Base field 4.4.13676.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, 2w^{3} + w^{2} - 10w - 2]$ |
| Dimension: | $13$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $31$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{13} + 3x^{12} - 13x^{11} - 43x^{10} + 52x^{9} + 219x^{8} - 43x^{7} - 473x^{6} - 121x^{5} + 398x^{4} + 168x^{3} - 99x^{2} - 36x + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{2} - w + 3]$ | $-\frac{380}{641}e^{12} - \frac{507}{641}e^{11} + \frac{5766}{641}e^{10} + \frac{6563}{641}e^{9} - \frac{30728}{641}e^{8} - \frac{29780}{641}e^{7} + \frac{68410}{641}e^{6} + \frac{56084}{641}e^{5} - \frac{60615}{641}e^{4} - \frac{35483}{641}e^{3} + \frac{18075}{641}e^{2} + \frac{2172}{641}e - \frac{437}{641}$ |
| 5 | $[5, 5, w^{3} - 5w + 1]$ | $\phantom{-}\frac{1565}{641}e^{12} + \frac{2670}{641}e^{11} - \frac{23595}{641}e^{10} - \frac{36349}{641}e^{9} + \frac{125505}{641}e^{8} + \frac{174770}{641}e^{7} - \frac{279329}{641}e^{6} - \frac{352835}{641}e^{5} + \frac{240740}{641}e^{4} + \frac{261826}{641}e^{3} - \frac{61359}{641}e^{2} - \frac{42817}{641}e - \frac{604}{641}$ |
| 11 | $[11, 11, -w^{3} + 6w - 2]$ | $\phantom{-}\frac{2185}{641}e^{12} + \frac{3396}{641}e^{11} - \frac{33475}{641}e^{10} - \frac{45910}{641}e^{9} + \frac{182455}{641}e^{8} + \frac{219951}{641}e^{7} - \frac{425087}{641}e^{6} - \frac{446196}{641}e^{5} + \frac{408630}{641}e^{4} + \frac{337195}{641}e^{3} - \frac{139667}{641}e^{2} - \frac{58000}{641}e + \frac{7160}{641}$ |
| 13 | $[13, 13, -w^{2} + 4]$ | $-\frac{104}{641}e^{12} - \frac{800}{641}e^{11} + \frac{1099}{641}e^{10} + \frac{11897}{641}e^{9} - \frac{3329}{641}e^{8} - \frac{61522}{641}e^{7} + \frac{741}{641}e^{6} + \frac{129589}{641}e^{5} + \frac{10670}{641}e^{4} - \frac{100443}{641}e^{3} - \frac{8278}{641}e^{2} + \frac{18394}{641}e + \frac{906}{641}$ |
| 17 | $[17, 17, 2w^{3} + w^{2} - 10w - 2]$ | $\phantom{-}1$ |
| 37 | $[37, 37, w^{3} + w^{2} - 6w - 3]$ | $\phantom{-}\frac{616}{641}e^{12} + \frac{498}{641}e^{11} - \frac{9320}{641}e^{10} - \frac{5430}{641}e^{9} + \frac{48415}{641}e^{8} + \frac{19295}{641}e^{7} - \frac{99898}{641}e^{6} - \frac{25830}{641}e^{5} + \frac{71608}{641}e^{4} + \frac{5754}{641}e^{3} - \frac{8856}{641}e^{2} + \frac{1155}{641}e - \frac{830}{641}$ |
| 37 | $[37, 37, -w^{3} + 6w - 4]$ | $\phantom{-}\frac{1140}{641}e^{12} + \frac{2162}{641}e^{11} - \frac{17298}{641}e^{10} - \frac{29945}{641}e^{9} + \frac{94107}{641}e^{8} + \frac{146389}{641}e^{7} - \frac{222537}{641}e^{6} - \frac{299657}{641}e^{5} + \frac{226074}{641}e^{4} + \frac{227598}{641}e^{3} - \frac{93326}{641}e^{2} - \frac{40489}{641}e + \frac{5798}{641}$ |
| 41 | $[41, 41, -w^{3} + 5w - 5]$ | $-\frac{5595}{641}e^{12} - \frac{9312}{641}e^{11} + \frac{85251}{641}e^{10} + \frac{127020}{641}e^{9} - \frac{461707}{641}e^{8} - \frac{612992}{641}e^{7} + \frac{1065224}{641}e^{6} + \frac{1245888}{641}e^{5} - \frac{1001269}{641}e^{4} - \frac{934730}{641}e^{3} + \frac{324217}{641}e^{2} + \frac{151442}{641}e - \frac{12684}{641}$ |
| 43 | $[43, 43, w^{3} - 4w + 4]$ | $-\frac{225}{641}e^{12} - \frac{646}{641}e^{11} + \frac{3296}{641}e^{10} + \frac{9461}{641}e^{9} - \frac{17452}{641}e^{8} - \frac{49413}{641}e^{7} + \frac{41265}{641}e^{6} + \frac{110465}{641}e^{5} - \frac{45244}{641}e^{4} - \frac{98208}{641}e^{3} + \frac{23497}{641}e^{2} + \frac{22574}{641}e - \frac{2342}{641}$ |
| 43 | $[43, 43, -2w^{3} + 11w - 2]$ | $-\frac{339}{641}e^{12} - \frac{93}{641}e^{11} + \frac{5154}{641}e^{10} + \frac{597}{641}e^{9} - \frac{25773}{641}e^{8} - \frac{1298}{641}e^{7} + \frac{44481}{641}e^{6} + \frac{7295}{641}e^{5} - \frac{6700}{641}e^{4} - \frac{17895}{641}e^{3} - \frac{27168}{641}e^{2} + \frac{12585}{641}e + \frac{3360}{641}$ |
| 47 | $[47, 47, -2w^{3} - w^{2} + 12w]$ | $-\frac{5595}{641}e^{12} - \frac{8671}{641}e^{11} + \frac{85251}{641}e^{10} + \frac{116764}{641}e^{9} - \frac{459784}{641}e^{8} - \frac{556584}{641}e^{7} + \frac{1047276}{641}e^{6} + \frac{1121534}{641}e^{5} - \frac{953194}{641}e^{4} - \frac{837939}{641}e^{3} + \frac{283193}{641}e^{2} + \frac{143109}{641}e - \frac{11402}{641}$ |
| 47 | $[47, 47, 2w - 1]$ | $\phantom{-}\frac{2824}{641}e^{12} + \frac{4564}{641}e^{11} - \frac{42810}{641}e^{10} - \frac{62113}{641}e^{9} + \frac{229147}{641}e^{8} + \frac{300594}{641}e^{7} - \frac{515614}{641}e^{6} - \frac{619794}{641}e^{5} + \frac{459844}{641}e^{4} + \frac{484752}{641}e^{3} - \frac{132504}{641}e^{2} - \frac{95342}{641}e + \frac{940}{641}$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 6w - 5]$ | $\phantom{-}\frac{2647}{641}e^{12} + \frac{4090}{641}e^{11} - \frac{40465}{641}e^{10} - \frac{54790}{641}e^{9} + \frac{219888}{641}e^{8} + \frac{258620}{641}e^{7} - \frac{509305}{641}e^{6} - \frac{512041}{641}e^{5} + \frac{481566}{641}e^{4} + \frac{370676}{641}e^{3} - \frac{155924}{641}e^{2} - \frac{57294}{641}e + \frac{4294}{641}$ |
| 71 | $[71, 71, w^{3} + w^{2} - 4w - 3]$ | $-\frac{5482}{641}e^{12} - \frac{8640}{641}e^{11} + \frac{84174}{641}e^{10} + \frac{117206}{641}e^{9} - \frac{460808}{641}e^{8} - \frac{563416}{641}e^{7} + \frac{1081806}{641}e^{6} + \frac{1145597}{641}e^{5} - \frac{1049461}{641}e^{4} - \frac{865947}{641}e^{3} + \frac{351862}{641}e^{2} + \frac{145324}{641}e - \frac{8676}{641}$ |
| 71 | $[71, 71, 2w^{3} + 2w^{2} - 9w - 2]$ | $-\frac{3058}{641}e^{12} - \frac{5723}{641}e^{11} + \frac{46084}{641}e^{10} + \frac{79106}{641}e^{9} - \frac{246733}{641}e^{8} - \frac{386777}{641}e^{7} + \frac{561350}{641}e^{6} + \frac{797111}{641}e^{5} - \frac{513718}{641}e^{4} - \frac{621169}{641}e^{3} + \frac{156505}{641}e^{2} + \frac{123588}{641}e - \frac{3068}{641}$ |
| 79 | $[79, 79, w^{3} + w^{2} - 6w - 5]$ | $-\frac{4365}{641}e^{12} - \frac{7148}{641}e^{11} + \frac{66891}{641}e^{10} + \frac{97393}{641}e^{9} - \frac{365619}{641}e^{8} - \frac{469401}{641}e^{7} + \frac{857590}{641}e^{6} + \frac{953966}{641}e^{5} - \frac{834402}{641}e^{4} - \frac{722462}{641}e^{3} + \frac{293797}{641}e^{2} + \frac{127307}{641}e - \frac{16718}{641}$ |
| 81 | $[81, 3, -3]$ | $-\frac{3355}{641}e^{12} - \frac{5345}{641}e^{11} + \frac{51127}{641}e^{10} + \frac{72544}{641}e^{9} - \frac{276154}{641}e^{8} - \frac{349596}{641}e^{7} + \frac{631332}{641}e^{6} + \frac{716139}{641}e^{5} - \frac{577363}{641}e^{4} - \frac{553914}{641}e^{3} + \frac{168650}{641}e^{2} + \frac{103721}{641}e - \frac{3698}{641}$ |
| 83 | $[83, 83, -3w^{3} - w^{2} + 16w + 3]$ | $\phantom{-}\frac{3725}{641}e^{12} + \frac{5923}{641}e^{11} - \frac{56775}{641}e^{10} - \frac{79997}{641}e^{9} + \frac{307018}{641}e^{8} + \frac{381966}{641}e^{7} - \frac{704959}{641}e^{6} - \frac{769094}{641}e^{5} + \frac{656878}{641}e^{4} + \frac{574007}{641}e^{3} - \frac{213728}{641}e^{2} - \frac{99662}{641}e + \frac{12136}{641}$ |
| 97 | $[97, 97, w^{3} + w^{2} - 6w + 1]$ | $-\frac{3861}{641}e^{12} - \frac{5342}{641}e^{11} + \frac{59149}{641}e^{10} + \frac{70457}{641}e^{9} - \frac{320296}{641}e^{8} - \frac{328153}{641}e^{7} + \frac{732209}{641}e^{6} + \frac{645373}{641}e^{5} - \frac{674186}{641}e^{4} - \frac{463452}{641}e^{3} + \frac{206601}{641}e^{2} + \frac{73126}{641}e - \frac{6908}{641}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, 2w^{3} + w^{2} - 10w - 2]$ | $-1$ |