Base field \(\Q(\sqrt{321}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 80\); narrow class number \(6\) and class number \(3\).
Form
Weight: | $[2, 2]$ |
Level: | $[1, 1, 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $69$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + x^{3} + 4x^{2} - 3x + 9\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}e$ |
2 | $[2, 2, w + 1]$ | $-\frac{1}{4}e^{3} - e + \frac{3}{4}$ |
3 | $[3, 3, -2w + 19]$ | $-2$ |
5 | $[5, 5, w]$ | $\phantom{-}\frac{1}{4}e^{3} + e^{2} + e - \frac{3}{4}$ |
5 | $[5, 5, w + 4]$ | $-\frac{1}{4}e^{3} - e^{2} - e - \frac{9}{4}$ |
13 | $[13, 13, w + 1]$ | $\phantom{-}\frac{1}{12}e^{3} + \frac{1}{3}e^{2} - \frac{5}{3}e + \frac{3}{4}$ |
13 | $[13, 13, w + 11]$ | $\phantom{-}\frac{5}{12}e^{3} - \frac{1}{3}e^{2} + \frac{5}{3}e - \frac{5}{4}$ |
17 | $[17, 17, w + 3]$ | $\phantom{-}\frac{3}{4}e^{3} + e^{2} + 3e - \frac{9}{4}$ |
17 | $[17, 17, w + 13]$ | $-\frac{1}{4}e^{3} - e^{2} - 3e - \frac{9}{4}$ |
19 | $[19, 19, w + 6]$ | $-\frac{7}{12}e^{3} - \frac{1}{3}e^{2} - \frac{7}{3}e + \frac{7}{4}$ |
19 | $[19, 19, w + 12]$ | $\phantom{-}\frac{1}{12}e^{3} + \frac{1}{3}e^{2} + \frac{7}{3}e + \frac{3}{4}$ |
37 | $[37, 37, w + 2]$ | $-\frac{7}{12}e^{3} - \frac{7}{3}e^{2} - \frac{7}{3}e + \frac{7}{4}$ |
37 | $[37, 37, w + 34]$ | $\phantom{-}\frac{7}{12}e^{3} + \frac{7}{3}e^{2} + \frac{7}{3}e + \frac{21}{4}$ |
49 | $[49, 7, -7]$ | $-\frac{1}{2}e^{3} + \frac{19}{2}$ |
59 | $[59, 59, -4w - 33]$ | $-\frac{1}{2}e^{3} + \frac{15}{2}$ |
59 | $[59, 59, 4w - 37]$ | $-\frac{1}{2}e^{3} + \frac{15}{2}$ |
61 | $[61, 61, w + 28]$ | $-\frac{5}{12}e^{3} - \frac{5}{3}e^{2} + \frac{1}{3}e - \frac{15}{4}$ |
61 | $[61, 61, w + 32]$ | $-\frac{1}{12}e^{3} + \frac{5}{3}e^{2} - \frac{1}{3}e + \frac{1}{4}$ |
71 | $[71, 71, w + 22]$ | $-\frac{3}{4}e^{3} + e^{2} - 3e + \frac{9}{4}$ |
71 | $[71, 71, w + 48]$ | $-\frac{1}{4}e^{3} - e^{2} + 3e - \frac{9}{4}$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).