Base field \(\Q(\sqrt{197}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 49\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 3, 3]$ |
| Dimension: | $6$ |
| 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:
| \(x^{6} + 3x^{5} - 28x^{4} - 72x^{3} + 226x^{2} + 383x - 577\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $-\frac{3}{49}e^{5} + \frac{4}{49}e^{4} + \frac{83}{49}e^{3} - \frac{111}{49}e^{2} - \frac{540}{49}e + \frac{701}{49}$ |
| 7 | $[7, 7, w - 7]$ | $-\frac{1}{49}e^{5} - \frac{1}{49}e^{4} + \frac{30}{49}e^{3} + \frac{12}{49}e^{2} - \frac{250}{49}e + \frac{19}{49}$ |
| 7 | $[7, 7, w + 6]$ | $\phantom{-}e$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}1$ |
| 19 | $[19, 19, w + 5]$ | $-\frac{1}{112}e^{5} + \frac{1}{28}e^{4} + \frac{2}{7}e^{3} - \frac{9}{14}e^{2} - \frac{85}{56}e + \frac{535}{112}$ |
| 19 | $[19, 19, w - 6]$ | $-\frac{57}{784}e^{5} + \frac{5}{196}e^{4} + \frac{99}{49}e^{3} - \frac{135}{98}e^{2} - \frac{5333}{392}e + \frac{12479}{784}$ |
| 23 | $[23, 23, w + 8]$ | $-\frac{73}{1568}e^{5} - \frac{27}{392}e^{4} + \frac{87}{98}e^{3} + \frac{183}{196}e^{2} - \frac{2349}{784}e - \frac{3009}{1568}$ |
| 23 | $[23, 23, -w + 9]$ | $\phantom{-}\frac{361}{1568}e^{5} - \frac{13}{392}e^{4} - \frac{599}{98}e^{3} + \frac{561}{196}e^{2} + \frac{29277}{784}e - \frac{56223}{1568}$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}\frac{1}{49}e^{5} - \frac{6}{49}e^{4} - \frac{23}{49}e^{3} + \frac{135}{49}e^{2} + \frac{138}{49}e - \frac{663}{49}$ |
| 29 | $[29, 29, -w - 4]$ | $-\frac{47}{1568}e^{5} + \frac{11}{392}e^{4} + \frac{61}{98}e^{3} - \frac{199}{196}e^{2} - \frac{1227}{784}e + \frac{8873}{1568}$ |
| 29 | $[29, 29, w - 5]$ | $\phantom{-}\frac{111}{1568}e^{5} + \frac{5}{392}e^{4} - \frac{181}{98}e^{3} + \frac{103}{196}e^{2} + \frac{7659}{784}e - \frac{19497}{1568}$ |
| 37 | $[37, 37, -w - 3]$ | $\phantom{-}\frac{33}{784}e^{5} - \frac{25}{196}e^{4} - \frac{75}{49}e^{3} + \frac{367}{98}e^{2} + \frac{5021}{392}e - \frac{19527}{784}$ |
| 37 | $[37, 37, w - 4]$ | $\phantom{-}\frac{143}{784}e^{5} - \frac{15}{196}e^{4} - \frac{234}{49}e^{3} + \frac{251}{98}e^{2} + \frac{11155}{392}e - \frac{17865}{784}$ |
| 41 | $[41, 41, -w - 9]$ | $-\frac{361}{1568}e^{5} + \frac{13}{392}e^{4} + \frac{599}{98}e^{3} - \frac{561}{196}e^{2} - \frac{29277}{784}e + \frac{49951}{1568}$ |
| 41 | $[41, 41, w - 10]$ | $\phantom{-}\frac{73}{1568}e^{5} + \frac{27}{392}e^{4} - \frac{87}{98}e^{3} - \frac{183}{196}e^{2} + \frac{2349}{784}e - \frac{3263}{1568}$ |
| 43 | $[43, 43, -w - 2]$ | $-\frac{15}{98}e^{5} + \frac{3}{49}e^{4} + \frac{190}{49}e^{3} - \frac{155}{49}e^{2} - \frac{1070}{49}e + \frac{3001}{98}$ |
| 43 | $[43, 43, w - 3]$ | $\phantom{-}\frac{13}{98}e^{5} + \frac{3}{49}e^{4} - \frac{167}{49}e^{3} + \frac{20}{49}e^{2} + \frac{932}{49}e - \frac{1675}{98}$ |
| 47 | $[47, 47, -w - 1]$ | $\phantom{-}\frac{3}{1568}e^{5} - \frac{15}{392}e^{4} - \frac{17}{98}e^{3} + \frac{363}{196}e^{2} + \frac{2223}{784}e - \frac{28981}{1568}$ |
| 47 | $[47, 47, w - 2]$ | $-\frac{67}{1568}e^{5} - \frac{1}{392}e^{4} + \frac{137}{98}e^{3} - \frac{267}{196}e^{2} - \frac{8655}{784}e + \frac{20789}{1568}$ |
| 53 | $[53, 53, 2w - 13]$ | $\phantom{-}\frac{57}{784}e^{5} + \frac{23}{196}e^{4} - \frac{106}{49}e^{3} - \frac{159}{98}e^{2} + \frac{5837}{392}e - \frac{4527}{784}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, 3]$ | $-1$ |