Properties

Label 2.2.44.1-14.1-b
Base field \(\Q(\sqrt{11}) \)
Weight $[2, 2]$
Level norm $14$
Level $[14, 14, -w - 5]$
Dimension $2$
CM no
Base change no

Related objects

Downloads

Learn more

Base field \(\Q(\sqrt{11}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 11\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[14, 14, -w - 5]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 3]$ $\phantom{-}1$
5 $[5, 5, w - 4]$ $\phantom{-}e$
5 $[5, 5, -w - 4]$ $-\frac{1}{2}e + 2$
7 $[7, 7, w + 2]$ $\phantom{-}\frac{1}{2}e - 2$
7 $[7, 7, w - 2]$ $\phantom{-}1$
9 $[9, 3, 3]$ $-e + 2$
11 $[11, 11, -w]$ $-2$
19 $[19, 19, 2w - 5]$ $\phantom{-}e$
19 $[19, 19, -2w - 5]$ $-\frac{5}{2}e$
37 $[37, 37, 2w - 9]$ $\phantom{-}\frac{3}{2}e - 6$
37 $[37, 37, -2w - 9]$ $\phantom{-}e + 4$
43 $[43, 43, 2w - 1]$ $\phantom{-}2$
43 $[43, 43, -2w - 1]$ $-2e$
53 $[53, 53, -w - 8]$ $\phantom{-}2e$
53 $[53, 53, w - 8]$ $-\frac{1}{2}e - 6$
79 $[79, 79, 5w - 14]$ $\phantom{-}e - 10$
79 $[79, 79, 8w - 25]$ $\phantom{-}e + 4$
83 $[83, 83, -3w - 4]$ $-2e + 12$
83 $[83, 83, 3w - 4]$ $\phantom{-}\frac{5}{2}e - 8$
89 $[89, 89, -w - 10]$ $\phantom{-}\frac{3}{2}e + 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w + 3]$ $-1$
$7$ $[7, 7, w - 2]$ $-1$