Properties

Base field \(\Q(\sqrt{229}) \)
Weight [2, 2]
Level norm 1
Level $[1, 1, 1]$
Label 2.2.229.1-1.1-a
Dimension 1
CM no
Base change yes

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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 $[1, 1, 1]$
Label 2.2.229.1-1.1-a
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 27

Hecke eigenvalues ($q$-expansion)

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

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).