Base field 3.3.1396.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[5, 5, -w + 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 32x^{8} + 314x^{6} - 936x^{4} + 584x^{2} - 32\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $-\frac{1}{1620}e^{8} + \frac{1}{180}e^{6} + \frac{149}{810}e^{4} - \frac{355}{162}e^{2} + \frac{1109}{405}$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{2} + 6]$ | $-\frac{53}{3240}e^{9} + \frac{47}{90}e^{7} - \frac{8303}{1620}e^{5} + \frac{1270}{81}e^{3} - \frac{5239}{405}e$ |
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w + 2]$ | $\phantom{-}\frac{1}{1620}e^{9} - \frac{1}{180}e^{7} - \frac{149}{810}e^{5} + \frac{355}{162}e^{3} - \frac{1514}{405}e$ |
| 11 | $[11, 11, 2w - 1]$ | $\phantom{-}\frac{71}{1620}e^{9} - \frac{251}{180}e^{7} + \frac{5443}{405}e^{5} - \frac{6061}{162}e^{3} + \frac{6716}{405}e$ |
| 13 | $[13, 13, w^{2} + w - 3]$ | $\phantom{-}\frac{2}{45}e^{9} - \frac{7}{5}e^{7} + \frac{1193}{90}e^{5} - \frac{317}{9}e^{3} + \frac{533}{45}e$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}\frac{1}{810}e^{8} - \frac{1}{90}e^{6} - \frac{149}{405}e^{4} + \frac{274}{81}e^{2} + \frac{212}{405}$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $\phantom{-}\frac{1}{216}e^{9} - \frac{1}{6}e^{7} + \frac{229}{108}e^{5} - \frac{292}{27}e^{3} + \frac{377}{27}e$ |
| 41 | $[41, 41, 3w^{2} - w - 23]$ | $-\frac{1}{45}e^{8} + \frac{7}{10}e^{6} - \frac{287}{45}e^{4} + \frac{127}{9}e^{2} - \frac{154}{45}$ |
| 41 | $[41, 41, w^{2} - 2]$ | $\phantom{-}\frac{49}{3240}e^{9} - \frac{23}{45}e^{7} + \frac{8899}{1620}e^{5} - \frac{1625}{81}e^{3} + \frac{8267}{405}e$ |
| 43 | $[43, 43, w^{2} - w - 3]$ | $-\frac{7}{90}e^{9} + \frac{49}{20}e^{7} - \frac{2099}{90}e^{5} + \frac{1141}{18}e^{3} - \frac{944}{45}e$ |
| 47 | $[47, 47, -w - 4]$ | $\phantom{-}\frac{23}{1620}e^{8} - \frac{17}{45}e^{6} + \frac{2243}{810}e^{4} - \frac{332}{81}e^{2} + \frac{8}{405}$ |
| 49 | $[49, 7, 3w^{2} - 2w - 24]$ | $-\frac{2}{45}e^{9} + \frac{7}{5}e^{7} - \frac{1193}{90}e^{5} + \frac{317}{9}e^{3} - \frac{533}{45}e$ |
| 53 | $[53, 53, 2w^{2} - w - 12]$ | $\phantom{-}\frac{299}{3240}e^{9} - \frac{133}{45}e^{7} + \frac{46979}{1620}e^{5} - \frac{6937}{81}e^{3} + \frac{18277}{405}e$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $\phantom{-}\frac{44}{405}e^{9} - \frac{313}{90}e^{7} + \frac{27641}{810}e^{5} - \frac{8207}{81}e^{3} + \frac{24326}{405}e$ |
| 61 | $[61, 61, -w^{2} + 3w - 3]$ | $\phantom{-}\frac{8}{405}e^{8} - \frac{61}{90}e^{6} + \frac{2881}{405}e^{4} - \frac{1772}{81}e^{2} + \frac{2582}{405}$ |
| 71 | $[71, 71, w^{2} + w - 7]$ | $-\frac{19}{1620}e^{8} + \frac{16}{45}e^{6} - \frac{2839}{810}e^{4} + \frac{1042}{81}e^{2} - \frac{2824}{405}$ |
| 79 | $[79, 79, 2w + 3]$ | $-\frac{23}{540}e^{9} + \frac{83}{60}e^{7} - \frac{1864}{135}e^{5} + \frac{2257}{54}e^{3} - \frac{2978}{135}e$ |
| 89 | $[89, 89, 2w - 7]$ | $\phantom{-}\frac{17}{810}e^{8} - \frac{31}{45}e^{6} + \frac{2732}{405}e^{4} - \frac{1498}{81}e^{2} + \frac{2794}{405}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w + 2]$ | $-1$ |