Properties

Label 2.2.97.1-4.1-b
Base field \(\Q(\sqrt{97}) \)
Weight $[2, 2]$
Level norm $4$
Level $[4, 2, 2]$
Dimension $3$
CM no
Base change yes

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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: $[4, 2, 2]$
Dimension: $3$
CM: no
Base change: yes
Newspace dimension: $5$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{3} + x^{2} - 7x - 4\)

  Show full eigenvalues   Hide large eigenvalues

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

Atkin-Lehner eigenvalues

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