Properties

Label 2.2.97.1-9.1-b
Base field \(\Q(\sqrt{97}) \)
Weight $[2, 2]$
Level norm $9$
Level $[9, 3, 3]$
Dimension $1$
CM no
Base change yes

Related objects

Downloads

Learn more

Base field \(\Q(\sqrt{97}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 24\); 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: $13$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, 7w - 38]$ $\phantom{-}1$
2 $[2, 2, -7w - 31]$ $\phantom{-}1$
3 $[3, 3, 2w + 9]$ $\phantom{-}1$
3 $[3, 3, 2w - 11]$ $\phantom{-}1$
11 $[11, 11, -12w + 65]$ $\phantom{-}4$
11 $[11, 11, -12w - 53]$ $\phantom{-}4$
25 $[25, 5, 5]$ $\phantom{-}2$
31 $[31, 31, 8w - 43]$ $\phantom{-}0$
31 $[31, 31, 8w + 35]$ $\phantom{-}0$
43 $[43, 43, 54w + 239]$ $\phantom{-}4$
43 $[43, 43, -54w + 293]$ $\phantom{-}4$
47 $[47, 47, 2w - 13]$ $-8$
47 $[47, 47, -2w - 11]$ $-8$
49 $[49, 7, -7]$ $\phantom{-}6$
53 $[53, 53, 4w + 19]$ $-6$
53 $[53, 53, 4w - 23]$ $-6$
61 $[61, 61, 2w - 7]$ $\phantom{-}2$
61 $[61, 61, -2w - 5]$ $\phantom{-}2$
73 $[73, 73, 22w + 97]$ $\phantom{-}14$
73 $[73, 73, -22w + 119]$ $\phantom{-}14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, 2w + 9]$ $-1$
$3$ $[3, 3, 2w - 11]$ $-1$