Properties

Base field \(\Q(\sqrt{34}) \)
Weight [2, 2]
Level norm 5
Level $[5, 5, w + 2]$
Label 2.2.136.1-5.1-b
Dimension 5
CM no
Base change no

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Base field \(\Q(\sqrt{34}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 34\); narrow class number \(4\) and class number \(2\).

Form

Weight [2, 2]
Level $[5, 5, w + 2]$
Label 2.2.136.1-5.1-b
Dimension 5
Is CM no
Is base change no
Parent newspace dimension 20

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} \) \(\mathstrut -\mathstrut x^{4} \) \(\mathstrut -\mathstrut 5x^{3} \) \(\mathstrut +\mathstrut 3x^{2} \) \(\mathstrut +\mathstrut 4x \) \(\mathstrut -\mathstrut 1\)

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Norm Prime Eigenvalue
2 $[2, 2, w - 6]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $\phantom{-}e^{3} - e^{2} - 3e + 1$
3 $[3, 3, w + 2]$ $-e^{4} + 5e^{2} + e - 3$
5 $[5, 5, w + 2]$ $\phantom{-}1$
5 $[5, 5, w + 3]$ $\phantom{-}e^{4} - e^{3} - 5e^{2} + 3e + 2$
11 $[11, 11, w + 1]$ $-e^{4} + 2e^{3} + 4e^{2} - 7e - 3$
11 $[11, 11, w + 10]$ $\phantom{-}2e^{4} - 2e^{3} - 9e^{2} + 3e + 5$
17 $[17, 17, -3w + 17]$ $\phantom{-}e^{4} - e^{3} - 4e^{2} + e$
29 $[29, 29, w + 11]$ $-e^{4} + 3e^{3} + 3e^{2} - 9e - 3$
29 $[29, 29, w + 18]$ $-2e^{4} + 2e^{3} + 9e^{2} - 5e - 7$
37 $[37, 37, w + 16]$ $\phantom{-}e^{3} + 3e^{2} - 5e - 11$
37 $[37, 37, w + 21]$ $\phantom{-}e^{4} - 2e^{3} - 3e^{2} + 5e - 4$
47 $[47, 47, -w - 9]$ $\phantom{-}2e^{4} + e^{3} - 13e^{2} - 3e + 11$
47 $[47, 47, w - 9]$ $\phantom{-}e^{4} - 3e^{3} - 2e^{2} + 9e$
49 $[49, 7, -7]$ $-e^{4} - e^{3} + 6e^{2} + e - 3$
61 $[61, 61, w + 20]$ $\phantom{-}3e^{4} - e^{3} - 17e^{2} + 2e + 10$
61 $[61, 61, w + 41]$ $-4e^{4} + e^{3} + 20e^{2} + 5e - 16$
89 $[89, 89, 2w - 15]$ $\phantom{-}2e^{4} - 4e^{3} - 10e^{2} + 7e + 14$
89 $[89, 89, -2w - 15]$ $-e^{4} + 2e^{3} + 3e^{2} - 6e + 4$
103 $[103, 103, -14w + 81]$ $-4e^{4} + 2e^{3} + 23e^{2} + e - 18$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w + 2]$ $-1$