Properties

Label 2.2.44.1-19.2-a
Base field \(\Q(\sqrt{11}) \)
Weight $[2, 2]$
Level norm $19$
Level $[19,19,-2w - 5]$
Dimension $4$
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: $[19,19,-2w - 5]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 3]$ $\phantom{-}e$
5 $[5, 5, w - 4]$ $\phantom{-}e^{3} - 2e^{2} - 2e + 3$
5 $[5, 5, -w - 4]$ $-e^{3} + e^{2} + 3e$
7 $[7, 7, w + 2]$ $-e^{3} + 2e^{2} + 3e - 2$
7 $[7, 7, w - 2]$ $-e^{2} + e + 4$
9 $[9, 3, 3]$ $-e^{3} + 2e^{2} + 3e - 5$
11 $[11, 11, -w]$ $-2e + 3$
19 $[19, 19, 2w - 5]$ $\phantom{-}e^{3} - e^{2} - 4e + 4$
19 $[19, 19, -2w - 5]$ $-1$
37 $[37, 37, 2w - 9]$ $\phantom{-}e^{3} - 7e + 2$
37 $[37, 37, -2w - 9]$ $\phantom{-}4e^{3} - 5e^{2} - 14e + 2$
43 $[43, 43, 2w - 1]$ $\phantom{-}e^{3} - 3e^{2} - e + 7$
43 $[43, 43, -2w - 1]$ $\phantom{-}3e^{3} - 3e^{2} - 13e + 4$
53 $[53, 53, -w - 8]$ $-e^{3} + 6e + 3$
53 $[53, 53, w - 8]$ $\phantom{-}e^{3} - 2e^{2} - 5e$
79 $[79, 79, 5w - 14]$ $\phantom{-}2e^{3} - 2e^{2} - 10e + 4$
79 $[79, 79, 8w - 25]$ $-e^{3} + 10e + 7$
83 $[83, 83, -3w - 4]$ $-3e^{3} + 2e^{2} + 7e + 6$
83 $[83, 83, 3w - 4]$ $-3e^{3} + e^{2} + 14e - 6$
89 $[89, 89, -w - 10]$ $-2e^{2} + 3$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19,19,-2w - 5]$ $1$