Base field \(\Q(\sqrt{133}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 33\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[23,23,w - 8]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $58$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 40x^{12} + 657x^{10} - 5671x^{8} + 27240x^{6} - 70570x^{4} + 87156x^{2} - 39204\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w - 5]$ | $\phantom{-}\frac{155}{594}e^{13} - \frac{5111}{594}e^{11} + \frac{7333}{66}e^{9} - \frac{208585}{297}e^{7} + \frac{436243}{198}e^{5} - \frac{907552}{297}e^{3} + \frac{48490}{33}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}\frac{7}{18}e^{12} - \frac{122}{9}e^{10} + \frac{369}{2}e^{8} - \frac{22021}{18}e^{6} + \frac{11980}{3}e^{4} - \frac{51119}{9}e^{2} + 2778$ |
| 7 | $[7, 7, 3w - 19]$ | $-1$ |
| 11 | $[11, 11, -2w - 11]$ | $-\frac{7}{6}e^{12} + \frac{119}{3}e^{10} - \frac{1055}{2}e^{8} + \frac{20551}{6}e^{6} - 10983e^{4} + \frac{46262}{3}e^{2} - 7467$ |
| 11 | $[11, 11, -2w + 13]$ | $-\frac{20}{9}e^{12} + \frac{665}{9}e^{10} - 962e^{8} + \frac{55154}{9}e^{6} - \frac{58057}{3}e^{4} + \frac{242579}{9}e^{2} - 13011$ |
| 13 | $[13, 13, w + 4]$ | $-\frac{53}{198}e^{13} + \frac{862}{99}e^{11} - \frac{2439}{22}e^{9} + \frac{136817}{198}e^{7} - \frac{70604}{33}e^{5} + \frac{290857}{99}e^{3} - \frac{15473}{11}e$ |
| 13 | $[13, 13, -w + 5]$ | $\phantom{-}\frac{193}{297}e^{13} - \frac{6433}{297}e^{11} + \frac{9326}{33}e^{9} - \frac{535549}{297}e^{7} + \frac{564110}{99}e^{5} - \frac{2354206}{297}e^{3} + \frac{125974}{33}e$ |
| 19 | $[19, 19, 5w - 31]$ | $-\frac{101}{594}e^{13} + \frac{3347}{594}e^{11} - \frac{1607}{22}e^{9} + \frac{137440}{297}e^{7} - \frac{287209}{198}e^{5} + \frac{593191}{297}e^{3} - \frac{31211}{33}e$ |
| 23 | $[23, 23, -w - 7]$ | $\phantom{-}\frac{47}{18}e^{12} - \frac{787}{9}e^{10} + \frac{2293}{2}e^{8} - \frac{132329}{18}e^{6} + \frac{70034}{3}e^{4} - \frac{293626}{9}e^{2} + 15780$ |
| 23 | $[23, 23, w - 8]$ | $\phantom{-}1$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}\frac{1}{6}e^{12} - \frac{14}{3}e^{10} + \frac{99}{2}e^{8} - \frac{1483}{6}e^{6} + 592e^{4} - \frac{1922}{3}e^{2} + 249$ |
| 31 | $[31, 31, -w - 1]$ | $-\frac{181}{297}e^{13} + \frac{12203}{594}e^{11} - \frac{8945}{33}e^{9} + \frac{1038647}{594}e^{7} - \frac{1105627}{198}e^{5} + \frac{2330353}{297}e^{3} - \frac{126025}{33}e$ |
| 31 | $[31, 31, w - 2]$ | $-\frac{14}{99}e^{13} + \frac{1021}{198}e^{11} - \frac{802}{11}e^{9} + \frac{98695}{198}e^{7} - \frac{109667}{66}e^{5} + \frac{235382}{99}e^{3} - \frac{12739}{11}e$ |
| 41 | $[41, 41, 6w + 31]$ | $\phantom{-}\frac{23}{66}e^{13} - \frac{394}{33}e^{11} + \frac{3519}{22}e^{9} - \frac{69053}{66}e^{7} + \frac{37188}{11}e^{5} - \frac{158056}{33}e^{3} + \frac{25757}{11}e$ |
| 41 | $[41, 41, 6w - 37]$ | $\phantom{-}\frac{2}{27}e^{13} - \frac{71}{27}e^{11} + \frac{109}{3}e^{9} - \frac{6590}{27}e^{7} + \frac{7267}{9}e^{5} - \frac{31628}{27}e^{3} + \frac{1778}{3}e$ |
| 43 | $[43, 43, -3w - 17]$ | $-\frac{1}{9}e^{12} + \frac{22}{9}e^{10} - 16e^{8} + \frac{82}{9}e^{6} + \frac{628}{3}e^{4} - \frac{4202}{9}e^{2} + 255$ |
| 43 | $[43, 43, -3w + 20]$ | $\phantom{-}\frac{47}{18}e^{12} - \frac{787}{9}e^{10} + \frac{2293}{2}e^{8} - \frac{132311}{18}e^{6} + \frac{69986}{3}e^{4} - \frac{292969}{9}e^{2} + 15705$ |
| 59 | $[59, 59, 3w - 17]$ | $-\frac{224}{297}e^{13} + \frac{15049}{594}e^{11} - \frac{3665}{11}e^{9} + \frac{1272715}{594}e^{7} - \frac{1350521}{198}e^{5} + \frac{2835314}{297}e^{3} - \frac{152212}{33}e$ |
| 59 | $[59, 59, 3w + 14]$ | $-\frac{28}{297}e^{13} + \frac{2339}{594}e^{11} - \frac{2033}{33}e^{9} + \frac{270353}{594}e^{7} - \frac{319027}{198}e^{5} + \frac{717274}{297}e^{3} - \frac{40273}{33}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23,23,w - 8]$ | $-1$ |