Base field \(\Q(\sqrt{241}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 60\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[10, 10, 3w + 22]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $49$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} + 3x^{11} - 14x^{10} - 44x^{9} + 67x^{8} + 230x^{7} - 119x^{6} - 514x^{5} + 12x^{4} + 430x^{3} + 124x^{2} - 38x - 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -393w - 2854]$ | $\phantom{-}1$ |
| 2 | $[2, 2, -393w + 3247]$ | $\phantom{-}e$ |
| 3 | $[3, 3, 4w - 33]$ | $\phantom{-}\frac{151}{509}e^{11} + \frac{317}{509}e^{10} - \frac{2204}{509}e^{9} - \frac{4305}{509}e^{8} + \frac{11328}{509}e^{7} + \frac{20189}{509}e^{6} - \frac{24014}{509}e^{5} - \frac{39084}{509}e^{4} + \frac{16640}{509}e^{3} + \frac{27429}{509}e^{2} + \frac{1948}{509}e - \frac{1580}{509}$ |
| 3 | $[3, 3, 4w + 29]$ | $-\frac{132}{509}e^{11} - \frac{267}{509}e^{10} + \frac{1866}{509}e^{9} + \frac{3406}{509}e^{8} - \frac{9188}{509}e^{7} - \frac{14625}{509}e^{6} + \frac{18444}{509}e^{5} + \frac{25530}{509}e^{4} - \frac{12490}{509}e^{3} - \frac{17091}{509}e^{2} + \frac{832}{509}e + \frac{1843}{509}$ |
| 5 | $[5, 5, 42w + 305]$ | $-\frac{120}{509}e^{11} - \frac{289}{509}e^{10} + \frac{1465}{509}e^{9} + \frac{3374}{509}e^{8} - \frac{5345}{509}e^{7} - \frac{11861}{509}e^{6} + \frac{3996}{509}e^{5} + \frac{11826}{509}e^{4} + \frac{7571}{509}e^{3} + \frac{1815}{509}e^{2} - \frac{3547}{509}e - \frac{777}{509}$ |
| 5 | $[5, 5, -42w + 347]$ | $-1$ |
| 29 | $[29, 29, 1820w + 13217]$ | $-\frac{308}{509}e^{11} - \frac{623}{509}e^{10} + \frac{4354}{509}e^{9} + \frac{8117}{509}e^{8} - \frac{21269}{509}e^{7} - \frac{36161}{509}e^{6} + \frac{41000}{509}e^{5} + \frac{66696}{509}e^{4} - \frac{21678}{509}e^{3} - \frac{45478}{509}e^{2} - \frac{6033}{509}e + \frac{1416}{509}$ |
| 29 | $[29, 29, 1820w - 15037]$ | $-\frac{122}{509}e^{11} + \frac{54}{509}e^{10} + \frac{2465}{509}e^{9} - \frac{523}{509}e^{8} - \frac{17438}{509}e^{7} + \frac{573}{509}e^{6} + \frac{51196}{509}e^{5} + \frac{6475}{509}e^{4} - \frac{55071}{509}e^{3} - \frac{16606}{509}e^{2} + \frac{7787}{509}e + \frac{2544}{509}$ |
| 41 | $[41, 41, -80w - 581]$ | $\phantom{-}\frac{202}{509}e^{11} + \frac{478}{509}e^{10} - \frac{2763}{509}e^{9} - \frac{5968}{509}e^{8} + \frac{13027}{509}e^{7} + \frac{23792}{509}e^{6} - \frac{25356}{509}e^{5} - \frac{32174}{509}e^{4} + \frac{20841}{509}e^{3} + \frac{5725}{509}e^{2} - \frac{9664}{509}e + \frac{519}{509}$ |
| 41 | $[41, 41, 80w - 661]$ | $\phantom{-}\frac{625}{509}e^{11} + \frac{975}{509}e^{10} - \frac{9645}{509}e^{9} - \frac{12695}{509}e^{8} + \frac{53437}{509}e^{7} + \frac{56580}{509}e^{6} - \frac{126430}{509}e^{5} - \frac{106513}{509}e^{4} + \frac{112483}{509}e^{3} + \frac{81976}{509}e^{2} - \frac{17050}{509}e - \frac{7851}{509}$ |
| 47 | $[47, 47, 34w - 281]$ | $-\frac{29}{509}e^{11} - \frac{371}{509}e^{10} - \frac{770}{509}e^{9} + \frac{3810}{509}e^{8} + \frac{12218}{509}e^{7} - \frac{9055}{509}e^{6} - \frac{49578}{509}e^{5} - \frac{8620}{509}e^{4} + \frac{61845}{509}e^{3} + \frac{34478}{509}e^{2} - \frac{4136}{509}e - \frac{4527}{509}$ |
| 47 | $[47, 47, 34w + 247]$ | $-\frac{525}{509}e^{11} - \frac{310}{509}e^{10} + \frac{9018}{509}e^{9} + \frac{3436}{509}e^{8} - \frac{55515}{509}e^{7} - \frac{11490}{509}e^{6} + \frac{143969}{509}e^{5} + \frac{14709}{509}e^{4} - \frac{139237}{509}e^{3} - \frac{12992}{509}e^{2} + \frac{29083}{509}e - \frac{918}{509}$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{307}{509}e^{11} + \frac{31}{509}e^{10} - \frac{5381}{509}e^{9} + \frac{369}{509}e^{8} + \frac{33801}{509}e^{7} - \frac{5977}{509}e^{6} - \frac{89169}{509}e^{5} + \frac{16395}{509}e^{4} + \frac{85540}{509}e^{3} - \frac{5725}{509}e^{2} - \frac{13241}{509}e + \frac{5080}{509}$ |
| 53 | $[53, 53, 6w + 43]$ | $\phantom{-}\frac{321}{509}e^{11} + \frac{684}{509}e^{10} - \frac{4237}{509}e^{9} - \frac{7982}{509}e^{8} + \frac{18688}{509}e^{7} + \frac{28636}{509}e^{6} - \frac{30184}{509}e^{5} - \frac{33187}{509}e^{4} + \frac{7908}{509}e^{3} + \frac{6152}{509}e^{2} + \frac{6676}{509}e + \frac{666}{509}$ |
| 53 | $[53, 53, 6w - 49]$ | $\phantom{-}\frac{320}{509}e^{11} + \frac{601}{509}e^{10} - \frac{4246}{509}e^{9} - \frac{7131}{509}e^{8} + \frac{17986}{509}e^{7} + \frac{26709}{509}e^{6} - \frac{22363}{509}e^{5} - \frac{36117}{509}e^{4} - \frac{12215}{509}e^{3} + \frac{17047}{509}e^{2} + \frac{15906}{509}e - \frac{3018}{509}$ |
| 59 | $[59, 59, 10w + 73]$ | $\phantom{-}\frac{278}{509}e^{11} + \frac{678}{509}e^{10} - \frac{3097}{509}e^{9} - \frac{7019}{509}e^{8} + \frac{9371}{509}e^{7} + \frac{17035}{509}e^{6} - \frac{1826}{509}e^{5} + \frac{13374}{509}e^{4} - \frac{14986}{509}e^{3} - \frac{56250}{509}e^{2} - \frac{8724}{509}e + \frac{5643}{509}$ |
| 59 | $[59, 59, 10w - 83]$ | $-\frac{269}{509}e^{11} - \frac{949}{509}e^{10} + \frac{3178}{509}e^{9} + \frac{12594}{509}e^{8} - \frac{11706}{509}e^{7} - \frac{56700}{509}e^{6} + \frac{13895}{509}e^{5} + \frac{101562}{509}e^{4} - \frac{890}{509}e^{3} - \frac{61147}{509}e^{2} - \frac{32}{509}e + \frac{6135}{509}$ |
| 61 | $[61, 61, 4178w + 30341]$ | $\phantom{-}\frac{272}{509}e^{11} + \frac{689}{509}e^{10} - \frac{4169}{509}e^{9} - \frac{10057}{509}e^{8} + \frac{23483}{509}e^{7} + \frac{52301}{509}e^{6} - \frac{59245}{509}e^{5} - \frac{116695}{509}e^{4} + \frac{59732}{509}e^{3} + \frac{97686}{509}e^{2} - \frac{6789}{509}e - \frac{8317}{509}$ |
| 61 | $[61, 61, 4178w - 34519]$ | $-\frac{227}{509}e^{11} - \frac{8}{509}e^{10} + \frac{4065}{509}e^{9} - \frac{243}{509}e^{8} - \frac{25996}{509}e^{7} + \frac{2856}{509}e^{6} + \frac{69708}{509}e^{5} - \frac{6464}{509}e^{4} - \frac{68361}{509}e^{3} + \frac{443}{509}e^{2} + \frac{10346}{509}e - \frac{5071}{509}$ |
| 67 | $[67, 67, -332w + 2743]$ | $\phantom{-}\frac{23}{509}e^{11} + \frac{382}{509}e^{10} + \frac{716}{509}e^{9} - \frac{4303}{509}e^{8} - \frac{10831}{509}e^{7} + \frac{13272}{509}e^{6} + \frac{42041}{509}e^{5} - \frac{2343}{509}e^{4} - \frac{44644}{509}e^{3} - \frac{27134}{509}e^{2} - \frac{10217}{509}e + \frac{1256}{509}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -393w - 2854]$ | $-1$ |
| $5$ | $[5, 5, -42w + 347]$ | $1$ |