Properties

Base field \(\Q(\sqrt{55}) \)
Weight [2, 2]
Level norm 3
Level $[3, 3, w + 1]$
Label 2.2.220.1-3.1-c
Dimension 16
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 $[3, 3, w + 1]$
Label 2.2.220.1-3.1-c
Dimension 16
Is CM no
Is base change no
Parent newspace dimension 24

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{16} \) \(\mathstrut +\mathstrut 60x^{14} \) \(\mathstrut +\mathstrut 1346x^{12} \) \(\mathstrut +\mathstrut 14040x^{10} \) \(\mathstrut +\mathstrut 67921x^{8} \) \(\mathstrut +\mathstrut 129884x^{6} \) \(\mathstrut +\mathstrut 74064x^{4} \) \(\mathstrut +\mathstrut 13504x^{2} \) \(\mathstrut +\mathstrut 256\)

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Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $...$
3 $[3, 3, w + 1]$ $-\frac{11523}{1313824}e^{15} - \frac{686685}{1313824}e^{13} - \frac{951877}{82114}e^{11} - \frac{9723097}{82114}e^{9} - \frac{719100509}{1313824}e^{7} - \frac{1202061251}{1313824}e^{5} - \frac{11145560}{41057}e^{3} + \frac{59629}{41057}e$
3 $[3, 3, w + 2]$ $...$
5 $[5, 5, -2w + 15]$ $...$
11 $[11, 11, 3w - 22]$ $...$
13 $[13, 13, w + 4]$ $...$
13 $[13, 13, w + 9]$ $...$
17 $[17, 17, w + 2]$ $...$
17 $[17, 17, w + 15]$ $...$
19 $[19, 19, -w - 6]$ $...$
19 $[19, 19, w - 6]$ $...$
23 $[23, 23, w + 3]$ $...$
23 $[23, 23, w + 20]$ $...$
47 $[47, 47, w + 14]$ $...$
47 $[47, 47, w + 33]$ $...$
49 $[49, 7, -7]$ $...$
67 $[67, 67, w + 16]$ $...$
67 $[67, 67, w + 51]$ $...$
73 $[73, 73, w + 36]$ $...$
73 $[73, 73, w + 37]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\frac{11523}{1313824}e^{15} + \frac{686685}{1313824}e^{13} + \frac{951877}{82114}e^{11} + \frac{9723097}{82114}e^{9} + \frac{719100509}{1313824}e^{7} + \frac{1202061251}{1313824}e^{5} + \frac{11145560}{41057}e^{3} - \frac{59629}{41057}e$