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: | $[1, 1, 1]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 50x^{10} + 857x^{8} - 5988x^{6} + 16760x^{4} - 19952x^{2} + 8464\) |
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 | $[73, 73, w + 37]$ | $-\frac{256053}{5168192}e^{11} + \frac{3109985}{1292048}e^{9} - \frac{201803413}{5168192}e^{7} + \frac{623425487}{2584096}e^{5} - \frac{630009053}{1292048}e^{3} + \frac{193176963}{646024}e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).