Properties

Label 2.2.152.1-19.1-e
Base field \(\Q(\sqrt{38}) \)
Weight $[2, 2]$
Level norm $19$
Level $[19, 19, -3w + 19]$
Dimension $1$
CM no
Base change yes

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Base field \(\Q(\sqrt{38}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 38\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[19, 19, -3w + 19]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $56$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w - 6]$ $\phantom{-}0$
9 $[9, 3, 3]$ $-2$
11 $[11, 11, -w + 7]$ $\phantom{-}3$
11 $[11, 11, w + 7]$ $\phantom{-}3$
13 $[13, 13, -w - 5]$ $\phantom{-}4$
13 $[13, 13, w - 5]$ $\phantom{-}4$
17 $[17, 17, -2w + 13]$ $-3$
17 $[17, 17, -2w - 13]$ $-3$
19 $[19, 19, -3w + 19]$ $\phantom{-}1$
25 $[25, 5, 5]$ $-1$
29 $[29, 29, -w - 3]$ $-6$
29 $[29, 29, w - 3]$ $-6$
31 $[31, 31, -2w + 11]$ $\phantom{-}4$
31 $[31, 31, -8w + 49]$ $\phantom{-}4$
37 $[37, 37, -w - 1]$ $-2$
37 $[37, 37, w - 1]$ $-2$
43 $[43, 43, -w - 9]$ $-1$
43 $[43, 43, w - 9]$ $-1$
49 $[49, 7, -7]$ $-13$
53 $[53, 53, -3w + 17]$ $-12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19, 19, -3w + 19]$ $-1$