Properties

Label 4.4.1957.1-49.1-a
Base field 4.4.1957.1
Weight $[2, 2, 2, 2]$
Level norm $49$
Level $[49, 49, w + 3]$
Dimension $1$
CM no
Base change no

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Base field 4.4.1957.1

Generator \(w\), with minimal polynomial \(x^{4} - 4x^{2} - x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[49, 49, w + 3]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $3$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 3w + 1]$ $-2$
7 $[7, 7, -w^{2} + 2]$ $\phantom{-}0$
16 $[16, 2, 2]$ $-5$
19 $[19, 19, -w^{3} + w^{2} + 4w]$ $-8$
23 $[23, 23, w^{3} + w^{2} - 4w - 2]$ $-6$
27 $[27, 3, -2w^{3} + w^{2} + 6w - 1]$ $-4$
31 $[31, 31, -w^{3} + 5w]$ $\phantom{-}10$
37 $[37, 37, -w^{3} + 5w + 1]$ $-4$
43 $[43, 43, w^{2} + w - 3]$ $-8$
43 $[43, 43, -w^{2} + 2w + 3]$ $\phantom{-}2$
47 $[47, 47, -w^{3} + w^{2} + 2w + 2]$ $\phantom{-}0$
47 $[47, 47, 3w^{3} - w^{2} - 10w - 2]$ $\phantom{-}12$
53 $[53, 53, -w^{3} + w^{2} + 2w - 3]$ $-6$
59 $[59, 59, -2w^{3} + w^{2} + 8w + 1]$ $-12$
59 $[59, 59, w^{3} - 2w^{2} - 3w + 3]$ $\phantom{-}0$
61 $[61, 61, -w^{3} + w^{2} + w - 2]$ $-10$
67 $[67, 67, 2w^{3} - 5w - 2]$ $-2$
71 $[71, 71, 2w^{2} - w - 3]$ $-6$
73 $[73, 73, 2w^{2} - w - 5]$ $-4$
73 $[73, 73, w^{3} - 2w^{2} - 2w + 5]$ $\phantom{-}16$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, -w^{2} + 2]$ $-1$