Properties

Label 2.2.193.1-9.1-a
Base field \(\Q(\sqrt{193}) \)
Weight $[2, 2]$
Level norm $9$
Level $[9, 3, 3]$
Dimension $1$
CM no
Base change yes

Related objects

Downloads

Learn more

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: $[9, 3, 3]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $35$

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 $[3, 3, -2w + 15]$ $-1$
3 $[3, 3, 2w + 13]$ $-1$
7 $[7, 7, 186w - 1385]$ $-3$
7 $[7, 7, -186w - 1199]$ $-3$
23 $[23, 23, -38w - 245]$ $\phantom{-}6$
23 $[23, 23, 38w - 283]$ $\phantom{-}6$
25 $[25, 5, 5]$ $\phantom{-}6$
31 $[31, 31, 16w - 119]$ $\phantom{-}0$
31 $[31, 31, 16w + 103]$ $\phantom{-}0$
43 $[43, 43, 4w + 25]$ $-3$
43 $[43, 43, -4w + 29]$ $-3$
59 $[59, 59, 12w - 89]$ $\phantom{-}6$
59 $[59, 59, -12w - 77]$ $\phantom{-}6$
67 $[67, 67, 92w + 593]$ $-5$
67 $[67, 67, 92w - 685]$ $-5$
83 $[83, 83, 204w - 1519]$ $\phantom{-}6$
83 $[83, 83, 204w + 1315]$ $\phantom{-}6$
97 $[97, 97, -24w + 179]$ $\phantom{-}3$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -2w + 15]$ $1$
$3$ $[3, 3, 2w + 13]$ $1$