Base field 4.4.11525.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} + 5x + 25\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[11,11,\frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 20x^{2} - 4x + 52\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ | $\phantom{-}e$ |
5 | $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ | $-\frac{3}{34}e^{3} - \frac{2}{17}e^{2} + \frac{16}{17}e + \frac{50}{17}$ |
11 | $[11, 11, w + 1]$ | $\phantom{-}\frac{3}{17}e^{3} - \frac{9}{34}e^{2} - \frac{32}{17}e + \frac{70}{17}$ |
11 | $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ | $-1$ |
16 | $[16, 2, 2]$ | $-\frac{3}{34}e^{3} + \frac{13}{34}e^{2} + \frac{16}{17}e - \frac{86}{17}$ |
19 | $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ | $\phantom{-}\frac{1}{34}e^{3} - \frac{5}{17}e^{2} + \frac{6}{17}e + \frac{40}{17}$ |
19 | $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ | $\phantom{-}\frac{9}{34}e^{3} - \frac{5}{34}e^{2} - \frac{82}{17}e + \frac{20}{17}$ |
19 | $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ | $\phantom{-}\frac{1}{34}e^{3} - \frac{5}{17}e^{2} + \frac{6}{17}e + \frac{40}{17}$ |
19 | $[19, 19, w - 1]$ | $-\frac{1}{17}e^{3} - \frac{7}{17}e^{2} + \frac{5}{17}e + \frac{90}{17}$ |
29 | $[29, 29, w^{2} - w - 8]$ | $-\frac{3}{34}e^{3} - \frac{2}{17}e^{2} + \frac{50}{17}e + \frac{84}{17}$ |
29 | $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ | $\phantom{-}\frac{5}{34}e^{3} + \frac{1}{34}e^{2} - \frac{38}{17}e + \frac{64}{17}$ |
31 | $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ | $-\frac{2}{17}e^{3} + \frac{3}{17}e^{2} + \frac{10}{17}e + \frac{44}{17}$ |
31 | $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ | $-\frac{4}{17}e^{3} + \frac{6}{17}e^{2} + \frac{37}{17}e - \frac{48}{17}$ |
61 | $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ | $-\frac{2}{17}e^{3} + \frac{3}{17}e^{2} + \frac{61}{17}e + \frac{78}{17}$ |
61 | $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ | $-\frac{2}{17}e^{3} + \frac{3}{17}e^{2} + \frac{10}{17}e - \frac{109}{17}$ |
61 | $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ | $\phantom{-}\frac{9}{17}e^{3} - \frac{5}{17}e^{2} - \frac{164}{17}e - \frac{11}{17}$ |
61 | $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ | $\phantom{-}\frac{1}{17}e^{3} + \frac{31}{34}e^{2} - \frac{22}{17}e - \frac{124}{17}$ |
71 | $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ | $\phantom{-}\frac{3}{34}e^{3} + \frac{2}{17}e^{2} - \frac{16}{17}e + \frac{86}{17}$ |
71 | $[71, 71, w^{2} - 8]$ | $-\frac{3}{34}e^{3} + \frac{13}{34}e^{2} + \frac{16}{17}e - \frac{188}{17}$ |
79 | $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ | $\phantom{-}\frac{1}{17}e^{3} + \frac{7}{17}e^{2} - \frac{22}{17}e - \frac{73}{17}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$11$ | $[11,11,\frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ | $1$ |