Properties

Label 2.2.97.1-12.1-b
Base field \(\Q(\sqrt{97}) \)
Weight $[2, 2]$
Level norm $12$
Level $[12, 6, 4w + 18]$
Dimension $1$
CM no
Base change no

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: $[12, 6, 4w + 18]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $3$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, 7w - 38]$ $-1$
2 $[2, 2, -7w - 31]$ $\phantom{-}1$
3 $[3, 3, 2w + 9]$ $\phantom{-}1$
3 $[3, 3, 2w - 11]$ $\phantom{-}2$
11 $[11, 11, -12w + 65]$ $-2$
11 $[11, 11, -12w - 53]$ $\phantom{-}4$
25 $[25, 5, 5]$ $\phantom{-}4$
31 $[31, 31, 8w - 43]$ $-8$
31 $[31, 31, 8w + 35]$ $\phantom{-}0$
43 $[43, 43, 54w + 239]$ $\phantom{-}8$
43 $[43, 43, -54w + 293]$ $\phantom{-}0$
47 $[47, 47, 2w - 13]$ $\phantom{-}6$
47 $[47, 47, -2w - 11]$ $\phantom{-}10$
49 $[49, 7, -7]$ $-2$
53 $[53, 53, 4w + 19]$ $-4$
53 $[53, 53, 4w - 23]$ $-2$
61 $[61, 61, 2w - 7]$ $-10$
61 $[61, 61, -2w - 5]$ $\phantom{-}10$
73 $[73, 73, 22w + 97]$ $\phantom{-}4$
73 $[73, 73, -22w + 119]$ $-16$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, 7w - 38]$ $1$
$2$ $[2, 2, -7w - 31]$ $-1$
$3$ $[3, 3, 2w + 9]$ $-1$