Properties

Base field \(\Q(\sqrt{34}) \)
Weight [2, 2]
Level norm 9
Level $[9, 3, 3]$
Label 2.2.136.1-9.1-a
Dimension 1
CM no
Base change no

Related objects

Downloads

Learn more about

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 $[9, 3, 3]$
Label 2.2.136.1-9.1-a
Dimension 1
Is CM no
Is base change no
Parent newspace dimension 48

Hecke eigenvalues ($q$-expansion)

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

Atkin-Lehner eigenvalues

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