Properties

Label 2.2.321.1-2.2-a
Base field \(\Q(\sqrt{321}) \)
Weight $[2, 2]$
Level norm $2$
Level $[2,2,-w + 1]$
Dimension $1$
CM no
Base change no

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Base field \(\Q(\sqrt{321}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 80\); narrow class number \(6\) and class number \(3\).

Form

Weight: $[2, 2]$
Level: $[2,2,-w + 1]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $30$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
2 $[2, 2, w + 1]$ $-1$
3 $[3, 3, -2w + 19]$ $\phantom{-}1$
5 $[5, 5, w]$ $\phantom{-}0$
5 $[5, 5, w + 4]$ $\phantom{-}3$
13 $[13, 13, w + 1]$ $\phantom{-}5$
13 $[13, 13, w + 11]$ $-4$
17 $[17, 17, w + 3]$ $\phantom{-}3$
17 $[17, 17, w + 13]$ $-3$
19 $[19, 19, w + 6]$ $\phantom{-}2$
19 $[19, 19, w + 12]$ $\phantom{-}2$
37 $[37, 37, w + 2]$ $\phantom{-}2$
37 $[37, 37, w + 34]$ $\phantom{-}2$
49 $[49, 7, -7]$ $-4$
59 $[59, 59, -4w - 33]$ $\phantom{-}15$
59 $[59, 59, 4w - 37]$ $-3$
61 $[61, 61, w + 28]$ $\phantom{-}8$
61 $[61, 61, w + 32]$ $-10$
71 $[71, 71, w + 22]$ $\phantom{-}12$
71 $[71, 71, w + 48]$ $\phantom{-}6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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