Base field 3.3.1492.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, w^{2} - 2w - 8]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} - 64x^{14} + 1674x^{12} - 23264x^{10} + 187400x^{8} - 895688x^{6} + 2481888x^{4} - 3644800x^{2} + 2166784\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}\frac{2468813}{3126308992}e^{14} - \frac{18544069}{390788624}e^{12} + \frac{1776729913}{1563154496}e^{10} - \frac{2723370391}{195394312}e^{8} + \frac{36617989801}{390788624}e^{6} - \frac{134125437461}{390788624}e^{4} + \frac{61699591449}{97697156}e^{2} - \frac{10937189444}{24424289}$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{2} - 2w - 8]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -2w^{2} + 3w + 16]$ | $\phantom{-}\frac{121815755}{287620427264}e^{15} - \frac{462266045}{17976276704}e^{13} + \frac{89780389751}{143810213632}e^{11} - \frac{35002439513}{4494069176}e^{9} + \frac{1922839291979}{35952553408}e^{7} - \frac{7210970909923}{35952553408}e^{5} + \frac{3391395973953}{8988138352}e^{3} - \frac{612231816793}{2247034588}e$ |
| 7 | $[7, 7, -w^{2} + 2w + 6]$ | $\phantom{-}\frac{71197597}{143810213632}e^{15} - \frac{539958317}{17976276704}e^{13} + \frac{52383433553}{71905106816}e^{11} - \frac{81600709907}{8988138352}e^{9} + \frac{1119754427453}{17976276704}e^{7} - \frac{4199339681885}{17976276704}e^{5} + \frac{1975211456013}{4494069176}e^{3} - \frac{355861204525}{1123517294}e$ |
| 11 | $[11, 11, w^{2} - 2w - 2]$ | $\phantom{-}\frac{14237051}{12505235968}e^{15} - \frac{53387733}{781577248}e^{13} + \frac{10210654887}{6252617984}e^{11} - \frac{3903971665}{195394312}e^{9} + \frac{209471076123}{1563154496}e^{7} - \frac{765265583955}{1563154496}e^{5} + \frac{350336518977}{390788624}e^{3} - \frac{61362749713}{97697156}e$ |
| 19 | $[19, 19, -w + 2]$ | $-\frac{105537359}{287620427264}e^{15} + \frac{386950811}{17976276704}e^{13} - \frac{71788902891}{143810213632}e^{11} + \frac{6587039499}{1123517294}e^{9} - \frac{1340728423199}{35952553408}e^{7} + \frac{4604598773031}{35952553408}e^{5} - \frac{1999695401141}{8988138352}e^{3} + \frac{351846455881}{2247034588}e$ |
| 23 | $[23, 23, -w^{2} + 3w + 1]$ | $\phantom{-}\frac{18347}{48848578}e^{14} - \frac{2051197}{97697156}e^{12} + \frac{22116385}{48848578}e^{10} - \frac{231610591}{48848578}e^{8} + \frac{1215908615}{48848578}e^{6} - \frac{1467057244}{24424289}e^{4} + \frac{1115942476}{24424289}e^{2} + \frac{427799382}{24424289}$ |
| 25 | $[25, 5, w^{2} - w - 9]$ | $-\frac{20213789}{287620427264}e^{15} + \frac{90948361}{17976276704}e^{13} - \frac{21166246513}{143810213632}e^{11} + \frac{2491720305}{1123517294}e^{9} - \frac{663094341165}{35952553408}e^{7} + \frac{2997099366181}{35952553408}e^{5} - \frac{1676919037951}{8988138352}e^{3} + \frac{351332224815}{2247034588}e$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}\frac{684491}{1563154496}e^{14} - \frac{5479209}{195394312}e^{12} + \frac{565438839}{781577248}e^{10} - \frac{942191931}{97697156}e^{8} + \frac{13823512723}{195394312}e^{6} - \frac{54796568419}{195394312}e^{4} + \frac{26585848031}{48848578}e^{2} - \frac{9517102822}{24424289}$ |
| 29 | $[29, 29, -w^{2} - w + 1]$ | $\phantom{-}\frac{120407381}{143810213632}e^{15} - \frac{453656579}{8988138352}e^{13} + \frac{87380707225}{71905106816}e^{11} - \frac{8442285077}{561758647}e^{9} + \frac{1841298050925}{17976276704}e^{7} - \frac{6885988291197}{17976276704}e^{5} + \frac{3254338864359}{4494069176}e^{3} - \frac{593549509419}{1123517294}e$ |
| 29 | $[29, 29, w^{2} - 2w - 4]$ | $-\frac{362630517}{287620427264}e^{15} + \frac{1369579203}{17976276704}e^{13} - \frac{264541804201}{143810213632}e^{11} + \frac{102540720129}{4494069176}e^{9} - \frac{5605435393829}{35952553408}e^{7} + \frac{20982947492317}{35952553408}e^{5} - \frac{9900073702671}{8988138352}e^{3} + \frac{1799330835631}{2247034588}e$ |
| 29 | $[29, 29, -w^{2} + w + 11]$ | $-\frac{2468813}{1563154496}e^{14} + \frac{18544069}{195394312}e^{12} - \frac{1776729913}{781577248}e^{10} + \frac{2723370391}{97697156}e^{8} - \frac{36617989801}{195394312}e^{6} + \frac{134125437461}{195394312}e^{4} - \frac{61699591449}{48848578}e^{2} + \frac{21923227466}{24424289}$ |
| 43 | $[43, 43, 2w^{2} - 3w - 18]$ | $-\frac{18347}{48848578}e^{14} + \frac{2051197}{97697156}e^{12} - \frac{22116385}{48848578}e^{10} + \frac{231610591}{48848578}e^{8} - \frac{1215908615}{48848578}e^{6} + \frac{1467057244}{24424289}e^{4} - \frac{1115942476}{24424289}e^{2} - \frac{427799382}{24424289}$ |
| 47 | $[47, 47, -2w + 7]$ | $-\frac{3935393}{287620427264}e^{15} + \frac{15633127}{17976276704}e^{13} - \frac{3174759653}{143810213632}e^{11} + \frac{1312599703}{4494069176}e^{9} - \frac{80983472385}{35952553408}e^{7} + \frac{390727229289}{35952553408}e^{5} - \frac{285218465139}{8988138352}e^{3} + \frac{88699829315}{2247034588}e$ |
| 53 | $[53, 53, w^{2} - w - 3]$ | $\phantom{-}\frac{453568971}{287620427264}e^{15} - \frac{846280471}{8988138352}e^{13} + \frac{321620442647}{143810213632}e^{11} - \frac{243874843463}{8988138352}e^{9} + \frac{6475232736955}{35952553408}e^{7} - \frac{23393415657843}{35952553408}e^{5} + \frac{10616462275685}{8988138352}e^{3} - \frac{1864927326125}{2247034588}e$ |
| 61 | $[61, 61, w^{2} + 2w + 2]$ | $\phantom{-}\frac{4652129}{1563154496}e^{14} - \frac{34760831}{195394312}e^{12} + \frac{3308055581}{781577248}e^{10} - \frac{5028619831}{97697156}e^{8} + \frac{66973120581}{195394312}e^{6} - \frac{242812022305}{195394312}e^{4} + \frac{110367895885}{48848578}e^{2} - \frac{38523366678}{24424289}$ |
| 67 | $[67, 67, -2w^{2} + 5w + 8]$ | $\phantom{-}\frac{1591199}{143810213632}e^{15} - \frac{3962843}{17976276704}e^{13} - \frac{690202053}{71905106816}e^{11} + \frac{3404734739}{8988138352}e^{9} - \frac{91671148065}{17976276704}e^{7} + \frac{579712837441}{17976276704}e^{5} - \frac{421888940345}{4494069176}e^{3} + \frac{104991474317}{1123517294}e$ |
| 79 | $[79, 79, w^{2} - 3w - 9]$ | $-\frac{118513}{97697156}e^{14} + \frac{13944677}{195394312}e^{12} - \frac{162452007}{97697156}e^{10} + \frac{1924430561}{97697156}e^{8} - \frac{3110973658}{24424289}e^{6} + \frac{11002698991}{24424289}e^{4} - \frac{19869778138}{24424289}e^{2} + \frac{14167421644}{24424289}$ |
| 97 | $[97, 97, -w^{2} - 2w + 2]$ | $-\frac{213940265}{143810213632}e^{15} + \frac{49854223}{561758647}e^{13} - \frac{151148570077}{71905106816}e^{11} + \frac{113838723609}{4494069176}e^{9} - \frac{2979465222673}{17976276704}e^{7} + \frac{10470392257633}{17976276704}e^{5} - \frac{4530112694775}{4494069176}e^{3} + \frac{736406736247}{1123517294}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w^{2} - 2w - 8]$ | $-1$ |