Properties

Label 2.2.97.1-6.1-d
Base field \(\Q(\sqrt{97}) \)
Weight $[2, 2]$
Level norm $6$
Level $[6, 6, w - 6]$
Dimension $3$
CM no
Base change no

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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: $[6, 6, w - 6]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $7$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

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

Atkin-Lehner eigenvalues

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