Properties

Label 2.2.205.1-4.1-f
Base field \(\Q(\sqrt{205}) \)
Weight $[2, 2]$
Level norm $4$
Level $[4, 2, 2]$
Dimension $10$
CM no
Base change yes

Related objects

Downloads

Learn more

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: $[4, 2, 2]$
Dimension: $10$
CM: no
Base change: yes
Newspace dimension: $28$

Hecke eigenvalues ($q$-expansion)

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

\(x^{10} - 18x^{8} + 102x^{6} - 192x^{4} + 120x^{2} - 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}e$
4 $[4, 2, 2]$ $-1$
5 $[5, 5, -w + 8]$ $-e^{8} + \frac{33}{2}e^{6} - 78e^{4} + 82e^{2} - 6$
7 $[7, 7, w + 1]$ $-\frac{1}{4}e^{9} + 4e^{7} - 17e^{5} + 7e^{3} + 12e$
7 $[7, 7, w + 5]$ $-\frac{1}{4}e^{9} + 4e^{7} - 17e^{5} + 7e^{3} + 12e$
13 $[13, 13, w + 3]$ $-\frac{5}{4}e^{9} + 21e^{7} - \frac{205}{2}e^{5} + 120e^{3} - 20e$
13 $[13, 13, w + 9]$ $-\frac{5}{4}e^{9} + 21e^{7} - \frac{205}{2}e^{5} + 120e^{3} - 20e$
17 $[17, 17, w]$ $-\frac{1}{2}e^{9} + 8e^{7} - \frac{69}{2}e^{5} + 18e^{3} + 21e$
17 $[17, 17, w + 16]$ $-\frac{1}{2}e^{9} + 8e^{7} - \frac{69}{2}e^{5} + 18e^{3} + 21e$
31 $[31, 31, -w - 4]$ $\phantom{-}\frac{1}{2}e^{8} - 8e^{6} + 36e^{4} - 32e^{2} - 2$
31 $[31, 31, w - 5]$ $\phantom{-}\frac{1}{2}e^{8} - 8e^{6} + 36e^{4} - 32e^{2} - 2$
41 $[41, 41, 3w - 22]$ $\phantom{-}e^{8} - 17e^{6} + 82e^{4} - 82e^{2} - 2$
47 $[47, 47, w + 19]$ $\phantom{-}\frac{7}{4}e^{9} - \frac{59}{2}e^{7} + 145e^{5} - 175e^{3} + 36e$
47 $[47, 47, w + 27]$ $\phantom{-}\frac{7}{4}e^{9} - \frac{59}{2}e^{7} + 145e^{5} - 175e^{3} + 36e$
53 $[53, 53, w + 14]$ $\phantom{-}\frac{3}{4}e^{9} - 13e^{7} + \frac{137}{2}e^{5} - 108e^{3} + 54e$
53 $[53, 53, w + 38]$ $\phantom{-}\frac{3}{4}e^{9} - 13e^{7} + \frac{137}{2}e^{5} - 108e^{3} + 54e$
59 $[59, 59, -w - 10]$ $\phantom{-}\frac{1}{2}e^{8} - \frac{17}{2}e^{6} + 43e^{4} - 57e^{2} + 12$
59 $[59, 59, w - 11]$ $\phantom{-}\frac{1}{2}e^{8} - \frac{17}{2}e^{6} + 43e^{4} - 57e^{2} + 12$
61 $[61, 61, 2w - 13]$ $-\frac{1}{2}e^{8} + 8e^{6} - 35e^{4} + 24e^{2} + 8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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