Base field 3.3.1436.1
Generator \(w\), with minimal polynomial \(x^{3} - 11x - 12\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[11, 11, -w^{2} + w + 11]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 13x^{10} + 60x^{8} - 119x^{6} + 102x^{4} - 36x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $-\frac{3}{2}e^{10} + \frac{37}{2}e^{8} - 78e^{6} + \frac{259}{2}e^{4} - 75e^{2} + 11$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w^{2} - w - 9]$ | $-\frac{1}{2}e^{11} + \frac{13}{2}e^{9} - 30e^{7} + \frac{119}{2}e^{5} - 50e^{3} + 13e$ |
| 9 | $[9, 3, -w^{2} + 3w + 5]$ | $\phantom{-}\frac{5}{2}e^{11} - \frac{63}{2}e^{9} + 137e^{7} - \frac{479}{2}e^{5} + 153e^{3} - 28e$ |
| 11 | $[11, 11, -w^{2} + w + 11]$ | $-1$ |
| 13 | $[13, 13, 2w^{2} - 4w - 13]$ | $-\frac{7}{2}e^{11} + \frac{87}{2}e^{9} - 185e^{7} + \frac{619}{2}e^{5} - 177e^{3} + 23e$ |
| 23 | $[23, 23, -w^{2} + w + 7]$ | $-\frac{3}{2}e^{11} + \frac{37}{2}e^{9} - 77e^{7} + \frac{241}{2}e^{5} - 53e^{3} + e$ |
| 29 | $[29, 29, -w^{2} - w + 1]$ | $\phantom{-}\frac{9}{2}e^{11} - \frac{111}{2}e^{9} + 233e^{7} - \frac{761}{2}e^{5} + 206e^{3} - 20e$ |
| 41 | $[41, 41, -2w^{2} + 2w + 19]$ | $-\frac{9}{2}e^{11} + \frac{113}{2}e^{9} - 245e^{7} + \frac{859}{2}e^{5} - 284e^{3} + 59e$ |
| 41 | $[41, 41, w^{2} - 3w - 7]$ | $\phantom{-}e^{10} - 13e^{8} + 59e^{6} - 108e^{4} + 67e^{2} - 10$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $-\frac{5}{2}e^{11} + \frac{61}{2}e^{9} - 127e^{7} + \frac{415}{2}e^{5} - 115e^{3} + 10e$ |
| 47 | $[47, 47, 3w^{2} - 7w - 17]$ | $\phantom{-}e^{10} - 12e^{8} + 50e^{6} - 84e^{4} + 47e^{2} - 4$ |
| 53 | $[53, 53, -2w - 1]$ | $\phantom{-}\frac{9}{2}e^{11} - \frac{111}{2}e^{9} + 235e^{7} - \frac{795}{2}e^{5} + 247e^{3} - 45e$ |
| 61 | $[61, 61, -2w + 7]$ | $\phantom{-}\frac{1}{2}e^{11} - \frac{11}{2}e^{9} + 19e^{7} - \frac{37}{2}e^{5} - 10e^{3} + 13e$ |
| 67 | $[67, 67, 3w^{2} - 5w - 23]$ | $\phantom{-}\frac{7}{2}e^{11} - \frac{85}{2}e^{9} + 173e^{7} - \frac{527}{2}e^{5} + 117e^{3} + e$ |
| 67 | $[67, 67, 2w^{2} - 4w - 11]$ | $-4e^{11} + 48e^{9} - 192e^{7} + 283e^{5} - 116e^{3} + 4e$ |
| 67 | $[67, 67, 3w^{2} - 7w - 13]$ | $-2e^{10} + 23e^{8} - 88e^{6} + 124e^{4} - 47e^{2}$ |
| 79 | $[79, 79, w^{2} + w - 5]$ | $-\frac{11}{2}e^{11} + \frac{139}{2}e^{9} - 303e^{7} + \frac{1055}{2}e^{5} - 320e^{3} + 39e$ |
| 89 | $[89, 89, 5w^{2} - 7w - 47]$ | $-e^{10} + 12e^{8} - 47e^{6} + 66e^{4} - 31e^{2} + 4$ |
| 97 | $[97, 97, 5w^{2} - 11w - 29]$ | $\phantom{-}\frac{3}{2}e^{11} - \frac{41}{2}e^{9} + 102e^{7} - \frac{447}{2}e^{5} + 202e^{3} - 50e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -w^{2} + w + 11]$ | $1$ |