Properties

Base field \(\Q(\zeta_{15})^+\)
Weight [2, 2, 2, 2]
Level norm 61
Level $[61,61,-3w^{3} + w^{2} + 10w - 5]$
Label 4.4.1125.1-61.4-b
Dimension 2
CM no
Base change no

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Base field \(\Q(\zeta_{15})^+\)

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

Form

Weight [2, 2, 2, 2]
Level $[61,61,-3w^{3} + w^{2} + 10w - 5]$
Label 4.4.1125.1-61.4-b
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 4

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} \) \(\mathstrut +\mathstrut 4x \) \(\mathstrut +\mathstrut 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w^{2} + 1]$ $\phantom{-}e$
9 $[9, 3, w^{3} + w^{2} - 4w - 3]$ $\phantom{-}e + 4$
16 $[16, 2, 2]$ $\phantom{-}2e + 5$
29 $[29, 29, -w^{3} - w^{2} + 2w + 3]$ $-4e - 8$
29 $[29, 29, -w^{2} + w + 3]$ $\phantom{-}3e + 12$
29 $[29, 29, w^{3} - w^{2} - 4w + 2]$ $-4e - 8$
29 $[29, 29, 2w^{3} + w^{2} - 7w]$ $-4e - 8$
31 $[31, 31, -2w + 1]$ $\phantom{-}4e + 8$
31 $[31, 31, 2w^{2} - 5]$ $\phantom{-}4e + 8$
31 $[31, 31, 2w^{3} + 2w^{2} - 6w - 3]$ $-4e - 6$
31 $[31, 31, 2w^{3} - 8w + 1]$ $-4e - 6$
59 $[59, 59, w^{3} + w^{2} - 2w - 5]$ $-8e - 16$
59 $[59, 59, -w^{3} + 2w^{2} + 4w - 5]$ $\phantom{-}e - 8$
59 $[59, 59, -3w^{3} + 10w - 4]$ $\phantom{-}e - 8$
59 $[59, 59, -2w^{3} - w^{2} + 7w - 2]$ $-e + 4$
61 $[61, 61, 4w^{3} + w^{2} - 13w - 1]$ $\phantom{-}0$
61 $[61, 61, 2w^{3} - w^{2} - 5w + 2]$ $\phantom{-}8e + 14$
61 $[61, 61, -3w^{3} - w^{2} + 8w]$ $-8e - 14$
61 $[61, 61, 3w^{3} - w^{2} - 10w + 5]$ $-1$
89 $[89, 89, w^{3} + w^{2} - w - 4]$ $-5e - 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
61 $[61,61,-3w^{3} + w^{2} + 10w - 5]$ $1$