Properties

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

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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: $[1, 1, 1]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $27$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{2} + x + 1\)

  Show full eigenvalues   Hide large eigenvalues

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

Atkin-Lehner eigenvalues

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