Base field \(\Q(\sqrt{401}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 100\); narrow class number \(5\) and class number \(5\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $64$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $120$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{64} + x^{63} + 23x^{62} + 25x^{61} + 319x^{60} + 330x^{59} + 3440x^{58} + 3331x^{57} + 32006x^{56} + 29254x^{55} + 251610x^{54} + 217234x^{53} + 1709114x^{52} + 1329986x^{51} + 10231845x^{50} + 7098402x^{49} + 54733221x^{48} + 33829623x^{47} + 259300295x^{46} + 139262950x^{45} + 1095954981x^{44} + 482358627x^{43} + 4150562319x^{42} + 1491541449x^{41} + 14142251539x^{40} + 4188136772x^{39} + 43090194429x^{38} + 10234962501x^{37} + 117883608398x^{36} + 21695496952x^{35} + 288863469306x^{34} + 45659298027x^{33} + 630731494832x^{32} + 95017225775x^{31} + 1210710636246x^{30} + 176273382284x^{29} + 2064166446706x^{28} + 312400465129x^{27} + 3100758925069x^{26} + 581425042716x^{25} + 4027455827778x^{24} + 957301309014x^{23} + 4407592637758x^{22} + 1225618175372x^{21} + 4277730155374x^{20} + 1296596670704x^{19} + 3589746778495x^{18} + 1043295040654x^{17} + 2372061827104x^{16} + 563235907080x^{15} + 1080250303796x^{14} + 65463729417x^{13} + 381203506178x^{12} - 78597736911x^{11} + 74563402869x^{10} - 10210624700x^{9} + 12437120173x^{8} + 340346154x^{7} + 558737720x^{6} + 14144664x^{5} + 29445712x^{4} - 3580512x^{3} + 814464x^{2} - 65664x + 20736\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $...$ |
| 5 | $[5, 5, w]$ | $...$ |
| 5 | $[5, 5, w + 4]$ | $...$ |
| 7 | $[7, 7, w + 1]$ | $...$ |
| 7 | $[7, 7, w + 5]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, w + 3]$ | $...$ |
| 11 | $[11, 11, w + 7]$ | $...$ |
| 29 | $[29, 29, w + 6]$ | $...$ |
| 29 | $[29, 29, w + 22]$ | $...$ |
| 41 | $[41, 41, w + 13]$ | $...$ |
| 41 | $[41, 41, w + 27]$ | $...$ |
| 43 | $[43, 43, w + 16]$ | $...$ |
| 43 | $[43, 43, w + 26]$ | $...$ |
| 47 | $[47, 47, w + 2]$ | $...$ |
| 47 | $[47, 47, w + 44]$ | $...$ |
| 73 | $[73, 73, w + 33]$ | $...$ |
| 73 | $[73, 73, w + 39]$ | $...$ |
| 83 | $[83, 83, -4w - 37]$ | $...$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).