Properties

Label 4.4.4400.1-49.1-a
Base field 4.4.4400.1
Weight $[2, 2, 2, 2]$
Level norm $49$
Level $[49, 7, -w^{3} + w^{2} + 4w - 1]$
Dimension $1$
CM no
Base change no

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Base field 4.4.4400.1

Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} + 11\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[49, 7, -w^{3} + w^{2} + 4w - 1]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $14$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}1$
5 $[5, 5, w + 1]$ $\phantom{-}4$
5 $[5, 5, -w^{3} + w^{2} + 4w - 4]$ $\phantom{-}2$
11 $[11, 11, w]$ $\phantom{-}2$
29 $[29, 29, w^{3} - 2w^{2} - 3w + 7]$ $\phantom{-}4$
29 $[29, 29, -w^{3} - 2w^{2} + 3w + 7]$ $\phantom{-}0$
31 $[31, 31, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}4$
31 $[31, 31, -w^{3} - w^{2} + 4w + 2]$ $-8$
41 $[41, 41, w^{3} + 2w^{2} - 4w - 6]$ $\phantom{-}10$
41 $[41, 41, w^{3} - 5w + 2]$ $-10$
49 $[49, 7, -w^{3} + w^{2} + 4w - 1]$ $-1$
49 $[49, 7, w^{3} + w^{2} - 4w - 1]$ $\phantom{-}6$
59 $[59, 59, -3w^{2} - w + 10]$ $-4$
59 $[59, 59, -3w^{2} + w + 10]$ $-2$
61 $[61, 61, -2w^{3} + 2w^{2} + 7w - 5]$ $-12$
61 $[61, 61, 2w^{3} + w^{2} - 8w - 6]$ $-6$
71 $[71, 71, 2w^{2} + w - 9]$ $-12$
71 $[71, 71, 2w^{2} - w - 9]$ $\phantom{-}4$
81 $[81, 3, -3]$ $-10$
101 $[101, 101, 2w^{2} - w - 10]$ $\phantom{-}18$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$49$ $[49, 7, -w^{3} + w^{2} + 4w - 1]$ $1$