Base field \(\Q(\sqrt{157}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 39\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[11,11,3w - 20]$ |
| Dimension: | $13$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{13} - 16x^{11} - 6x^{10} + 90x^{9} + 57x^{8} - 209x^{7} - 159x^{6} + 201x^{5} + 166x^{4} - 58x^{3} - 54x^{2} - 5x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w + 7]$ | $-\frac{47}{53}e^{12} + \frac{26}{53}e^{11} + \frac{741}{53}e^{10} - \frac{111}{53}e^{9} - \frac{4234}{53}e^{8} - \frac{586}{53}e^{7} + \frac{10499}{53}e^{6} + \frac{2866}{53}e^{5} - \frac{11585}{53}e^{4} - \frac{3396}{53}e^{3} + \frac{4811}{53}e^{2} + \frac{949}{53}e - \frac{246}{53}$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}\frac{28}{53}e^{12} - \frac{20}{53}e^{11} - \frac{411}{53}e^{10} + \frac{118}{53}e^{9} + \frac{2095}{53}e^{8} + \frac{92}{53}e^{7} - \frac{4199}{53}e^{6} - \frac{1006}{53}e^{5} + \frac{3106}{53}e^{4} + \frac{1430}{53}e^{3} - \frac{480}{53}e^{2} - \frac{677}{53}e - \frac{35}{53}$ |
| 11 | $[11, 11, -3w - 17]$ | $\phantom{-}\frac{93}{53}e^{12} - \frac{21}{53}e^{11} - \frac{1473}{53}e^{10} - \frac{210}{53}e^{9} + \frac{8255}{53}e^{8} + \frac{3160}{53}e^{7} - \frac{19347}{53}e^{6} - \frac{8895}{53}e^{5} + \frac{19421}{53}e^{4} + \frac{8312}{53}e^{3} - \frac{6758}{53}e^{2} - \frac{2065}{53}e + \frac{56}{53}$ |
| 11 | $[11, 11, 3w - 20]$ | $\phantom{-}1$ |
| 13 | $[13, 13, 2w - 13]$ | $-\frac{34}{53}e^{12} - \frac{6}{53}e^{11} + \frac{571}{53}e^{10} + \frac{258}{53}e^{9} - \frac{3373}{53}e^{8} - \frac{2103}{53}e^{7} + \frac{8381}{53}e^{6} + \frac{5613}{53}e^{5} - \frac{8958}{53}e^{4} - \frac{5560}{53}e^{3} + \frac{3460}{53}e^{2} + \frac{1530}{53}e - \frac{249}{53}$ |
| 13 | $[13, 13, 2w + 11]$ | $\phantom{-}\frac{34}{53}e^{12} + \frac{6}{53}e^{11} - \frac{571}{53}e^{10} - \frac{258}{53}e^{9} + \frac{3373}{53}e^{8} + \frac{2103}{53}e^{7} - \frac{8381}{53}e^{6} - \frac{5613}{53}e^{5} + \frac{8958}{53}e^{4} + \frac{5507}{53}e^{3} - \frac{3354}{53}e^{2} - \frac{1265}{53}e + \frac{37}{53}$ |
| 17 | $[17, 17, w + 7]$ | $-\frac{91}{53}e^{12} + \frac{12}{53}e^{11} + \frac{1455}{53}e^{10} + \frac{332}{53}e^{9} - \frac{8253}{53}e^{8} - \frac{3744}{53}e^{7} + \frac{19755}{53}e^{6} + \frac{10080}{53}e^{5} - \frac{20827}{53}e^{4} - \frac{9285}{53}e^{3} + \frac{8344}{53}e^{2} + \frac{2134}{53}e - \frac{562}{53}$ |
| 17 | $[17, 17, -w + 8]$ | $\phantom{-}\frac{3}{53}e^{12} + \frac{66}{53}e^{11} - \frac{133}{53}e^{10} - \frac{930}{53}e^{9} + \frac{1063}{53}e^{8} + \frac{4583}{53}e^{7} - \frac{2992}{53}e^{6} - \frac{8849}{53}e^{5} + \frac{3880}{53}e^{4} + \frac{6093}{53}e^{3} - \frac{2285}{53}e^{2} - \frac{665}{53}e + \frac{301}{53}$ |
| 19 | $[19, 19, -w - 4]$ | $-\frac{168}{53}e^{12} + \frac{67}{53}e^{11} + \frac{2625}{53}e^{10} - \frac{19}{53}e^{9} - \frac{14584}{53}e^{8} - \frac{3838}{53}e^{7} + \frac{34045}{53}e^{6} + \frac{12767}{53}e^{5} - \frac{34059}{53}e^{4} - \frac{13138}{53}e^{3} + \frac{11678}{53}e^{2} + \frac{3532}{53}e - \frac{55}{53}$ |
| 19 | $[19, 19, -w + 5]$ | $\phantom{-}\frac{216}{53}e^{12} - \frac{124}{53}e^{11} - \frac{3375}{53}e^{10} + \frac{562}{53}e^{9} + \frac{19031}{53}e^{8} + \frac{2436}{53}e^{7} - \frac{46142}{53}e^{6} - \frac{12576}{53}e^{5} + \frac{49022}{53}e^{4} + \frac{15597}{53}e^{3} - \frac{18823}{53}e^{2} - \frac{5056}{53}e + \frac{631}{53}$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}\frac{274}{53}e^{12} - \frac{173}{53}e^{11} - \frac{4268}{53}e^{10} + \frac{973}{53}e^{9} + \frac{23965}{53}e^{8} + \frac{1559}{53}e^{7} - \frac{57577}{53}e^{6} - \frac{12131}{53}e^{5} + \frac{59605}{53}e^{4} + \frac{15788}{53}e^{3} - \frac{21430}{53}e^{2} - \frac{5175}{53}e + \frac{585}{53}$ |
| 31 | $[31, 31, -6w - 35]$ | $-\frac{84}{53}e^{12} + \frac{60}{53}e^{11} + \frac{1286}{53}e^{10} - \frac{354}{53}e^{9} - \frac{7080}{53}e^{8} - \frac{541}{53}e^{7} + \frac{16519}{53}e^{6} + \frac{5085}{53}e^{5} - \frac{16102}{53}e^{4} - \frac{7682}{53}e^{3} + \frac{4885}{53}e^{2} + \frac{2985}{53}e - \frac{1}{53}$ |
| 31 | $[31, 31, -6w + 41]$ | $\phantom{-}\frac{5}{53}e^{12} + \frac{57}{53}e^{11} - \frac{151}{53}e^{10} - \frac{861}{53}e^{9} + \frac{1171}{53}e^{8} + \frac{4635}{53}e^{7} - \frac{3538}{53}e^{6} - \frac{10473}{53}e^{5} + \frac{5071}{53}e^{4} + \frac{10155}{53}e^{3} - \frac{2819}{53}e^{2} - \frac{3246}{53}e - \frac{99}{53}$ |
| 37 | $[37, 37, -w - 1]$ | $-\frac{119}{53}e^{12} + \frac{85}{53}e^{11} + \frac{1760}{53}e^{10} - \frac{528}{53}e^{9} - \frac{9129}{53}e^{8} + \frac{33}{53}e^{7} + \frac{19078}{53}e^{6} + \frac{2235}{53}e^{5} - \frac{15824}{53}e^{4} - \frac{2606}{53}e^{3} + \frac{3842}{53}e^{2} + \frac{1009}{53}e + \frac{3}{53}$ |
| 37 | $[37, 37, w - 2]$ | $\phantom{-}\frac{325}{53}e^{12} - \frac{164}{53}e^{11} - \frac{5045}{53}e^{10} + \frac{480}{53}e^{9} + \frac{28044}{53}e^{8} + \frac{5482}{53}e^{7} - \frac{66094}{53}e^{6} - \frac{21637}{53}e^{5} + \frac{67371}{53}e^{4} + \frac{23651}{53}e^{3} - \frac{24606}{53}e^{2} - \frac{6410}{53}e + \frac{879}{53}$ |
| 47 | $[47, 47, 3w + 16]$ | $-\frac{142}{53}e^{12} + \frac{56}{53}e^{11} + \frac{2232}{53}e^{10} + \frac{30}{53}e^{9} - \frac{12597}{53}e^{8} - \frac{3745}{53}e^{7} + \frac{30339}{53}e^{6} + \frac{12802}{53}e^{5} - \frac{32038}{53}e^{4} - \frac{13756}{53}e^{3} + \frac{12792}{53}e^{2} + \frac{3846}{53}e - \frac{697}{53}$ |
| 47 | $[47, 47, -3w + 19]$ | $-\frac{71}{53}e^{12} + \frac{28}{53}e^{11} + \frac{1063}{53}e^{10} + \frac{15}{53}e^{9} - \frac{5477}{53}e^{8} - \frac{1687}{53}e^{7} + \frac{11009}{53}e^{6} + \frac{4970}{53}e^{5} - \frac{8334}{53}e^{4} - \frac{4970}{53}e^{3} + \frac{1202}{53}e^{2} + \frac{1923}{53}e + \frac{367}{53}$ |
| 49 | $[49, 7, -7]$ | $-\frac{325}{53}e^{12} + \frac{111}{53}e^{11} + \frac{5151}{53}e^{10} + \frac{156}{53}e^{9} - \frac{29051}{53}e^{8} - \frac{8185}{53}e^{7} + \frac{69115}{53}e^{6} + \frac{26354}{53}e^{5} - \frac{70657}{53}e^{4} - \frac{27520}{53}e^{3} + \frac{25136}{53}e^{2} + \frac{8106}{53}e - \frac{561}{53}$ |
| 67 | $[67, 67, 3w - 22]$ | $-\frac{16}{53}e^{12} - \frac{34}{53}e^{11} + \frac{250}{53}e^{10} + \frac{614}{53}e^{9} - \frac{1129}{53}e^{8} - \frac{3596}{53}e^{7} + \frac{923}{53}e^{6} + \frac{7904}{53}e^{5} + \frac{2397}{53}e^{4} - \frac{7003}{53}e^{3} - \frac{3254}{53}e^{2} + \frac{2416}{53}e + \frac{550}{53}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11,11,3w - 20]$ | $-1$ |