Base field 6.6.300125.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 7x^{4} + 2x^{3} + 7x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[211,211,7w^{5} - 3w^{4} - 49w^{3} - 16w^{2} + 31w + 5]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 7x^{4} - 66x^{3} - 262x^{2} + 1569x - 449\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 29 | $[29, 29, -9w^{5} + 3w^{4} + 64w^{3} + 26w^{2} - 40w - 10]$ | $\phantom{-}\frac{1}{80}e^{4} + \frac{1}{10}e^{3} - \frac{9}{40}e^{2} - \frac{5}{2}e - \frac{591}{80}$ |
| 29 | $[29, 29, w^{5} - 7w^{3} - 5w^{2} + 2w + 2]$ | $\phantom{-}\frac{3}{8}e^{3} + \frac{9}{8}e^{2} - \frac{127}{8}e + \frac{51}{8}$ |
| 29 | $[29, 29, w^{4} - w^{3} - 6w^{2} + 2]$ | $\phantom{-}e$ |
| 29 | $[29, 29, 5w^{5} - w^{4} - 36w^{3} - 19w^{2} + 21w + 9]$ | $-\frac{3}{80}e^{4} - \frac{4}{5}e^{3} - \frac{33}{40}e^{2} + 26e - \frac{587}{80}$ |
| 29 | $[29, 29, -w^{5} + w^{4} + 7w^{3} - 2w^{2} - 6w + 1]$ | $\phantom{-}\frac{1}{80}e^{4} - \frac{1}{40}e^{3} - \frac{17}{20}e^{2} + \frac{17}{8}e + \frac{59}{80}$ |
| 29 | $[29, 29, 2w^{5} - 15w^{3} - 10w^{2} + 11w + 5]$ | $-\frac{1}{10}e^{4} - \frac{47}{40}e^{3} + \frac{57}{40}e^{2} + \frac{263}{8}e - \frac{721}{40}$ |
| 41 | $[41, 41, 5w^{5} - w^{4} - 36w^{3} - 18w^{2} + 21w + 5]$ | $-\frac{1}{20}e^{4} - \frac{2}{5}e^{3} + \frac{7}{5}e^{2} + 10e - \frac{239}{20}$ |
| 41 | $[41, 41, -5w^{5} + 2w^{4} + 36w^{3} + 11w^{2} - 25w - 2]$ | $\phantom{-}\frac{1}{8}e^{4} + \frac{5}{4}e^{3} - \frac{5}{2}e^{2} - \frac{131}{4}e + \frac{143}{8}$ |
| 41 | $[41, 41, 6w^{5} - w^{4} - 44w^{3} - 23w^{2} + 30w + 8]$ | $\phantom{-}\frac{1}{10}e^{4} + \frac{47}{40}e^{3} - \frac{37}{40}e^{2} - \frac{247}{8}e - \frac{19}{40}$ |
| 41 | $[41, 41, 13w^{5} - 4w^{4} - 93w^{3} - 39w^{2} + 59w + 16]$ | $\phantom{-}\frac{1}{16}e^{4} + \frac{1}{2}e^{3} - \frac{15}{8}e^{2} - 12e + \frac{213}{16}$ |
| 41 | $[41, 41, -4w^{5} + 30w^{3} + 19w^{2} - 19w - 8]$ | $-\frac{1}{80}e^{4} - \frac{1}{10}e^{3} + \frac{9}{40}e^{2} + \frac{5}{2}e - \frac{49}{80}$ |
| 41 | $[41, 41, w^{5} - 7w^{3} - 6w^{2} + 2w + 3]$ | $\phantom{-}\frac{1}{80}e^{4} - \frac{1}{40}e^{3} - \frac{3}{5}e^{2} + \frac{21}{8}e - \frac{641}{80}$ |
| 49 | $[49, 7, -5w^{5} + w^{4} + 36w^{3} + 19w^{2} - 22w - 6]$ | $-\frac{7}{80}e^{4} - \frac{23}{40}e^{3} + \frac{27}{10}e^{2} + \frac{83}{8}e - \frac{1073}{80}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{1}{10}e^{4} + \frac{67}{40}e^{3} + \frac{33}{40}e^{2} - \frac{407}{8}e + \frac{251}{40}$ |
| 71 | $[71, 71, -8w^{5} + w^{4} + 58w^{3} + 34w^{2} - 34w - 16]$ | $-\frac{3}{80}e^{4} - \frac{7}{40}e^{3} + \frac{4}{5}e^{2} - \frac{9}{8}e + \frac{923}{80}$ |
| 71 | $[71, 71, -6w^{5} + 2w^{4} + 42w^{3} + 18w^{2} - 23w - 6]$ | $\phantom{-}\frac{1}{4}e^{3} + e^{2} - \frac{35}{4}e - \frac{11}{2}$ |
| 71 | $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 27w^{2} - 38w - 10]$ | $-\frac{1}{20}e^{4} - \frac{23}{20}e^{3} - \frac{11}{10}e^{2} + \frac{157}{4}e - \frac{419}{20}$ |
| 71 | $[71, 71, 4w^{5} - 30w^{3} - 19w^{2} + 20w + 8]$ | $\phantom{-}\frac{9}{80}e^{4} + \frac{23}{20}e^{3} - \frac{81}{40}e^{2} - \frac{119}{4}e + \frac{921}{80}$ |
| 71 | $[71, 71, -10w^{5} + 3w^{4} + 72w^{3} + 30w^{2} - 48w - 10]$ | $-\frac{1}{80}e^{4} + \frac{1}{40}e^{3} + \frac{17}{20}e^{2} - \frac{9}{8}e - \frac{459}{80}$ |
| 71 | $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 26w^{2} - 37w - 8]$ | $\phantom{-}\frac{1}{20}e^{4} + \frac{9}{10}e^{3} + \frac{3}{5}e^{2} - 28e + \frac{149}{20}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $211$ | $[211,211,7w^{5} - 3w^{4} - 49w^{3} - 16w^{2} + 31w + 5]$ | $-1$ |