Properties

Label 3.3.1957.1-1.1-a
Base field 3.3.1957.1
Weight $[2, 2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $2$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 3.3.1957.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 10\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2, 2]$
Level: $[1, 1, 1]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w^{2}]$ $\phantom{-}e$
4 $[4, 2, w^{2} + w + 1]$ $-e$
5 $[5, 5, w]$ $\phantom{-}0$
11 $[11, 11, 10w + 4]$ $-2e$
13 $[13, 13, 12w^{2} + w + 7]$ $\phantom{-}0$
17 $[17, 17, w + 1]$ $-6$
17 $[17, 17, 16w^{2} + 16]$ $\phantom{-}4e$
17 $[17, 17, 16w^{2} + 16w + 8]$ $\phantom{-}0$
19 $[19, 19, 18w^{2} + 18w + 1]$ $\phantom{-}2e$
19 $[19, 19, -w^{2} + 7]$ $-8$
25 $[25, 5, 4w^{2} + w + 4]$ $\phantom{-}4e$
27 $[27, 3, -3]$ $-8$
29 $[29, 29, w + 7]$ $-4e$
41 $[41, 41, 40w^{2} + 18]$ $-4e$
43 $[43, 43, w^{2} - 11]$ $\phantom{-}4$
47 $[47, 47, 2w^{2} + 2w - 13]$ $\phantom{-}0$
59 $[59, 59, w^{2} - 3]$ $\phantom{-}0$
73 $[73, 73, w^{2} + 2w - 1]$ $-2$
79 $[79, 79, w^{2} + 37]$ $-6e$
97 $[97, 97, w^{2} + 2w - 7]$ $\phantom{-}2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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