Properties

Base field \(\Q(\sqrt{34}) \)
Weight [2, 2]
Level norm 3
Level $[3,3,-w + 1]$
Label 2.2.136.1-3.2-a
Dimension 2
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 $[3,3,-w + 1]$
Label 2.2.136.1-3.2-a
Dimension 2
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:
\(x^{2} \) \(\mathstrut -\mathstrut x \) \(\mathstrut -\mathstrut 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 6]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $-e + 2$
3 $[3, 3, w + 2]$ $-1$
5 $[5, 5, w + 2]$ $\phantom{-}2e + 1$
5 $[5, 5, w + 3]$ $-3e + 2$
11 $[11, 11, w + 1]$ $\phantom{-}e + 2$
11 $[11, 11, w + 10]$ $\phantom{-}e + 2$
17 $[17, 17, -3w + 17]$ $-2e + 3$
29 $[29, 29, w + 11]$ $\phantom{-}4e - 1$
29 $[29, 29, w + 18]$ $\phantom{-}3e + 5$
37 $[37, 37, w + 16]$ $-e - 4$
37 $[37, 37, w + 21]$ $\phantom{-}4e - 5$
47 $[47, 47, -w - 9]$ $\phantom{-}e - 5$
47 $[47, 47, w - 9]$ $\phantom{-}4e + 6$
49 $[49, 7, -7]$ $\phantom{-}3e - 9$
61 $[61, 61, w + 20]$ $-4e - 3$
61 $[61, 61, w + 41]$ $\phantom{-}7e - 11$
89 $[89, 89, 2w - 15]$ $\phantom{-}4e - 12$
89 $[89, 89, -2w - 15]$ $-4e + 7$
103 $[103, 103, -14w + 81]$ $-8e - 5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3,3,-w + 1]$ $1$