Properties

Label 2.2.220.1-9.3-f
Base field \(\Q(\sqrt{55}) \)
Weight $[2, 2]$
Level norm $9$
Level $[9,9,w + 8]$
Dimension $4$
CM no
Base change no

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Base field \(\Q(\sqrt{55}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 55\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[9,9,w + 8]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $68$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 22x^{2} + 289\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}\frac{1}{34}e^{3} - \frac{5}{34}e$
3 $[3, 3, w + 1]$ $\phantom{-}0$
3 $[3, 3, w + 2]$ $\phantom{-}0$
5 $[5, 5, -2w + 15]$ $\phantom{-}2$
11 $[11, 11, 3w - 22]$ $-\frac{1}{34}e^{3} + \frac{39}{34}e$
13 $[13, 13, w + 4]$ $\phantom{-}\frac{1}{17}e^{3} - \frac{5}{17}e$
13 $[13, 13, w + 9]$ $\phantom{-}0$
17 $[17, 17, w + 2]$ $\phantom{-}0$
17 $[17, 17, w + 15]$ $\phantom{-}\frac{2}{17}e^{3} - \frac{10}{17}e$
19 $[19, 19, -w - 6]$ $\phantom{-}\frac{1}{34}e^{3} - \frac{39}{34}e$
19 $[19, 19, w - 6]$ $\phantom{-}\frac{1}{34}e^{3} - \frac{39}{34}e$
23 $[23, 23, w + 3]$ $-\frac{1}{2}e^{2} + \frac{11}{2}$
23 $[23, 23, w + 20]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{11}{2}$
47 $[47, 47, w + 14]$ $-\frac{1}{2}e^{2} + \frac{11}{2}$
47 $[47, 47, w + 33]$ $-\frac{1}{2}e^{2} + \frac{11}{2}$
49 $[49, 7, -7]$ $\phantom{-}0$
67 $[67, 67, w + 16]$ $\phantom{-}e^{2} - 11$
67 $[67, 67, w + 51]$ $\phantom{-}e^{2} - 11$
73 $[73, 73, w + 36]$ $\phantom{-}0$
73 $[73, 73, w + 37]$ $\phantom{-}\frac{2}{17}e^{3} - \frac{10}{17}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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