{103}{4}e^{3} + \frac{2135}{16}e$ |
| 19 | $[19, 19, -w^{2} + 7]$ | $\phantom{-}\frac{1}{16}e^{8} + \frac{13}{8}e^{6} + \frac{53}{4}e^{4} + \frac{263}{8}e^{2} - \frac{77}{16}$ |
| 25 | $[25, 5, 4w^{2} + w + 4]$ | $\phantom{-}\frac{1}{8}e^{9} + 4e^{7} + \frac{187}{4}e^{5} + 237e^{3} + \frac{3521}{8}e$ |
| 27 | $[27, 3, -3]$ | $-\frac{1}{4}e^{8} - \frac{25}{4}e^{6} - \frac{199}{4}e^{4} - \frac{503}{4}e^{2}$ |
| 29 | $[29, 29, w + 7]$ | $\phantom{-}\frac{1}{4}e^{9} + \frac{15}{2}e^{7} + \frac{161}{2}e^{5} + \frac{733}{2}e^{3} + \frac{2389}{4}e$ |
| 41 | $[41, 41, 40w^{2} + 18]$ | $\phantom{-}\frac{1}{16}e^{9} + \frac{7}{4}e^{7} + \frac{133}{8}e^{5} + \frac{241}{4}e^{3} + \frac{981}{16}e$ |
| 43 | $[43, 43, w^{2} - 11]$ | $-\frac{1}{16}e^{8} - \frac{3}{2}e^{6} - \frac{93}{8}e^{4} - 30e^{2} + \frac{3}{16}$ |
| 47 | $[47, 47, 2w^{2} + 2w - 13]$ | $-\frac{1}{8}e^{8} - \frac{13}{4}e^{6} - 27e^{4} - \frac{291}{4}e^{2} - \frac{103}{8}$ |
| 59 | $[59, 59, w^{2} - 3]$ | $-\frac{1}{8}e^{8} - \frac{13}{4}e^{6} - 27e^{4} - \frac{291}{4}e^{2} - \frac{87}{8}$ |
| 73 | $[73, 73, w^{2} + 2w - 1]$ | $-\frac{7}{16}e^{8} - \frac{43}{4}e^{6} - \frac{665}{8}e^{4} - \frac{799}{4}e^{2} + \frac{113}{16}$ |
| 79 | $[79, 79, w^{2} + 37]$ | $\phantom{-}\frac{5}{16}e^{9} + 10e^{7} + \frac{935}{8}e^{5} + 593e^{3} + \frac{17629}{16}e$ |
| 97 | $[97, 97, w^{2} + 2w - 7]$ | $\phantom{-}\frac{1}{8}e^{8} + 3e^{6} + \frac{87}{4}e^{4} + 43e^{2} - \frac{143}{8}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w^{2}]$ | $\frac{1}{8}e^{7} + \frac{25}{8}e^{5} + \frac{199}{8}e^{3} + \frac{503}{8}e$ |
| $5$ | $[5, 5, w]$ | $\frac{1}{8}e^{7} + \frac{25}{8}e^{5} + \frac{199}{8}e^{3} + \frac{503}{8}e$ |