Properties

Label 2.2.493.1-1.1-a
Base field \(\Q(\sqrt{493}) \)
Weight $[2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $2$
CM no
Base change yes

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Base field \(\Q(\sqrt{493}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 123\); narrow class number \(2\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[1, 1, 1]$
Dimension: $2$
CM: no
Base change: yes
Newspace dimension: $50$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}e$
4 $[4, 2, 2]$ $-1$
11 $[11, 11, w + 1]$ $-e$
11 $[11, 11, w + 9]$ $-e$
13 $[13, 13, w - 11]$ $-1$
13 $[13, 13, w + 10]$ $-1$
17 $[17, 17, w + 8]$ $\phantom{-}2e$
25 $[25, 5, -5]$ $-1$
29 $[29, 29, w + 14]$ $-4e$
31 $[31, 31, w + 5]$ $-3e$
31 $[31, 31, w + 25]$ $-3e$
37 $[37, 37, w + 3]$ $\phantom{-}0$
37 $[37, 37, w + 33]$ $\phantom{-}0$
41 $[41, 41, w]$ $\phantom{-}2e$
41 $[41, 41, w + 40]$ $\phantom{-}2e$
49 $[49, 7, -7]$ $-10$
53 $[53, 53, -4w - 43]$ $-9$
53 $[53, 53, 4w - 47]$ $-9$
59 $[59, 59, -w - 13]$ $\phantom{-}6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).