Properties

Base field \(\Q(\sqrt{55}) \)
Weight [2, 2]
Level norm 4
Level $[4, 2, 2]$
Label 2.2.220.1-4.1-a
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 $[4, 2, 2]$
Label 2.2.220.1-4.1-a
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 16

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut -\mathstrut 82x^{2} \) \(\mathstrut +\mathstrut 2209\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}0$
3 $[3, 3, w + 1]$ $\phantom{-}\frac{1}{94}e^{3} - \frac{35}{94}e$
3 $[3, 3, w + 2]$ $-\frac{1}{94}e^{3} + \frac{35}{94}e$
5 $[5, 5, -2w + 15]$ $-4$
11 $[11, 11, 3w - 22]$ $-\frac{1}{94}e^{3} + \frac{129}{94}e$
13 $[13, 13, w + 4]$ $\phantom{-}0$
13 $[13, 13, w + 9]$ $\phantom{-}0$
17 $[17, 17, w + 2]$ $\phantom{-}\frac{1}{4}e^{2} - \frac{41}{4}$
17 $[17, 17, w + 15]$ $-\frac{1}{4}e^{2} + \frac{41}{4}$
19 $[19, 19, -w - 6]$ $-\frac{1}{188}e^{3} + \frac{129}{188}e$
19 $[19, 19, w - 6]$ $-\frac{1}{188}e^{3} + \frac{129}{188}e$
23 $[23, 23, w + 3]$ $\phantom{-}\frac{1}{47}e^{3} - \frac{35}{47}e$
23 $[23, 23, w + 20]$ $-\frac{1}{47}e^{3} + \frac{35}{47}e$
47 $[47, 47, w + 14]$ $-\frac{1}{47}e^{3} + \frac{35}{47}e$
47 $[47, 47, w + 33]$ $\phantom{-}\frac{1}{47}e^{3} - \frac{35}{47}e$
49 $[49, 7, -7]$ $\phantom{-}3$
67 $[67, 67, w + 16]$ $\phantom{-}\frac{1}{47}e^{3} - \frac{35}{47}e$
67 $[67, 67, w + 51]$ $-\frac{1}{47}e^{3} + \frac{35}{47}e$
73 $[73, 73, w + 36]$ $-\frac{1}{2}e^{2} + \frac{41}{2}$
73 $[73, 73, w + 37]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{41}{2}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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