Properties

Label 2.2.21.1-67.1-c
Base field \(\Q(\sqrt{21}) \)
Weight $[2, 2]$
Level norm $67$
Level $[67, 67, -w - 8]$
Dimension $4$
CM no
Base change no

Related objects

Downloads

Learn more

Base field \(\Q(\sqrt{21}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 5\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[67, 67, -w - 8]$
Dimension: $4$
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:

\(x^{4} - 8x^{2} + 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
4 $[4, 2, 2]$ $-2$
5 $[5, 5, w]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{7}{2}e$
5 $[5, 5, w - 1]$ $-\frac{1}{2}e^{3} + \frac{5}{2}e$
7 $[7, 7, -w - 3]$ $-\frac{1}{2}e^{2} - \frac{1}{2}$
17 $[17, 17, -2w + 3]$ $-e^{3} + 7e$
17 $[17, 17, -2w - 1]$ $\phantom{-}e^{3} - 10e$
37 $[37, 37, w + 6]$ $-\frac{3}{2}e^{2} + \frac{5}{2}$
37 $[37, 37, -w + 7]$ $\phantom{-}2e^{2} - 11$
41 $[41, 41, 3w + 1]$ $\phantom{-}3e^{3} - 19e$
41 $[41, 41, -3w + 4]$ $-e^{3} + 10e$
43 $[43, 43, 3w + 8]$ $\phantom{-}e^{2} - 11$
43 $[43, 43, 3w - 11]$ $-e^{2} - 2$
47 $[47, 47, 3w - 2]$ $-e^{3} + 10e$
47 $[47, 47, 3w - 1]$ $-\frac{5}{2}e^{3} + \frac{39}{2}e$
59 $[59, 59, -5w - 6]$ $-\frac{1}{2}e^{3} + \frac{3}{2}e$
59 $[59, 59, -4w - 3]$ $-\frac{1}{2}e^{3} + \frac{9}{2}e$
67 $[67, 67, -w - 8]$ $\phantom{-}1$
67 $[67, 67, w - 9]$ $-\frac{5}{2}e^{2} + \frac{13}{2}$
79 $[79, 79, 2w - 11]$ $\phantom{-}3e^{2} - 13$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$67$ $[67, 67, -w - 8]$ $-1$