Properties

Label 2.2.24.1-29.2-b
Base field \(\Q(\sqrt{6}) \)
Weight $[2, 2]$
Level norm $29$
Level $[29,29,3w + 5]$
Dimension $3$
CM no
Base change no

Related objects

Downloads

Learn more

Base field \(\Q(\sqrt{6}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 6\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[29,29,3w + 5]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{3} + 2x^{2} - 3x - 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 2]$ $\phantom{-}e$
3 $[3, 3, w - 3]$ $-e^{2} + 3$
5 $[5, 5, w + 1]$ $-e^{2} - e$
5 $[5, 5, w - 1]$ $\phantom{-}e^{2} - 5$
19 $[19, 19, w + 5]$ $\phantom{-}3e^{2} + 3e - 8$
19 $[19, 19, -w + 5]$ $-e - 3$
23 $[23, 23, -2w + 1]$ $\phantom{-}2e^{2} - e - 5$
23 $[23, 23, -2w - 1]$ $-e^{2} + 5$
29 $[29, 29, -3w + 5]$ $\phantom{-}e^{2} + 3e - 5$
29 $[29, 29, -3w - 5]$ $\phantom{-}1$
43 $[43, 43, -w - 7]$ $\phantom{-}e^{2} - 5e - 5$
43 $[43, 43, w - 7]$ $-e^{2} - e$
47 $[47, 47, 4w - 7]$ $\phantom{-}e^{2} + 4e$
47 $[47, 47, 6w - 13]$ $-4e - 5$
49 $[49, 7, -7]$ $-3e^{2} - e + 4$
53 $[53, 53, -3w - 1]$ $-2e^{2} + 2e + 5$
53 $[53, 53, 3w - 1]$ $\phantom{-}2e^{2} - e - 10$
67 $[67, 67, -7w + 19]$ $-e^{2} - e - 6$
67 $[67, 67, -3w + 11]$ $-4e^{2} + 9$
71 $[71, 71, -4w - 5]$ $\phantom{-}4e^{2} + 6e - 15$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29,29,3w + 5]$ $-1$