Base field 6.6.1683101.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 4x^{4} + 13x^{3} + 7x^{2} - 14x - 7\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[49, 7, -w^{5} + 4w^{4} - w^{3} - 11w^{2} + 7w + 7]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $49$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} - 4x^{8} - 30x^{7} + 123x^{6} + 256x^{5} - 1126x^{4} - 564x^{3} + 3273x^{2} - 756x - 522\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w]$ | $\phantom{-}0$ |
| 7 | $[7, 7, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + 5]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w^{2} - 3]$ | $\phantom{-}\frac{123638}{23686329}e^{8} + \frac{118432}{23686329}e^{7} - \frac{1872743}{7895443}e^{6} - \frac{358469}{7895443}e^{5} + \frac{77503487}{23686329}e^{4} - \frac{33317261}{23686329}e^{3} - \frac{101198025}{7895443}e^{2} + \frac{86057887}{7895443}e + \frac{9189056}{7895443}$ |
| 13 | $[13, 13, -w^{2} + 2w + 2]$ | $-\frac{173546}{23686329}e^{8} + \frac{644903}{23686329}e^{7} + \frac{1312302}{7895443}e^{6} - \frac{4980178}{7895443}e^{5} - \frac{16128926}{23686329}e^{4} + \frac{68537498}{23686329}e^{3} - \frac{650858}{7895443}e^{2} + \frac{6915730}{7895443}e - \frac{31321117}{7895443}$ |
| 29 | $[29, 29, w^{4} - 2w^{3} - 4w^{2} + 4w + 6]$ | $\phantom{-}\frac{372832}{23686329}e^{8} - \frac{1216489}{23686329}e^{7} - \frac{3328420}{7895443}e^{6} + \frac{10086373}{7895443}e^{5} + \frac{69481711}{23686329}e^{4} - \frac{171157876}{23686329}e^{3} - \frac{50238182}{7895443}e^{2} + \frac{50697655}{7895443}e + \frac{59008210}{7895443}$ |
| 29 | $[29, 29, -w^{4} + 2w^{3} + 4w^{2} - 6w - 5]$ | $-\frac{19136}{23686329}e^{8} + \frac{615410}{23686329}e^{7} - \frac{130725}{7895443}e^{6} - \frac{5724173}{7895443}e^{5} + \frac{17210902}{23686329}e^{4} + \frac{130371701}{23686329}e^{3} - \frac{31115517}{7895443}e^{2} - \frac{94149539}{7895443}e + \frac{32146078}{7895443}$ |
| 41 | $[41, 41, -w^{2} + 4]$ | $-\frac{83495}{7895443}e^{8} + \frac{291299}{7895443}e^{7} + \frac{1861517}{7895443}e^{6} - \frac{6835025}{7895443}e^{5} - \frac{5733111}{7895443}e^{4} + \frac{32560094}{7895443}e^{3} - \frac{29898766}{7895443}e^{2} - \frac{12041961}{7895443}e + \frac{44897392}{7895443}$ |
| 41 | $[41, 41, -w^{2} + 2w + 3]$ | $-\frac{71644}{7895443}e^{8} + \frac{175060}{7895443}e^{7} + \frac{2207129}{7895443}e^{6} - \frac{4755201}{7895443}e^{5} - \frac{21116118}{7895443}e^{4} + \frac{35051378}{7895443}e^{3} + \frac{76096180}{7895443}e^{2} - \frac{81938982}{7895443}e - \frac{40872740}{7895443}$ |
| 43 | $[43, 43, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ | $\phantom{-}\frac{317611}{23686329}e^{8} - \frac{680857}{23686329}e^{7} - \frac{3460160}{7895443}e^{6} + \frac{6736065}{7895443}e^{5} + \frac{101642620}{23686329}e^{4} - \frac{168379798}{23686329}e^{3} - \frac{98388170}{7895443}e^{2} + \frac{125948573}{7895443}e + \frac{497422}{7895443}$ |
| 43 | $[43, 43, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ | $-\frac{368810}{23686329}e^{8} + \frac{983168}{23686329}e^{7} + \frac{3305559}{7895443}e^{6} - \frac{8464895}{7895443}e^{5} - \frac{65489168}{23686329}e^{4} + \frac{163439702}{23686329}e^{3} + \frac{25495807}{7895443}e^{2} - \frac{88272592}{7895443}e + \frac{32609848}{7895443}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{424031}{23686329}e^{8} - \frac{1518800}{23686329}e^{7} - \frac{3173819}{7895443}e^{6} + \frac{11815203}{7895443}e^{5} + \frac{33328259}{23686329}e^{4} - \frac{166217780}{23686329}e^{3} + \frac{30549624}{7895443}e^{2} + \frac{5126231}{7895443}e + \frac{2214611}{7895443}$ |
| 71 | $[71, 71, w^{5} - 3w^{4} - w^{3} + 6w^{2} - 2w + 2]$ | $-\frac{91294}{23686329}e^{8} + \frac{643612}{23686329}e^{7} + \frac{334386}{7895443}e^{6} - \frac{5113670}{7895443}e^{5} + \frac{14155133}{23686329}e^{4} + \frac{71836873}{23686329}e^{3} - \frac{25101845}{7895443}e^{2} + \frac{4118905}{7895443}e - \frac{15892798}{7895443}$ |
| 71 | $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} - w + 5]$ | $\phantom{-}\frac{13835}{23686329}e^{8} - \frac{655355}{23686329}e^{7} + \frac{1026567}{7895443}e^{6} + \frac{3575285}{7895443}e^{5} - \frac{79380337}{23686329}e^{4} + \frac{33838558}{23686329}e^{3} + \frac{132792469}{7895443}e^{2} - \frac{164105630}{7895443}e + \frac{1586507}{7895443}$ |
| 71 | $[71, 71, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ | $-\frac{171640}{23686329}e^{8} - \frac{1114640}{23686329}e^{7} + \frac{3134970}{7895443}e^{6} + \frac{10318829}{7895443}e^{5} - \frac{146201893}{23686329}e^{4} - \frac{223007342}{23686329}e^{3} + \frac{212622421}{7895443}e^{2} + \frac{126822067}{7895443}e - \frac{69991387}{7895443}$ |
| 71 | $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 19w^{2} - w - 12]$ | $\phantom{-}\frac{135274}{23686329}e^{8} + \frac{585917}{23686329}e^{7} - \frac{1573752}{7895443}e^{6} - \frac{6468168}{7895443}e^{5} + \frac{50550730}{23686329}e^{4} + \frac{192205904}{23686329}e^{3} - \frac{53684733}{7895443}e^{2} - \frac{195214808}{7895443}e + \frac{16658843}{7895443}$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 5w^{2} - w - 6]$ | $\phantom{-}\frac{37376}{23686329}e^{8} + \frac{540802}{23686329}e^{7} - \frac{404825}{7895443}e^{6} - \frac{5983682}{7895443}e^{5} + \frac{10271102}{23686329}e^{4} + \frac{167753956}{23686329}e^{3} - \frac{4026606}{7895443}e^{2} - \frac{129893707}{7895443}e + \frac{3835763}{7895443}$ |
| 83 | $[83, 83, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 4w - 1]$ | $-\frac{214400}{23686329}e^{8} + \frac{953675}{23686329}e^{7} + \frac{1862532}{7895443}e^{6} - \frac{9208890}{7895443}e^{5} - \frac{32149340}{23686329}e^{4} + \frac{225273905}{23686329}e^{3} - \frac{4968852}{7895443}e^{2} - \frac{189337861}{7895443}e + \frac{64495271}{7895443}$ |
| 97 | $[97, 97, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 5w + 4]$ | $\phantom{-}\frac{101165}{7895443}e^{8} - \frac{158149}{7895443}e^{7} - \frac{2924494}{7895443}e^{6} + \frac{4637576}{7895443}e^{5} + \frac{23473929}{7895443}e^{4} - \frac{43037500}{7895443}e^{3} - \frac{55208480}{7895443}e^{2} + \frac{154901764}{7895443}e + \frac{59921566}{7895443}$ |
| 97 | $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + 2w - 2]$ | $-\frac{197087}{23686329}e^{8} - \frac{551254}{23686329}e^{7} + \frac{2743694}{7895443}e^{6} + \frac{4578789}{7895443}e^{5} - \frac{105780365}{23686329}e^{4} - \frac{65377900}{23686329}e^{3} + \frac{128272774}{7895443}e^{2} - \frac{19400750}{7895443}e + \frac{5906842}{7895443}$ |
| 113 | $[113, 113, -2w^{4} + 3w^{3} + 8w^{2} - 6w - 6]$ | $-\frac{71543}{23686329}e^{8} - \frac{2192365}{23686329}e^{7} + \frac{2693619}{7895443}e^{6} + \frac{19519327}{7895443}e^{5} - \frac{158349845}{23686329}e^{4} - \frac{390240001}{23686329}e^{3} + \frac{240348028}{7895443}e^{2} + \frac{186563474}{7895443}e - \frac{23574372}{7895443}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w]$ | $1$ |