Base field 4.4.19429.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} - 28x^{9} - 12x^{8} + 277x^{7} + 232x^{6} - 1078x^{5} - 1280x^{4} + 1127x^{3} + 1586x^{2} - 288x - 512\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{29621}{386912}e^{10} - \frac{2431}{24182}e^{9} - \frac{196851}{96728}e^{8} + \frac{159745}{96728}e^{7} + \frac{7555097}{386912}e^{6} - \frac{277325}{48364}e^{5} - \frac{15047831}{193456}e^{4} - \frac{112248}{12091}e^{3} + \frac{39239891}{386912}e^{2} + \frac{2294389}{193456}e - \frac{485598}{12091}$ |
| 7 | $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ | $-1$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}\frac{13145}{386912}e^{10} + \frac{49}{12091}e^{9} - \frac{75647}{96728}e^{8} - \frac{20371}{96728}e^{7} + \frac{2305613}{386912}e^{6} + \frac{78757}{48364}e^{5} - \frac{3424291}{193456}e^{4} + \frac{10006}{12091}e^{3} + \frac{9533327}{386912}e^{2} - \frac{1245455}{193456}e - \frac{115743}{12091}$ |
| 13 | $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ | $\phantom{-}\frac{13099}{386912}e^{10} - \frac{412}{12091}e^{9} - \frac{93109}{96728}e^{8} + \frac{53087}{96728}e^{7} + \frac{3866503}{386912}e^{6} - \frac{83561}{48364}e^{5} - \frac{8523049}{193456}e^{4} - \frac{56002}{12091}e^{3} + \frac{26950477}{386912}e^{2} + \frac{1489363}{193456}e - \frac{370889}{12091}$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{2431}{48364}e^{10} - \frac{656}{12091}e^{9} - \frac{15538}{12091}e^{8} + \frac{10155}{12091}e^{7} + \frac{568167}{48364}e^{6} - \frac{28684}{12091}e^{5} - \frac{1084683}{24182}e^{4} - \frac{91516}{12091}e^{3} + \frac{2915385}{48364}e^{2} + \frac{243191}{24182}e - \frac{345787}{12091}$ |
| 17 | $[17, 17, -w + 2]$ | $\phantom{-}\frac{739}{3616}e^{10} - \frac{20}{113}e^{9} - \frac{4917}{904}e^{8} + \frac{2215}{904}e^{7} + \frac{186911}{3616}e^{6} - \frac{877}{452}e^{5} - \frac{363057}{1808}e^{4} - \frac{6351}{113}e^{3} + \frac{900565}{3616}e^{2} + \frac{99259}{1808}e - \frac{10215}{113}$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ | $-\frac{7183}{96728}e^{10} + \frac{1188}{12091}e^{9} + \frac{46841}{24182}e^{8} - \frac{41057}{24182}e^{7} - \frac{1742475}{96728}e^{6} + \frac{85270}{12091}e^{5} + \frac{3304213}{48364}e^{4} + \frac{27424}{12091}e^{3} - \frac{7801897}{96728}e^{2} - \frac{277603}{48364}e + \frac{324158}{12091}$ |
| 27 | $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ | $\phantom{-}\frac{11857}{193456}e^{10} - \frac{1536}{12091}e^{9} - \frac{80943}{48364}e^{8} + \frac{101893}{48364}e^{7} + \frac{3256757}{193456}e^{6} - \frac{161751}{24182}e^{5} - \frac{6707739}{96728}e^{4} - \frac{242592}{12091}e^{3} + \frac{14927719}{193456}e^{2} + \frac{2396537}{96728}e - \frac{300646}{12091}$ |
| 31 | $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ | $\phantom{-}\frac{2235}{96728}e^{10} - \frac{1351}{12091}e^{9} - \frac{17921}{24182}e^{8} + \frac{51891}{24182}e^{7} + \frac{870615}{96728}e^{6} - \frac{128744}{12091}e^{5} - \frac{2132113}{48364}e^{4} + \frac{36759}{12091}e^{3} + \frac{5397469}{96728}e^{2} + \frac{141339}{48364}e - \frac{223644}{12091}$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 6w + 1]$ | $-\frac{6105}{96728}e^{10} + \frac{769}{12091}e^{9} + \frac{41811}{24182}e^{8} - \frac{28785}{24182}e^{7} - \frac{1640653}{96728}e^{6} + \frac{73658}{12091}e^{5} + \frac{3346035}{48364}e^{4} - \frac{57644}{12091}e^{3} - \frac{9555815}{96728}e^{2} - \frac{152693}{48364}e + \frac{467262}{12091}$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $\phantom{-}\frac{26125}{386912}e^{10} + \frac{43}{24182}e^{9} - \frac{169771}{96728}e^{8} - \frac{61127}{96728}e^{7} + \frac{6240017}{386912}e^{6} + \frac{493151}{48364}e^{5} - \frac{11772319}{193456}e^{4} - \frac{546367}{12091}e^{3} + \frac{31192187}{386912}e^{2} + \frac{7398669}{193456}e - \frac{410184}{12091}$ |
| 43 | $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ | $\phantom{-}\frac{2993}{48364}e^{10} + \frac{769}{12091}e^{9} - \frac{21413}{12091}e^{8} - \frac{20438}{12091}e^{7} + \frac{854277}{48364}e^{6} + \frac{182477}{12091}e^{5} - \frac{1730599}{24182}e^{4} - \frac{589648}{12091}e^{3} + \frac{5082303}{48364}e^{2} + \frac{800251}{24182}e - \frac{596746}{12091}$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ | $-\frac{6105}{96728}e^{10} + \frac{769}{12091}e^{9} + \frac{41811}{24182}e^{8} - \frac{28785}{24182}e^{7} - \frac{1640653}{96728}e^{6} + \frac{73658}{12091}e^{5} + \frac{3346035}{48364}e^{4} - \frac{57644}{12091}e^{3} - \frac{9459087}{96728}e^{2} - \frac{104329}{48364}e + \frac{418898}{12091}$ |
| 53 | $[53, 53, -w - 3]$ | $\phantom{-}\frac{26601}{386912}e^{10} - \frac{3033}{24182}e^{9} - \frac{165711}{96728}e^{8} + \frac{217517}{96728}e^{7} + \frac{5968413}{386912}e^{6} - \frac{531389}{48364}e^{5} - \frac{11311667}{193456}e^{4} + \frac{100925}{12091}e^{3} + \frac{28370111}{386912}e^{2} + \frac{1607433}{193456}e - \frac{280700}{12091}$ |
| 53 | $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ | $-\frac{62665}{386912}e^{10} + \frac{5645}{24182}e^{9} + \frac{404335}{96728}e^{8} - \frac{373061}{96728}e^{7} - \frac{14932285}{386912}e^{6} + \frac{664853}{48364}e^{5} + \frac{27903939}{193456}e^{4} + \frac{236831}{12091}e^{3} - \frac{59949599}{386912}e^{2} - \frac{5258633}{193456}e + \frac{521560}{12091}$ |
| 59 | $[59, 59, 2w^{2} - 3w - 6]$ | $-\frac{1101}{24182}e^{10} - \frac{2012}{12091}e^{9} + \frac{16780}{12091}e^{8} + \frac{48914}{12091}e^{7} - \frac{337021}{24182}e^{6} - \frac{399098}{12091}e^{5} + \frac{625005}{12091}e^{4} + \frac{1190582}{12091}e^{3} - \frac{1338323}{24182}e^{2} - \frac{788789}{12091}e + \frac{239892}{12091}$ |
| 59 | $[59, 59, w^{3} - w^{2} - 7w - 3]$ | $\phantom{-}\frac{1778}{12091}e^{10} - \frac{1760}{12091}e^{9} - \frac{51714}{12091}e^{8} + \frac{24591}{12091}e^{7} + \frac{541662}{12091}e^{6} + \frac{4436}{12091}e^{5} - \frac{2318242}{12091}e^{4} - \frac{834156}{12091}e^{3} + \frac{3103054}{12091}e^{2} + \frac{842606}{12091}e - \frac{1191364}{12091}$ |
| 79 | $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ | $-\frac{15493}{193456}e^{10} + \frac{2781}{12091}e^{9} + \frac{101139}{48364}e^{8} - \frac{216953}{48364}e^{7} - \frac{3934345}{193456}e^{6} + \frac{619055}{24182}e^{5} + \frac{8209079}{96728}e^{4} - \frac{462311}{12091}e^{3} - \frac{22225059}{193456}e^{2} + \frac{1736803}{96728}e + \frac{541736}{12091}$ |
| 79 | $[79, 79, w^{2} - 2w - 1]$ | $\phantom{-}\frac{1849}{48364}e^{10} - \frac{1056}{12091}e^{9} - \frac{14101}{12091}e^{8} + \frac{19591}{12091}e^{7} + \frac{649493}{48364}e^{6} - \frac{89230}{12091}e^{5} - \frac{1604227}{24182}e^{4} - \frac{21690}{12091}e^{3} + \frac{5457151}{48364}e^{2} + \frac{138157}{24182}e - \frac{709982}{12091}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ | $1$ |