Properties

Label 2.2.205.1-16.1-d
Base field \(\Q(\sqrt{205}) \)
Weight $[2, 2]$
Level norm $16$
Level $[16, 4, 4]$
Dimension $4$
CM no
Base change yes

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Base field \(\Q(\sqrt{205}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 51\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[16, 4, 4]$
Dimension: $4$
CM: no
Base change: yes
Newspace dimension: $108$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 6x^{2} + 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}e$
4 $[4, 2, 2]$ $\phantom{-}0$
5 $[5, 5, -w + 8]$ $\phantom{-}e^{2} + 2$
7 $[7, 7, w + 1]$ $-e^{3} - 5e$
7 $[7, 7, w + 5]$ $-e^{3} - 5e$
13 $[13, 13, w + 3]$ $\phantom{-}2e^{3} + 10e$
13 $[13, 13, w + 9]$ $\phantom{-}2e^{3} + 10e$
17 $[17, 17, w]$ $-2e^{3} - 8e$
17 $[17, 17, w + 16]$ $-2e^{3} - 8e$
31 $[31, 31, -w - 4]$ $-2e^{2} - 8$
31 $[31, 31, w - 5]$ $-2e^{2} - 8$
41 $[41, 41, 3w - 22]$ $\phantom{-}4e^{2} + 14$
47 $[47, 47, w + 19]$ $\phantom{-}2e^{3} + 9e$
47 $[47, 47, w + 27]$ $\phantom{-}2e^{3} + 9e$
53 $[53, 53, w + 14]$ $-2e^{3} - 14e$
53 $[53, 53, w + 38]$ $-2e^{3} - 14e$
59 $[59, 59, -w - 10]$ $\phantom{-}2e^{2} + 4$
59 $[59, 59, w - 11]$ $\phantom{-}2e^{2} + 4$
61 $[61, 61, 2w - 13]$ $\phantom{-}2e^{2}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, 2]$ $1$