Properties

Label 2.2.193.1-4.3-a
Base field \(\Q(\sqrt{193}) \)
Weight $[2, 2]$
Level norm $4$
Level $[4,4,65w + 419]$
Dimension $1$
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: $[4,4,65w + 419]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $9$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -9w - 58]$ $\phantom{-}0$
2 $[2, 2, -9w + 67]$ $\phantom{-}0$
3 $[3, 3, -2w + 15]$ $\phantom{-}1$
3 $[3, 3, 2w + 13]$ $-2$
7 $[7, 7, 186w - 1385]$ $-2$
7 $[7, 7, -186w - 1199]$ $\phantom{-}1$
23 $[23, 23, -38w - 245]$ $\phantom{-}0$
23 $[23, 23, 38w - 283]$ $-3$
25 $[25, 5, 5]$ $\phantom{-}1$
31 $[31, 31, 16w - 119]$ $\phantom{-}1$
31 $[31, 31, 16w + 103]$ $\phantom{-}10$
43 $[43, 43, 4w + 25]$ $\phantom{-}1$
43 $[43, 43, -4w + 29]$ $\phantom{-}10$
59 $[59, 59, 12w - 89]$ $\phantom{-}12$
59 $[59, 59, -12w - 77]$ $\phantom{-}9$
67 $[67, 67, 92w + 593]$ $-13$
67 $[67, 67, 92w - 685]$ $\phantom{-}8$
83 $[83, 83, 204w - 1519]$ $-12$
83 $[83, 83, 204w + 1315]$ $-6$
97 $[97, 97, -24w + 179]$ $-8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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