Properties

Label 2.2.205.1-5.1-i
Base field \(\Q(\sqrt{205}) \)
Weight $[2, 2]$
Level norm $5$
Level $[5, 5, -w + 8]$
Dimension $6$
CM no
Base change no

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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: $[5, 5, -w + 8]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $36$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 8x^{4} + 15x^{2} - 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-e$
3 $[3, 3, w + 2]$ $\phantom{-}e$
4 $[4, 2, 2]$ $-\frac{1}{2}e^{4} + \frac{7}{2}e^{2} - 5$
5 $[5, 5, -w + 8]$ $\phantom{-}1$
7 $[7, 7, w + 1]$ $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 9e$
7 $[7, 7, w + 5]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 9e$
13 $[13, 13, w + 3]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{7}{2}e^{3} + 4e$
13 $[13, 13, w + 9]$ $-\frac{1}{2}e^{5} + \frac{7}{2}e^{3} - 4e$
17 $[17, 17, w]$ $\phantom{-}e^{3} - 4e$
17 $[17, 17, w + 16]$ $-e^{3} + 4e$
31 $[31, 31, -w - 4]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{9}{2}e^{2} + 6$
31 $[31, 31, w - 5]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{9}{2}e^{2} + 6$
41 $[41, 41, 3w - 22]$ $-e^{4} + 5e^{2} - 6$
47 $[47, 47, w + 19]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{11}{2}e^{3} + 11e$
47 $[47, 47, w + 27]$ $-\frac{1}{2}e^{5} + \frac{11}{2}e^{3} - 11e$
53 $[53, 53, w + 14]$ $-2e^{5} + 12e^{3} - 10e$
53 $[53, 53, w + 38]$ $\phantom{-}2e^{5} - 12e^{3} + 10e$
59 $[59, 59, -w - 10]$ $-\frac{1}{2}e^{4} - \frac{1}{2}e^{2} + 2$
59 $[59, 59, w - 11]$ $-\frac{1}{2}e^{4} - \frac{1}{2}e^{2} + 2$
61 $[61, 61, 2w - 13]$ $\phantom{-}2e^{4} - 9e^{2} - 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -w + 8]$ $-1$