Properties

Label 2.2.440.1-4.1-c
Base field \(\Q(\sqrt{110}) \)
Weight $[2, 2]$
Level norm $4$
Level $[4, 2, 2]$
Dimension $4$
CM no
Base change no

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Base field \(\Q(\sqrt{110}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 110\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[4, 2, 2]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $32$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 64x^{2} + 256\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
5 $[5, 5, w]$ $-\frac{1}{32}e^{3} + \frac{3}{2}e$
9 $[9, 3, 3]$ $\phantom{-}0$
11 $[11, 11, -w + 11]$ $-2$
17 $[17, 17, w + 5]$ $-\frac{1}{32}e^{3} + \frac{5}{2}e$
17 $[17, 17, w + 12]$ $\phantom{-}\frac{1}{32}e^{3} - \frac{5}{2}e$
23 $[23, 23, w + 8]$ $\phantom{-}\frac{5}{64}e^{3} - \frac{15}{4}e$
23 $[23, 23, w + 15]$ $\phantom{-}\frac{5}{64}e^{3} - \frac{15}{4}e$
29 $[29, 29, w + 9]$ $\phantom{-}\frac{1}{4}e^{2} - 8$
29 $[29, 29, -w + 9]$ $-\frac{1}{4}e^{2} + 8$
37 $[37, 37, w + 6]$ $-\frac{1}{32}e^{3} + \frac{3}{2}e$
37 $[37, 37, w + 31]$ $-\frac{1}{32}e^{3} + \frac{3}{2}e$
43 $[43, 43, w + 14]$ $\phantom{-}\frac{1}{64}e^{3} - \frac{5}{4}e$
43 $[43, 43, w + 29]$ $-\frac{1}{64}e^{3} + \frac{5}{4}e$
47 $[47, 47, w + 4]$ $-\frac{3}{64}e^{3} + \frac{9}{4}e$
47 $[47, 47, w + 43]$ $-\frac{3}{64}e^{3} + \frac{9}{4}e$
49 $[49, 7, -7]$ $-12$
53 $[53, 53, w + 2]$ $\phantom{-}0$
53 $[53, 53, w + 51]$ $\phantom{-}0$
59 $[59, 59, -w - 13]$ $-2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $-1$