Properties

Label 3.3.257.1-49.2-b
Base field 3.3.257.1
Weight $[2, 2, 2]$
Level norm $49$
Level $[49, 49, w^{2} + w + 1]$
Dimension $1$
CM no
Base change no

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Base field 3.3.257.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 4x + 3\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[49, 49, w^{2} + w + 1]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}1$
5 $[5, 5, w + 1]$ $\phantom{-}3$
7 $[7, 7, -w^{2} + 2]$ $\phantom{-}0$
8 $[8, 2, 2]$ $\phantom{-}3$
9 $[9, 3, -w^{2} + w + 4]$ $-4$
19 $[19, 19, w^{2} + w - 4]$ $\phantom{-}7$
25 $[25, 5, -w^{2} + 2w + 2]$ $-2$
37 $[37, 37, 2w + 1]$ $\phantom{-}2$
41 $[41, 41, -2w^{2} - w + 7]$ $\phantom{-}0$
43 $[43, 43, -2w^{2} + 5]$ $\phantom{-}10$
47 $[47, 47, 3w - 4]$ $-9$
49 $[49, 7, 2w^{2} - w - 5]$ $\phantom{-}2$
53 $[53, 53, -2w^{2} + 2w + 7]$ $\phantom{-}6$
61 $[61, 61, -w^{2} - 3w + 4]$ $\phantom{-}8$
61 $[61, 61, 3w^{2} - w - 10]$ $-13$
61 $[61, 61, w^{2} - 2w - 4]$ $-8$
67 $[67, 67, 2w^{2} - w - 4]$ $-10$
67 $[67, 67, 2w^{2} - w - 2]$ $\phantom{-}4$
67 $[67, 67, w^{2} + 2w - 5]$ $\phantom{-}7$
71 $[71, 71, -2w^{2} - w + 10]$ $\phantom{-}9$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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