Properties

Base field \(\Q(\sqrt{3}) \)
Weight [2, 2]
Level norm 49
Level $[49, 7, -7]$
Label 2.2.12.1-49.1-a
Dimension 6
CM no
Base change yes

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

Generator \(w\), with minimal polynomial \(x^{2} - 3\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2]
Level $[49, 7, -7]$
Label 2.2.12.1-49.1-a
Dimension 6
Is CM no
Is base change yes
Parent newspace dimension 6

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 10x^{4} + 21x^{2} - 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}e$
3 $[3, 3, w]$ $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 7e$
11 $[11, 11, -2w + 1]$ $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + \frac{17}{2}e$
11 $[11, 11, 2w + 1]$ $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + \frac{17}{2}e$
13 $[13, 13, w + 4]$ $-\frac{1}{2}e^{4} + \frac{7}{2}e^{2} - 2$
13 $[13, 13, -w + 4]$ $-\frac{1}{2}e^{4} + \frac{7}{2}e^{2} - 2$
23 $[23, 23, -3w + 2]$ $\phantom{-}\frac{1}{2}e^{5} - 4e^{3} + \frac{7}{2}e$
23 $[23, 23, 3w + 2]$ $\phantom{-}\frac{1}{2}e^{5} - 4e^{3} + \frac{7}{2}e$
25 $[25, 5, 5]$ $\phantom{-}e^{4} - 7e^{2} + 8$
37 $[37, 37, 2w - 7]$ $-e^{4} + 9e^{2} - 12$
37 $[37, 37, -2w - 7]$ $-e^{4} + 9e^{2} - 12$
47 $[47, 47, -4w - 1]$ $\phantom{-}e^{5} - 8e^{3} + 7e$
47 $[47, 47, 4w - 1]$ $\phantom{-}e^{5} - 8e^{3} + 7e$
49 $[49, 7, -7]$ $-1$
59 $[59, 59, 5w - 4]$ $-\frac{1}{2}e^{5} + \frac{7}{2}e^{3} + 4e$
59 $[59, 59, -5w - 4]$ $-\frac{1}{2}e^{5} + \frac{7}{2}e^{3} + 4e$
61 $[61, 61, -w - 8]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{15}{2}e^{2} + 14$
61 $[61, 61, w - 8]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{15}{2}e^{2} + 14$
71 $[71, 71, 5w - 2]$ $-\frac{3}{2}e^{5} + 12e^{3} - \frac{25}{2}e$
71 $[71, 71, -5w - 2]$ $-\frac{3}{2}e^{5} + 12e^{3} - \frac{25}{2}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
49 $[49, 7, -7]$ $1$