Base field 5.5.138136.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 3x^{2} + 4x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[19, 19, -2w^{4} + w^{3} + 12w^{2} - 5]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $29$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} + 3x^{9} - 10x^{8} - 32x^{7} + 28x^{6} + 104x^{5} - 15x^{4} - 105x^{3} - 18x^{2} + 10x + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -2w^{4} + w^{3} + 12w^{2} + w - 5]$ | $-\frac{1}{4}e^{8} - \frac{1}{2}e^{7} + \frac{11}{4}e^{6} + \frac{19}{4}e^{5} - 9e^{4} - \frac{49}{4}e^{3} + 8e^{2} + 7e - \frac{1}{2}$ |
| 8 | $[8, 2, w^{4} - 7w^{2} - 3w + 5]$ | $\phantom{-}\frac{3}{4}e^{9} + 2e^{8} - \frac{33}{4}e^{7} - \frac{87}{4}e^{6} + \frac{57}{2}e^{5} + \frac{291}{4}e^{4} - \frac{67}{2}e^{3} - 76e^{2} + \frac{13}{2}e + 6$ |
| 19 | $[19, 19, -2w^{4} + w^{3} + 12w^{2} - 5]$ | $-1$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 5w - 1]$ | $-\frac{1}{2}e^{9} - \frac{3}{2}e^{8} + 5e^{7} + \frac{31}{2}e^{6} - \frac{31}{2}e^{5} - 48e^{4} + 19e^{3} + 45e^{2} - 10e - 3$ |
| 29 | $[29, 29, 2w^{4} - 2w^{3} - 11w^{2} + 4w + 3]$ | $\phantom{-}\frac{5}{2}e^{9} + \frac{29}{4}e^{8} - 26e^{7} - \frac{309}{4}e^{6} + \frac{329}{4}e^{5} + \frac{501}{2}e^{4} - \frac{335}{4}e^{3} - 251e^{2} + 8e + \frac{43}{2}$ |
| 31 | $[31, 31, -2w^{4} + w^{3} + 12w^{2} + 2w - 5]$ | $\phantom{-}\frac{15}{4}e^{9} + \frac{41}{4}e^{8} - \frac{159}{4}e^{7} - \frac{217}{2}e^{6} + \frac{515}{4}e^{5} + \frac{1391}{4}e^{4} - \frac{529}{4}e^{3} - 341e^{2} + \frac{11}{2}e + \frac{51}{2}$ |
| 37 | $[37, 37, -2w^{4} + 13w^{2} + 5w - 7]$ | $-\frac{9}{4}e^{9} - \frac{13}{2}e^{8} + \frac{97}{4}e^{7} + \frac{281}{4}e^{6} - 83e^{5} - \frac{931}{4}e^{4} + \frac{205}{2}e^{3} + 240e^{2} - \frac{57}{2}e - 20$ |
| 53 | $[53, 53, 3w^{4} - 2w^{3} - 18w^{2} + 3w + 9]$ | $-4e^{9} - \frac{41}{4}e^{8} + \frac{87}{2}e^{7} + \frac{431}{4}e^{6} - \frac{593}{4}e^{5} - 342e^{4} + \frac{691}{4}e^{3} + 330e^{2} - 33e - \frac{53}{2}$ |
| 59 | $[59, 59, 2w^{4} - 13w^{2} - 6w + 5]$ | $-\frac{13}{4}e^{9} - \frac{33}{4}e^{8} + \frac{143}{4}e^{7} + \frac{175}{2}e^{6} - \frac{495}{4}e^{5} - \frac{1127}{4}e^{4} + \frac{587}{4}e^{3} + 277e^{2} - \frac{63}{2}e - \frac{49}{2}$ |
| 61 | $[61, 61, -3w^{4} + 2w^{3} + 18w^{2} - 2w - 11]$ | $-\frac{11}{4}e^{9} - 8e^{8} + \frac{115}{4}e^{7} + \frac{341}{4}e^{6} - \frac{183}{2}e^{5} - \frac{1097}{4}e^{4} + 92e^{3} + 264e^{2} - \frac{7}{2}e - 18$ |
| 61 | $[61, 61, w^{2} - w - 3]$ | $-2e^{9} - 5e^{8} + 21e^{7} + 52e^{6} - 65e^{5} - 164e^{4} + 54e^{3} + 162e^{2} + 14e - 17$ |
| 61 | $[61, 61, 6w^{4} - 2w^{3} - 38w^{2} - 6w + 23]$ | $-\frac{7}{4}e^{9} - 4e^{8} + \frac{79}{4}e^{7} + \frac{169}{4}e^{6} - \frac{141}{2}e^{5} - \frac{541}{4}e^{4} + 87e^{3} + 133e^{2} - \frac{43}{2}e - 13$ |
| 67 | $[67, 67, -w^{4} + 7w^{2} + 4w - 5]$ | $\phantom{-}\frac{3}{4}e^{9} + \frac{3}{2}e^{8} - \frac{35}{4}e^{7} - \frac{63}{4}e^{6} + 34e^{5} + \frac{209}{4}e^{4} - \frac{109}{2}e^{3} - 61e^{2} + \frac{67}{2}e + 12$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + 2w - 1]$ | $\phantom{-}\frac{1}{4}e^{9} + \frac{5}{4}e^{8} - \frac{9}{4}e^{7} - 14e^{6} + \frac{23}{4}e^{5} + \frac{185}{4}e^{4} - \frac{25}{4}e^{3} - 41e^{2} + \frac{13}{2}e - \frac{1}{2}$ |
| 71 | $[71, 71, -w^{2} + 3]$ | $\phantom{-}\frac{3}{4}e^{9} + \frac{7}{4}e^{8} - \frac{35}{4}e^{7} - 19e^{6} + \frac{137}{4}e^{5} + \frac{259}{4}e^{4} - \frac{215}{4}e^{3} - 70e^{2} + \frac{55}{2}e + \frac{5}{2}$ |
| 73 | $[73, 73, 3w^{4} - w^{3} - 19w^{2} - 3w + 9]$ | $\phantom{-}\frac{5}{4}e^{9} + 3e^{8} - \frac{55}{4}e^{7} - \frac{129}{4}e^{6} + \frac{91}{2}e^{5} + \frac{425}{4}e^{4} - \frac{83}{2}e^{3} - 107e^{2} - \frac{21}{2}e - 1$ |
| 79 | $[79, 79, 3w^{4} - w^{3} - 19w^{2} - 4w + 11]$ | $-\frac{5}{2}e^{9} - \frac{29}{4}e^{8} + \frac{55}{2}e^{7} + \frac{315}{4}e^{6} - \frac{389}{4}e^{5} - 260e^{4} + \frac{497}{4}e^{3} + 260e^{2} - 31e - \frac{45}{2}$ |
| 83 | $[83, 83, -w^{4} - w^{3} + 7w^{2} + 8w - 3]$ | $-\frac{3}{2}e^{9} - \frac{19}{4}e^{8} + 15e^{7} + \frac{207}{4}e^{6} - \frac{171}{4}e^{5} - \frac{349}{2}e^{4} + \frac{113}{4}e^{3} + 187e^{2} + 14e - \frac{33}{2}$ |
| 97 | $[97, 97, -2w^{4} + w^{3} + 12w^{2} + 2w - 3]$ | $-\frac{11}{2}e^{9} - \frac{61}{4}e^{8} + 58e^{7} + \frac{649}{4}e^{6} - \frac{745}{4}e^{5} - \frac{1051}{2}e^{4} + \frac{763}{4}e^{3} + 525e^{2} - 22e - \frac{87}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -2w^{4} + w^{3} + 12w^{2} - 5]$ | $1$ |