Properties

Label 2.2.21.1-15.2-a
Base field \(\Q(\sqrt{21}) \)
Weight $[2, 2]$
Level norm $15$
Level $[15,15,-w + 5]$
Dimension $1$
CM no
Base change no

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Base field \(\Q(\sqrt{21}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 5\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[15,15,-w + 5]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $2$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $-1$
4 $[4, 2, 2]$ $\phantom{-}1$
5 $[5, 5, w]$ $-1$
5 $[5, 5, w - 1]$ $\phantom{-}2$
7 $[7, 7, -w - 3]$ $\phantom{-}0$
17 $[17, 17, -2w + 3]$ $\phantom{-}6$
17 $[17, 17, -2w - 1]$ $-2$
37 $[37, 37, w + 6]$ $-10$
37 $[37, 37, -w + 7]$ $\phantom{-}6$
41 $[41, 41, 3w + 1]$ $-2$
41 $[41, 41, -3w + 4]$ $-10$
43 $[43, 43, 3w + 8]$ $\phantom{-}4$
43 $[43, 43, 3w - 11]$ $\phantom{-}4$
47 $[47, 47, 3w - 2]$ $\phantom{-}0$
47 $[47, 47, 3w - 1]$ $\phantom{-}0$
59 $[59, 59, -5w - 6]$ $\phantom{-}4$
59 $[59, 59, -4w - 3]$ $\phantom{-}4$
67 $[67, 67, -w - 8]$ $-12$
67 $[67, 67, w - 9]$ $\phantom{-}4$
79 $[79, 79, 2w - 11]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3,3,-w + 2]$ $1$
$5$ $[5,5,-w]$ $1$