Base field 4.4.14656.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 4x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11, 11, w^{2} - 3]$ |
| Dimension: | $9$ |
| 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:
| \(x^{9} + 3x^{8} - 8x^{7} - 27x^{6} + 13x^{5} + 69x^{4} + 13x^{3} - 40x^{2} - 10x + 5\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{1}{2}e^{5} - \frac{9}{2}e^{4} - \frac{5}{2}e^{3} + \frac{21}{2}e^{2} + \frac{5}{2}e - \frac{7}{2}$ |
| 5 | $[5, 5, -w^{2} + w + 1]$ | $-\frac{1}{2}e^{8} - \frac{3}{2}e^{7} + \frac{9}{2}e^{6} + \frac{27}{2}e^{5} - \frac{23}{2}e^{4} - \frac{65}{2}e^{3} + \frac{13}{2}e^{2} + 12e - 2$ |
| 11 | $[11, 11, w^{2} - 3]$ | $-1$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $\phantom{-}\frac{3}{2}e^{8} + 3e^{7} - 14e^{6} - 25e^{5} + 35e^{4} + 57e^{3} - 15e^{2} - \frac{43}{2}e + 2$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 3w - 1]$ | $-2e^{8} - \frac{7}{2}e^{7} + \frac{39}{2}e^{6} + \frac{57}{2}e^{5} - \frac{107}{2}e^{4} - \frac{127}{2}e^{3} + \frac{71}{2}e^{2} + \frac{47}{2}e - 6$ |
| 27 | $[27, 3, w^{3} - 3w^{2} - w + 5]$ | $\phantom{-}2e^{8} + 4e^{7} - \frac{41}{2}e^{6} - \frac{69}{2}e^{5} + \frac{133}{2}e^{4} + \frac{167}{2}e^{3} - \frac{149}{2}e^{2} - \frac{83}{2}e + \frac{47}{2}$ |
| 41 | $[41, 41, -w^{3} + 2w^{2} + w - 1]$ | $-\frac{5}{2}e^{8} - 5e^{7} + 23e^{6} + 41e^{5} - 56e^{4} - 91e^{3} + 21e^{2} + \frac{65}{2}e - 2$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 2w - 1]$ | $\phantom{-}\frac{3}{2}e^{8} + 4e^{7} - 14e^{6} - 36e^{5} + 38e^{4} + 89e^{3} - 27e^{2} - \frac{77}{2}e + 9$ |
| 43 | $[43, 43, w^{3} - w^{2} - 5w + 1]$ | $-\frac{5}{2}e^{8} - \frac{11}{2}e^{7} + 24e^{6} + 48e^{5} - 67e^{4} - 118e^{3} + 49e^{2} + \frac{123}{2}e - \frac{13}{2}$ |
| 47 | $[47, 47, w^{2} - 2w - 5]$ | $-\frac{1}{2}e^{8} + \frac{1}{2}e^{7} + \frac{13}{2}e^{6} - \frac{11}{2}e^{5} - \frac{45}{2}e^{4} + \frac{31}{2}e^{3} + \frac{39}{2}e^{2} - 12e$ |
| 47 | $[47, 47, -2w^{3} + 6w^{2} + w - 5]$ | $\phantom{-}e^{8} - 12e^{6} + 2e^{5} + 42e^{4} - 7e^{3} - 45e^{2} + e + 14$ |
| 61 | $[61, 61, -2w^{3} + 5w^{2} + 4w - 7]$ | $\phantom{-}\frac{1}{2}e^{8} + 3e^{7} - \frac{7}{2}e^{6} - \frac{57}{2}e^{5} + \frac{17}{2}e^{4} + \frac{149}{2}e^{3} - \frac{21}{2}e^{2} - 41e + \frac{9}{2}$ |
| 67 | $[67, 67, -2w^{2} + 2w + 9]$ | $-\frac{5}{2}e^{8} - \frac{13}{2}e^{7} + \frac{47}{2}e^{6} + \frac{119}{2}e^{5} - \frac{125}{2}e^{4} - \frac{305}{2}e^{3} + \frac{75}{2}e^{2} + 80e - 6$ |
| 67 | $[67, 67, -w^{3} + 2w^{2} + 4w - 1]$ | $\phantom{-}\frac{11}{2}e^{8} + 11e^{7} - \frac{107}{2}e^{6} - \frac{191}{2}e^{5} + \frac{293}{2}e^{4} + \frac{465}{2}e^{3} - \frac{187}{2}e^{2} - 110e + \frac{37}{2}$ |
| 71 | $[71, 71, w^{3} - w^{2} - 6w + 3]$ | $-3e^{8} - 7e^{7} + \frac{57}{2}e^{6} + \frac{123}{2}e^{5} - \frac{159}{2}e^{4} - \frac{301}{2}e^{3} + \frac{129}{2}e^{2} + \frac{147}{2}e - \frac{41}{2}$ |
| 83 | $[83, 83, -w^{3} + 2w^{2} + 5w + 1]$ | $\phantom{-}\frac{1}{2}e^{8} - \frac{13}{2}e^{6} + \frac{1}{2}e^{5} + \frac{49}{2}e^{4} - \frac{3}{2}e^{3} - \frac{45}{2}e^{2} - \frac{3}{2}$ |
| 89 | $[89, 89, -w - 3]$ | $\phantom{-}\frac{1}{2}e^{8} + e^{7} - \frac{13}{2}e^{6} - \frac{19}{2}e^{5} + \frac{61}{2}e^{4} + \frac{47}{2}e^{3} - \frac{113}{2}e^{2} - 12e + \frac{51}{2}$ |
| 89 | $[89, 89, -w^{2} - 2w + 1]$ | $\phantom{-}2e^{7} + \frac{3}{2}e^{6} - \frac{41}{2}e^{5} - \frac{17}{2}e^{4} + \frac{111}{2}e^{3} + \frac{25}{2}e^{2} - \frac{61}{2}e - \frac{7}{2}$ |
| 97 | $[97, 97, w^{3} - w^{2} - 6w + 1]$ | $\phantom{-}3e^{8} + \frac{9}{2}e^{7} - \frac{59}{2}e^{6} - \frac{69}{2}e^{5} + \frac{163}{2}e^{4} + \frac{141}{2}e^{3} - \frac{111}{2}e^{2} - \frac{35}{2}e + 11$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, w^{2} - 3]$ | $1$ |