Base field \(\Q(\sqrt{29}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 7\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[53,53,-3w - 2]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - x^{4} - 17x^{3} + 24x^{2} + 61x - 97\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{5}{13}e^{4} + \frac{7}{13}e^{3} - \frac{76}{13}e^{2} - 4e + \frac{253}{13}$ |
5 | $[5, 5, w - 2]$ | $\phantom{-}\frac{5}{13}e^{4} + \frac{7}{13}e^{3} - \frac{63}{13}e^{2} - 3e + \frac{162}{13}$ |
7 | $[7, 7, w]$ | $\phantom{-}\frac{5}{13}e^{4} + \frac{7}{13}e^{3} - \frac{76}{13}e^{2} - 4e + \frac{227}{13}$ |
7 | $[7, 7, -w + 1]$ | $-\frac{14}{13}e^{4} - \frac{17}{13}e^{3} + \frac{192}{13}e^{2} + 7e - \frac{568}{13}$ |
9 | $[9, 3, 3]$ | $-\frac{14}{13}e^{4} - \frac{17}{13}e^{3} + \frac{205}{13}e^{2} + 8e - \frac{672}{13}$ |
13 | $[13, 13, w + 4]$ | $\phantom{-}\frac{6}{13}e^{4} - \frac{2}{13}e^{3} - \frac{99}{13}e^{2} + 2e + \frac{314}{13}$ |
13 | $[13, 13, w - 5]$ | $\phantom{-}e^{2} - 9$ |
23 | $[23, 23, -w - 5]$ | $\phantom{-}\frac{27}{13}e^{4} + \frac{30}{13}e^{3} - \frac{387}{13}e^{2} - 12e + \frac{1166}{13}$ |
23 | $[23, 23, w - 6]$ | $-\frac{1}{13}e^{4} - \frac{4}{13}e^{3} + \frac{10}{13}e^{2} + e - \frac{48}{13}$ |
29 | $[29, 29, 2w - 1]$ | $\phantom{-}\frac{4}{13}e^{4} + \frac{16}{13}e^{3} - \frac{40}{13}e^{2} - 8e + \frac{101}{13}$ |
53 | $[53, 53, 3w - 5]$ | $-\frac{5}{13}e^{4} - \frac{7}{13}e^{3} + \frac{50}{13}e^{2} + 3e - \frac{123}{13}$ |
53 | $[53, 53, -3w - 2]$ | $\phantom{-}1$ |
59 | $[59, 59, -3w - 1]$ | $-\frac{2}{13}e^{4} - \frac{8}{13}e^{3} + \frac{20}{13}e^{2} + 5e - \frac{44}{13}$ |
59 | $[59, 59, 3w - 4]$ | $\phantom{-}\frac{15}{13}e^{4} + \frac{21}{13}e^{3} - \frac{202}{13}e^{2} - 9e + \frac{512}{13}$ |
67 | $[67, 67, 3w - 13]$ | $\phantom{-}\frac{4}{13}e^{4} + \frac{3}{13}e^{3} - \frac{53}{13}e^{2} - 2e + \frac{88}{13}$ |
67 | $[67, 67, -3w - 10]$ | $-\frac{3}{13}e^{4} + \frac{1}{13}e^{3} + \frac{30}{13}e^{2} - 3e - \frac{66}{13}$ |
71 | $[71, 71, 2w - 11]$ | $-\frac{3}{13}e^{4} + \frac{14}{13}e^{3} + \frac{69}{13}e^{2} - 8e - \frac{170}{13}$ |
71 | $[71, 71, -2w - 9]$ | $\phantom{-}\frac{31}{13}e^{4} + \frac{33}{13}e^{3} - \frac{453}{13}e^{2} - 17e + \frac{1501}{13}$ |
83 | $[83, 83, -w - 9]$ | $-\frac{3}{13}e^{4} + \frac{14}{13}e^{3} + \frac{95}{13}e^{2} - 9e - \frac{378}{13}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$53$ | $[53,53,-3w - 2]$ | $-1$ |