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: | $[37,37,w - 4]$ |
| Dimension: | $71$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $148$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{71} + 5x^{70} - 162x^{69} - 829x^{68} + 12372x^{67} + 65043x^{66} - 592361x^{65} - 3214483x^{64} + 19944569x^{63} + 112375239x^{62} - 501981651x^{61} - 2958714261x^{60} + 9797305319x^{59} + 60994467792x^{58} - 151728289836x^{57} - 1010583598869x^{56} + 1890441502839x^{55} + 13707291354721x^{54} - 19066641507443x^{53} - 154258862712336x^{52} + 155306943777178x^{51} + 1454677218067583x^{50} - 1005753671542830x^{49} - 11579173298998858x^{48} + 4943313071664593x^{47} + 78214839594698425x^{46} - 15712334799447326x^{45} - 449987121552141636x^{44} + 1921853430777017x^{43} + 2210064196670777511x^{42} + 375146736877101041x^{41} - 9275901182934965903x^{40} - 3028802095376082589x^{39} + 33265497078501126016x^{38} + 15652565586913326747x^{37} - 101799953731511684689x^{36} - 61669213609319346552x^{35} + 265158371362628896470x^{34} + 195223331119432006924x^{33} - 585529075075274663492x^{32} - 507262086096480456084x^{31} + 1090004610051712295896x^{30} + 1091716059604235429603x^{29} - 1697271503983392536628x^{28} - 1951620219279224834972x^{27} + 2186699157763585886270x^{26} + 2894818406819778635067x^{25} - 2294665046155254608418x^{24} - 3548376508726197347076x^{23} + 1914098097406743325149x^{22} + 3570258157522143444195x^{21} - 1215721645201862391202x^{20} - 2920789189738323189590x^{19} + 533491560414500991114x^{18} + 1918198442913263163979x^{17} - 109187228450529770214x^{16} - 994415628666274618557x^{15} - 42380807578923280665x^{14} + 397964977227442915076x^{13} + 47581634516997513702x^{12} - 119334813478268853816x^{11} - 20909222178026483370x^{10} + 25749560607191054694x^{9} + 5354389255574870382x^{8} - 3784231865527136660x^{7} - 800450809601171176x^{6} + 352127530174117213x^{5} + 61076165283126287x^{4} - 18809527798937779x^{3} - 1567100902611872x^{2} + 442447686278679x - 18383180697883\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 7]$ | $...$ |
| 7 | $[7, 7, w + 6]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 19 | $[19, 19, w + 5]$ | $...$ |
| 19 | $[19, 19, w - 6]$ | $...$ |
| 23 | $[23, 23, w + 8]$ | $...$ |
| 23 | $[23, 23, -w + 9]$ | $...$ |
| 25 | $[25, 5, 5]$ | $...$ |
| 29 | $[29, 29, -w - 4]$ | $...$ |
| 29 | $[29, 29, w - 5]$ | $...$ |
| 37 | $[37, 37, -w - 3]$ | $...$ |
| 37 | $[37, 37, w - 4]$ | $\phantom{-}1$ |
| 41 | $[41, 41, -w - 9]$ | $...$ |
| 41 | $[41, 41, w - 10]$ | $...$ |
| 43 | $[43, 43, -w - 2]$ | $...$ |
| 43 | $[43, 43, w - 3]$ | $...$ |
| 47 | $[47, 47, -w - 1]$ | $...$ |
| 47 | $[47, 47, w - 2]$ | $...$ |
| 53 | $[53, 53, 2w - 13]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $37$ | $[37,37,w - 4]$ | $-1$ |