Properties

Label 2.2.28.1-19.1-b
Base field \(\Q(\sqrt{7}) \)
Weight $[2, 2]$
Level norm $19$
Level $[19, 19, 2w - 3]$
Dimension $3$
CM no
Base change no

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Base field \(\Q(\sqrt{7}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 7\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[19, 19, 2w - 3]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} + x^{2} - 4x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 3]$ $\phantom{-}e$
3 $[3, 3, w - 2]$ $\phantom{-}e^{2} + 2e - 4$
3 $[3, 3, w + 2]$ $-e - 1$
7 $[7, 7, w]$ $-2e^{2} - 3e + 4$
19 $[19, 19, 2w - 3]$ $\phantom{-}1$
19 $[19, 19, 2w + 3]$ $\phantom{-}e^{2} + 3e - 3$
25 $[25, 5, 5]$ $-e - 6$
29 $[29, 29, -w - 6]$ $-3e^{2} - 6e + 5$
29 $[29, 29, w - 6]$ $\phantom{-}3e^{2} + 2e - 8$
31 $[31, 31, 4w + 9]$ $\phantom{-}2e - 3$
31 $[31, 31, -4w + 9]$ $-e^{2} - e - 5$
37 $[37, 37, -3w + 10]$ $\phantom{-}3e - 1$
37 $[37, 37, -6w + 17]$ $\phantom{-}4e^{2} + 5e - 8$
47 $[47, 47, -3w - 4]$ $\phantom{-}e^{2} + e$
47 $[47, 47, 3w - 4]$ $-3e^{2} - 6e + 7$
53 $[53, 53, 2w - 9]$ $-e^{2} - 2e - 1$
53 $[53, 53, 2w + 9]$ $\phantom{-}4e^{2} + 8e - 11$
59 $[59, 59, 3w - 2]$ $-5$
59 $[59, 59, -3w - 2]$ $\phantom{-}e^{2} + 8e + 2$
83 $[83, 83, -6w - 13]$ $\phantom{-}3e^{2} - 2e - 10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19, 19, 2w - 3]$ $-1$