Properties

Label 2.2.85.1-19.2-g
Base field \(\Q(\sqrt{85}) \)
Weight $[2, 2]$
Level norm $19$
Level $[19,19,-w + 2]$
Dimension $6$
CM no
Base change no

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Base field \(\Q(\sqrt{85}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 21\); narrow class number \(2\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[19,19,-w + 2]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $54$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} + 11x^{4} + 13x^{2} + 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e^{5} + 10e^{3} + 3e$
3 $[3, 3, w + 2]$ $\phantom{-}e$
4 $[4, 2, 2]$ $-3e^{4} - 31e^{2} - 19$
5 $[5, 5, w + 2]$ $-e^{5} - 10e^{3} - 4e$
7 $[7, 7, w]$ $-e^{5} - 10e^{3} - 3e$
7 $[7, 7, w + 6]$ $\phantom{-}3e^{5} + 31e^{3} + 19e$
17 $[17, 17, w + 8]$ $-3e^{5} - 31e^{3} - 20e$
19 $[19, 19, w + 1]$ $-4e^{4} - 41e^{2} - 24$
19 $[19, 19, w - 2]$ $-1$
23 $[23, 23, w + 9]$ $-5e^{5} - 51e^{3} - 27e$
23 $[23, 23, w + 13]$ $\phantom{-}e^{5} + 10e^{3} + 3e$
37 $[37, 37, w + 11]$ $-10e^{5} - 104e^{3} - 70e$
37 $[37, 37, w + 25]$ $-7e^{5} - 73e^{3} - 46e$
59 $[59, 59, 3w + 10]$ $\phantom{-}2e^{4} + 21e^{2} + 24$
59 $[59, 59, 3w - 13]$ $\phantom{-}5e^{4} + 51e^{2} + 32$
73 $[73, 73, w + 15]$ $-20e^{5} - 207e^{3} - 126e$
73 $[73, 73, w + 57]$ $\phantom{-}20e^{5} + 207e^{3} + 126e$
89 $[89, 89, -w - 10]$ $-2e^{4} - 20e^{2} - 6$
89 $[89, 89, w - 11]$ $\phantom{-}e^{4} + 9e^{2} - 2$
97 $[97, 97, w + 22]$ $\phantom{-}6e^{5} + 62e^{3} + 36e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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