Properties

Label 2.2.229.1-9.3-a
Base field \(\Q(\sqrt{229}) \)
Weight $[2, 2]$
Level norm $9$
Level $[9,9,-w + 4]$
Dimension $1$
CM no
Base change no

Related objects

Downloads

Learn more

Base field \(\Q(\sqrt{229}) \)

Generator \(w\), with minimal polynomial \(x^2 - x - 57\); narrow class number \(3\) and class number \(3\).

Form

Weight: $[2, 2]$
Level: $[9,9,-w + 4]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $99$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w]$ $-1$
3 $[3, 3, w + 2]$ $\phantom{-}0$
4 $[4, 2, 2]$ $\phantom{-}1$
5 $[5, 5, w + 1]$ $\phantom{-}3$
5 $[5, 5, w + 3]$ $-3$
11 $[11, 11, w + 1]$ $\phantom{-}3$
11 $[11, 11, w + 9]$ $-3$
17 $[17, 17, w + 2]$ $\phantom{-}3$
17 $[17, 17, w + 14]$ $-3$
19 $[19, 19, w]$ $-1$
19 $[19, 19, w + 18]$ $-1$
37 $[37, 37, -w - 4]$ $\phantom{-}2$
37 $[37, 37, w - 5]$ $\phantom{-}2$
43 $[43, 43, w + 16]$ $\phantom{-}1$
43 $[43, 43, w + 26]$ $\phantom{-}1$
49 $[49, 7, -7]$ $\phantom{-}14$
53 $[53, 53, -w - 10]$ $-6$
53 $[53, 53, w - 11]$ $\phantom{-}6$
61 $[61, 61, w + 15]$ $-5$
61 $[61, 61, w + 45]$ $-5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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