Properties

Base field \(\Q(\sqrt{85}) \)
Weight [2, 2]
Level norm 15
Level $[15, 15, w + 2]$
Label 2.2.85.1-15.1-b
Dimension 2
CM no
Base change no

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Base field \(\Q(\sqrt{85}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 21\); narrow class number \(2\) and class number \(2\).

Form

Weight [2, 2]
Level $[15, 15, w + 2]$
Label 2.2.85.1-15.1-b
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 30

Hecke eigenvalues ($q$-expansion)

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-1$
3 $[3, 3, w + 2]$ $-1$
4 $[4, 2, 2]$ $\phantom{-}e$
5 $[5, 5, w + 2]$ $\phantom{-}1$
7 $[7, 7, w]$ $\phantom{-}e + 2$
7 $[7, 7, w + 6]$ $-e$
17 $[17, 17, w + 8]$ $\phantom{-}2e - 1$
19 $[19, 19, w + 1]$ $-1$
19 $[19, 19, w - 2]$ $-3e - 7$
23 $[23, 23, w + 9]$ $\phantom{-}3e + 3$
23 $[23, 23, w + 13]$ $-2e + 1$
37 $[37, 37, w + 11]$ $\phantom{-}4$
37 $[37, 37, w + 25]$ $-6e - 8$
59 $[59, 59, 3w + 10]$ $-e - 10$
59 $[59, 59, 3w - 13]$ $\phantom{-}3e - 3$
73 $[73, 73, w + 15]$ $-5$
73 $[73, 73, w + 57]$ $-e - 3$
89 $[89, 89, -w - 10]$ $-3e - 6$
89 $[89, 89, w - 11]$ $\phantom{-}6e + 9$
97 $[97, 97, w + 22]$ $-10e - 15$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 2]$ $1$
5 $[5, 5, w + 2]$ $-1$