Properties

Label 2.2.205.1-3.2-b
Base field \(\Q(\sqrt{205}) \)
Weight $[2, 2]$
Level norm $3$
Level $[3,3,-w + 1]$
Dimension $4$
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: $[3,3,-w + 1]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 3x^{3} - 5x^{2} - 11x + 4\)

  Show full eigenvalues   Hide large eigenvalues

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3,3,-w + 1]$ $-1$