Properties

Base field 4.4.9909.1
Weight [2, 2, 2, 2]
Level norm 25
Level $[25, 25, w^{3} - 2w^{2} - 4w + 5]$
Label 4.4.9909.1-25.1-j
Dimension 4
CM yes
Base change no

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Base field 4.4.9909.1

Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 3x + 3\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[25, 25, w^{3} - 2w^{2} - 4w + 5]$
Label 4.4.9909.1-25.1-j
Dimension 4
Is CM yes
Is base change no
Parent newspace dimension 21

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut -\mathstrut 3x^{3} \) \(\mathstrut -\mathstrut 12x^{2} \) \(\mathstrut +\mathstrut 30x \) \(\mathstrut +\mathstrut 21\)

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Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $\phantom{-}0$
7 $[7, 7, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}7e^{3} + 2e^{2} - 75e - 38$
11 $[11, 11, -w^{2} + w + 2]$ $\phantom{-}0$
13 $[13, 13, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}5e^{3} + 2e^{2} - 54e - 35$
16 $[16, 2, 2]$ $-4e^{3} - 2e^{2} + 42e + 32$
17 $[17, 17, -w^{3} + 5w + 2]$ $\phantom{-}0$
29 $[29, 29, -w^{2} + w + 1]$ $\phantom{-}0$
37 $[37, 37, -w^{3} + 2w^{2} + 4w - 4]$ $-11e^{3} - 5e^{2} + 117e + 80$
41 $[41, 41, -w^{3} + w^{2} + 5w + 1]$ $\phantom{-}0$
41 $[41, 41, w^{2} - 5]$ $\phantom{-}0$
47 $[47, 47, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}0$
47 $[47, 47, -w^{3} + 2w^{2} + 4w - 1]$ $\phantom{-}0$
53 $[53, 53, w^{3} - 4w - 4]$ $\phantom{-}0$
53 $[53, 53, 2w^{3} - 2w^{2} - 9w + 1]$ $\phantom{-}0$
61 $[61, 61, -w^{3} + w^{2} + 6w - 2]$ $-15e^{3} - 3e^{2} + 159e + 76$
71 $[71, 71, w^{3} - w^{2} - 6w - 2]$ $\phantom{-}0$
103 $[103, 103, 2w^{3} - 2w^{2} - 8w + 1]$ $\phantom{-}21e^{3} + 8e^{2} - 225e - 140$
103 $[103, 103, -3w^{3} + 3w^{2} + 13w - 5]$ $-26e^{3} - 8e^{2} + 276e + 155$
109 $[109, 109, 2w^{3} - w^{2} - 8w - 4]$ $-e^{3} + 2e^{2} + 9e - 11$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w - 1]$ $1$