Properties

Label 2.2.193.1-6.1-h
Base field \(\Q(\sqrt{193}) \)
Weight $[2, 2]$
Level norm $6$
Level $[6, 6, -w - 6]$
Dimension $4$
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: $[6, 6, -w - 6]$
Dimension: $4$
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:

\(x^{4} + 3x^{3} - 3x^{2} - 12x - 6\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -9w - 58]$ $\phantom{-}1$
2 $[2, 2, -9w + 67]$ $\phantom{-}e$
3 $[3, 3, -2w + 15]$ $-1$
3 $[3, 3, 2w + 13]$ $\phantom{-}e^{3} + 2e^{2} - 5e - 7$
7 $[7, 7, 186w - 1385]$ $-e^{3} - e^{2} + 5e + 3$
7 $[7, 7, -186w - 1199]$ $-e^{3} - 2e^{2} + 4e + 6$
23 $[23, 23, -38w - 245]$ $-2e^{2} + 9$
23 $[23, 23, 38w - 283]$ $-e^{2}$
25 $[25, 5, 5]$ $-e^{2} + 3$
31 $[31, 31, 16w - 119]$ $\phantom{-}4e^{3} + 7e^{2} - 19e - 24$
31 $[31, 31, 16w + 103]$ $\phantom{-}e^{3} + 2e^{2} - 4e - 9$
43 $[43, 43, 4w + 25]$ $\phantom{-}e^{3} + 2e^{2} - 6e - 12$
43 $[43, 43, -4w + 29]$ $-2e^{3} - 3e^{2} + 9e + 9$
59 $[59, 59, 12w - 89]$ $\phantom{-}5e^{3} + 9e^{2} - 24e - 27$
59 $[59, 59, -12w - 77]$ $-e^{3} + 5e - 6$
67 $[67, 67, 92w + 593]$ $\phantom{-}2e^{3} + 4e^{2} - 9e - 20$
67 $[67, 67, 92w - 685]$ $-3e^{3} - 6e^{2} + 12e + 25$
83 $[83, 83, 204w - 1519]$ $\phantom{-}e^{3} + 3e^{2} - e - 12$
83 $[83, 83, 204w + 1315]$ $-e^{3} - 2e^{2} + 6$
97 $[97, 97, -24w + 179]$ $-2e^{3} - 4e^{2} + 16e + 18$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -9w - 58]$ $-1$
$3$ $[3, 3, -2w + 15]$ $1$