Properties

Base field \(\Q(\sqrt{55}) \)
Weight [2, 2]
Level norm 6
Level $[6,6,w - 7]$
Label 2.2.220.1-6.2-c
Dimension 4
CM no
Base change no

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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 $[6,6,w - 7]$
Label 2.2.220.1-6.2-c
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 32

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut -\mathstrut 5x^{2} \) \(\mathstrut -\mathstrut x \) \(\mathstrut +\mathstrut 4\)

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Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}1$
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $-1$
5 $[5, 5, -2w + 15]$ $\phantom{-}e^{3} - e^{2} - 4e + 1$
11 $[11, 11, 3w - 22]$ $\phantom{-}e^{2} - 5$
13 $[13, 13, w + 4]$ $-e^{3} + e^{2} + 5e$
13 $[13, 13, w + 9]$ $-e^{2} - e + 3$
17 $[17, 17, w + 2]$ $\phantom{-}e^{3} + e^{2} - 6e - 4$
17 $[17, 17, w + 15]$ $-2e^{3} - e^{2} + 7e + 3$
19 $[19, 19, -w - 6]$ $-4e^{3} + 2e^{2} + 13e - 3$
19 $[19, 19, w - 6]$ $-e^{2} + e$
23 $[23, 23, w + 3]$ $\phantom{-}e^{3} + 2e^{2} - 3e - 4$
23 $[23, 23, w + 20]$ $\phantom{-}3e^{3} - 4e^{2} - 10e + 8$
47 $[47, 47, w + 14]$ $-2e^{3} + 5e^{2} + 3e - 14$
47 $[47, 47, w + 33]$ $\phantom{-}2e^{3} - e^{2} - 7e - 1$
49 $[49, 7, -7]$ $-2e^{3} + 5e^{2} + 8e - 11$
67 $[67, 67, w + 16]$ $\phantom{-}3e^{3} - 2e^{2} - 10e + 1$
67 $[67, 67, w + 51]$ $\phantom{-}3e^{3} - 10e^{2} - 8e + 22$
73 $[73, 73, w + 36]$ $-e^{3} + 7e^{2} + 3e - 21$
73 $[73, 73, w + 37]$ $-7e^{3} + 5e^{2} + 19e - 10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,-w + 1]$ $-1$
3 $[3,3,-w + 1]$ $1$