Properties

Base field \(\Q(\sqrt{55}) \)
Weight [2, 2]
Level norm 1
Level $[1, 1, 1]$
Label 2.2.220.1-1.1-f
Dimension 12
CM no
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-f
Dimension 12
Is CM no
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:
\(x^{12} \) \(\mathstrut -\mathstrut 50x^{10} \) \(\mathstrut +\mathstrut 857x^{8} \) \(\mathstrut -\mathstrut 5988x^{6} \) \(\mathstrut +\mathstrut 16760x^{4} \) \(\mathstrut -\mathstrut 19952x^{2} \) \(\mathstrut +\mathstrut 8464\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $-\frac{4893}{1292048}e^{11} + \frac{58529}{323012}e^{9} - \frac{3687761}{1292048}e^{7} + \frac{10639339}{646024}e^{5} - \frac{2173977}{80753}e^{3} + \frac{930274}{80753}e$
3 $[3, 3, w + 1]$ $\phantom{-}\frac{4893}{1292048}e^{11} - \frac{58529}{323012}e^{9} + \frac{3687761}{1292048}e^{7} - \frac{10639339}{646024}e^{5} + \frac{2173977}{80753}e^{3} - \frac{849521}{80753}e$
3 $[3, 3, w + 2]$ $\phantom{-}\frac{4893}{1292048}e^{11} - \frac{58529}{323012}e^{9} + \frac{3687761}{1292048}e^{7} - \frac{10639339}{646024}e^{5} + \frac{2173977}{80753}e^{3} - \frac{849521}{80753}e$
5 $[5, 5, -2w + 15]$ $\phantom{-}\frac{531}{28088}e^{10} - \frac{12895}{14044}e^{8} + \frac{418287}{28088}e^{6} - \frac{646745}{7022}e^{4} + \frac{1317987}{7022}e^{2} - \frac{410638}{3511}$
11 $[11, 11, 3w - 22]$ $-\frac{4553}{112352}e^{10} + \frac{55247}{28088}e^{8} - \frac{3577113}{112352}e^{6} + \frac{10987823}{56176}e^{4} - \frac{10915793}{28088}e^{2} + \frac{3293019}{14044}$
13 $[13, 13, w + 4]$ $\phantom{-}\frac{69317}{5168192}e^{11} - \frac{838529}{1292048}e^{9} + \frac{53984581}{5168192}e^{7} - \frac{163743903}{2584096}e^{5} + \frac{156719381}{1292048}e^{3} - \frac{43714187}{646024}e$
13 $[13, 13, w + 9]$ $\phantom{-}\frac{69317}{5168192}e^{11} - \frac{838529}{1292048}e^{9} + \frac{53984581}{5168192}e^{7} - \frac{163743903}{2584096}e^{5} + \frac{156719381}{1292048}e^{3} - \frac{43714187}{646024}e$
17 $[17, 17, w + 2]$ $-\frac{63195}{5168192}e^{11} + \frac{765431}{1292048}e^{9} - \frac{49426923}{5168192}e^{7} + \frac{151211601}{2584096}e^{5} - \frac{149492719}{1292048}e^{3} + \frac{45901585}{646024}e$
17 $[17, 17, w + 15]$ $-\frac{63195}{5168192}e^{11} + \frac{765431}{1292048}e^{9} - \frac{49426923}{5168192}e^{7} + \frac{151211601}{2584096}e^{5} - \frac{149492719}{1292048}e^{3} + \frac{45901585}{646024}e$
19 $[19, 19, -w - 6]$ $\phantom{-}\frac{445}{112352}e^{10} - \frac{2819}{14044}e^{8} + \frac{396165}{112352}e^{6} - \frac{1440249}{56176}e^{4} + \frac{2054521}{28088}e^{2} - \frac{868117}{14044}$
19 $[19, 19, w - 6]$ $\phantom{-}\frac{445}{112352}e^{10} - \frac{2819}{14044}e^{8} + \frac{396165}{112352}e^{6} - \frac{1440249}{56176}e^{4} + \frac{2054521}{28088}e^{2} - \frac{868117}{14044}$
23 $[23, 23, w + 3]$ $-\frac{19197}{2584096}e^{11} + \frac{117365}{323012}e^{9} - \frac{15434677}{2584096}e^{7} + \frac{49153705}{1292048}e^{5} - \frac{53758673}{646024}e^{3} + \frac{17308961}{323012}e$
23 $[23, 23, w + 20]$ $-\frac{19197}{2584096}e^{11} + \frac{117365}{323012}e^{9} - \frac{15434677}{2584096}e^{7} + \frac{49153705}{1292048}e^{5} - \frac{53758673}{646024}e^{3} + \frac{17308961}{323012}e$
47 $[47, 47, w + 14]$ $\phantom{-}\frac{66553}{2584096}e^{11} - \frac{404623}{323012}e^{9} + \frac{52626913}{2584096}e^{7} - \frac{163489093}{1292048}e^{5} + \frac{168426733}{646024}e^{3} - \frac{54114333}{323012}e$
47 $[47, 47, w + 33]$ $\phantom{-}\frac{66553}{2584096}e^{11} - \frac{404623}{323012}e^{9} + \frac{52626913}{2584096}e^{7} - \frac{163489093}{1292048}e^{5} + \frac{168426733}{646024}e^{3} - \frac{54114333}{323012}e$
49 $[49, 7, -7]$ $\phantom{-}\frac{1135}{56176}e^{10} - \frac{27695}{28088}e^{8} + \frac{906139}{56176}e^{6} - \frac{1426941}{14044}e^{4} + \frac{3047583}{14044}e^{2} - \frac{468308}{3511}$
67 $[67, 67, w + 16]$ $\phantom{-}\frac{19197}{2584096}e^{11} - \frac{117365}{323012}e^{9} + \frac{15434677}{2584096}e^{7} - \frac{49153705}{1292048}e^{5} + \frac{53758673}{646024}e^{3} - \frac{17308961}{323012}e$
67 $[67, 67, w + 51]$ $\phantom{-}\frac{19197}{2584096}e^{11} - \frac{117365}{323012}e^{9} + \frac{15434677}{2584096}e^{7} - \frac{49153705}{1292048}e^{5} + \frac{53758673}{646024}e^{3} - \frac{17308961}{323012}e$
73 $[73, 73, w + 36]$ $-\frac{256053}{5168192}e^{11} + \frac{3109985}{1292048}e^{9} - \frac{201803413}{5168192}e^{7} + \frac{623425487}{2584096}e^{5} - \frac{630009053}{1292048}e^{3} + \frac{193176963}{646024}e$
73 $[73, 73, w + 37]$ $-\frac{256053}{5168192}e^{11} + \frac{3109985}{1292048}e^{9} - \frac{201803413}{5168192}e^{7} + \frac{623425487}{2584096}e^{5} - \frac{630009053}{1292048}e^{3} + \frac{193176963}{646024}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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