Properties

Base field \(\Q(\sqrt{55}) \)
Weight [2, 2]
Level norm 1
Level $[1, 1, 1]$
Label 2.2.220.1-1.1-e
Dimension 4
CM yes
Base change yes

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Base field \(\Q(\sqrt{55}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 55\); narrow class number \(4\) and class number \(2\).

Form

Weight [2, 2]
Level $[1, 1, 1]$
Label 2.2.220.1-1.1-e
Dimension 4
Is CM yes
Is base change yes
Parent newspace dimension 28

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut -\mathstrut 8x^{2} \) \(\mathstrut +\mathstrut 11\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $\phantom{-}0$
3 $[3, 3, w + 2]$ $\phantom{-}0$
5 $[5, 5, -2w + 15]$ $\phantom{-}2e^{2} - 8$
11 $[11, 11, 3w - 22]$ $\phantom{-}0$
13 $[13, 13, w + 4]$ $-e^{3} + 7e$
13 $[13, 13, w + 9]$ $-e^{3} + 7e$
17 $[17, 17, w + 2]$ $-e^{3} + 3e$
17 $[17, 17, w + 15]$ $-e^{3} + 3e$
19 $[19, 19, -w - 6]$ $\phantom{-}0$
19 $[19, 19, w - 6]$ $\phantom{-}0$
23 $[23, 23, w + 3]$ $\phantom{-}0$
23 $[23, 23, w + 20]$ $\phantom{-}0$
47 $[47, 47, w + 14]$ $\phantom{-}0$
47 $[47, 47, w + 33]$ $\phantom{-}0$
49 $[49, 7, -7]$ $-2e^{2} + 8$
67 $[67, 67, w + 16]$ $\phantom{-}0$
67 $[67, 67, w + 51]$ $\phantom{-}0$
73 $[73, 73, w + 36]$ $-e^{3} + 11e$
73 $[73, 73, w + 37]$ $-e^{3} + 11e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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