Properties

Base field \(\Q(\sqrt{2}, \sqrt{3})\)
Weight [2, 2, 2, 2]
Level norm 49
Level $[49,7,-2w^{3} + 6w - 1]$
Label 4.4.2304.1-49.2-c
Dimension 6
CM no
Base change yes

Related objects

Downloads

Learn more about

Base field \(\Q(\sqrt{2}, \sqrt{3})\)

Generator \(w\), with minimal polynomial \(x^{4} - 4x^{2} + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[49,7,-2w^{3} + 6w - 1]$
Label 4.4.2304.1-49.2-c
Dimension 6
Is CM no
Is base change yes
Parent newspace dimension 8

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 14x^{4} + 53x^{2} - 32\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w^{3} - 4w + 1]$ $\phantom{-}e$
9 $[9, 3, -w^{2} + 2]$ $-e^{4} + 7e^{2} - 2$
23 $[23, 23, w^{3} - w^{2} - 4w + 1]$ $-2e$
23 $[23, 23, w^{2} - w - 3]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 8e$
23 $[23, 23, -w^{2} - w + 3]$ $-2e$
23 $[23, 23, -w^{3} - w^{2} + 4w + 1]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 8e$
25 $[25, 5, w^{3} - 5w + 1]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{9}{2}e^{2} + 6$
25 $[25, 5, w^{3} - 5w - 1]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{9}{2}e^{2} + 6$
47 $[47, 47, -3w^{3} + 2w^{2} + 12w - 8]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 6e$
47 $[47, 47, -2w^{3} - w^{2} + 6w]$ $-e^{5} + 9e^{3} - 14e$
47 $[47, 47, 2w^{3} - w^{2} - 6w]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 6e$
47 $[47, 47, w^{2} + w - 5]$ $-e^{5} + 9e^{3} - 14e$
49 $[49, 7, 2w^{3} - 6w - 1]$ $-e^{4} + 11e^{2} - 18$
49 $[49, 7, -2w^{3} + 6w - 1]$ $-1$
71 $[71, 71, 2w^{3} - w^{2} - 7w + 1]$ $\phantom{-}2e^{3} - 14e$
71 $[71, 71, 3w^{3} - w^{2} - 11w + 2]$ $-2e^{3} + 12e$
71 $[71, 71, 4w^{3} - 2w^{2} - 14w + 5]$ $\phantom{-}2e^{3} - 14e$
71 $[71, 71, -3w^{3} + 2w^{2} + 10w - 4]$ $-2e^{3} + 12e$
73 $[73, 73, -w^{3} - 2w^{2} + 3w + 5]$ $-2e^{2} + 2$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $-2e^{2} + 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
49 $[49,7,-2w^{3} + 6w - 1]$ $1$