Properties

Base field \(\Q(\sqrt{17}) \)
Weight [2, 2]
Level norm 144
Level $[144,48,-3w + 15]$
Label 2.2.17.1-144.5-f
Dimension 3
CM no
Base change no

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Base field \(\Q(\sqrt{17}) \)

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

Form

Weight [2, 2]
Level $[144,48,-3w + 15]$
Label 2.2.17.1-144.5-f
Dimension 3
Is CM no
Is base change no
Parent newspace dimension 8

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} \) \(\mathstrut -\mathstrut 7x \) \(\mathstrut -\mathstrut 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 2]$ $\phantom{-}e$
2 $[2, 2, -w - 1]$ $\phantom{-}0$
9 $[9, 3, 3]$ $-1$
13 $[13, 13, -2w + 3]$ $\phantom{-}e^{2} - 2e - 5$
13 $[13, 13, 2w + 1]$ $-e^{2} + 3$
17 $[17, 17, -2w + 1]$ $\phantom{-}2e$
19 $[19, 19, -2w + 7]$ $-e^{2} + 5$
19 $[19, 19, 2w + 5]$ $\phantom{-}e^{2} - 2e - 3$
25 $[25, 5, -5]$ $-e^{2} - 2e + 5$
43 $[43, 43, 4w - 7]$ $-e^{2} - 2e + 7$
43 $[43, 43, 4w + 3]$ $-e^{2} + 2e + 3$
47 $[47, 47, -2w + 9]$ $-2e + 2$
47 $[47, 47, 2w + 7]$ $-2e^{2} + 10$
49 $[49, 7, -7]$ $-2e^{2} + 2e + 6$
53 $[53, 53, 4w - 13]$ $\phantom{-}6$
53 $[53, 53, 6w - 13]$ $\phantom{-}2e^{2} - 2e - 10$
59 $[59, 59, -4w - 1]$ $\phantom{-}4$
59 $[59, 59, 4w - 5]$ $\phantom{-}4$
67 $[67, 67, 4w - 3]$ $\phantom{-}2e^{2} + 2e - 8$
67 $[67, 67, 4w - 1]$ $\phantom{-}4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,w + 1]$ $1$
9 $[9,3,3]$ $1$