Properties

Label 2.2.193.1-6.4-c
Base field \(\Q(\sqrt{193}) \)
Weight $[2, 2]$
Level norm $6$
Level $[6,6,w - 7]$
Dimension $2$
CM no
Base change no

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Base field \(\Q(\sqrt{193}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 48\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[6,6,w - 7]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $19$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -9w - 58]$ $\phantom{-}e$
2 $[2, 2, -9w + 67]$ $\phantom{-}1$
3 $[3, 3, -2w + 15]$ $\phantom{-}e + 1$
3 $[3, 3, 2w + 13]$ $\phantom{-}1$
7 $[7, 7, 186w - 1385]$ $\phantom{-}2e + 2$
7 $[7, 7, -186w - 1199]$ $-e - 3$
23 $[23, 23, -38w - 245]$ $-2e + 2$
23 $[23, 23, 38w - 283]$ $\phantom{-}2e - 3$
25 $[25, 5, 5]$ $\phantom{-}5$
31 $[31, 31, 16w - 119]$ $-2e + 3$
31 $[31, 31, 16w + 103]$ $\phantom{-}3e + 2$
43 $[43, 43, 4w + 25]$ $-5e + 3$
43 $[43, 43, -4w + 29]$ $\phantom{-}4e + 4$
59 $[59, 59, 12w - 89]$ $-5e - 2$
59 $[59, 59, -12w - 77]$ $-4e - 5$
67 $[67, 67, 92w + 593]$ $\phantom{-}5$
67 $[67, 67, 92w - 685]$ $-3e$
83 $[83, 83, 204w - 1519]$ $-4e - 2$
83 $[83, 83, 204w + 1315]$ $\phantom{-}e - 10$
97 $[97, 97, -24w + 179]$ $\phantom{-}6e + 10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2,2,9w - 67]$ $-1$
$3$ $[3,3,2w + 13]$ $-1$