Properties

Base field \(\Q(\sqrt{38}) \)
Weight [2, 2]
Level norm 38
Level $[38, 38, w]$
Label 2.2.152.1-38.1-d
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 $[38, 38, w]$
Label 2.2.152.1-38.1-d
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 64

Hecke eigenvalues ($q$-expansion)

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 6]$ $-1$
19 $[19, 19, -3w + 19]$ $1$