Base field \(\Q(\sqrt{357}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 89\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7, 7, w + 3]$ |
| Dimension: | $32$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $132$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{32} + 294x^{30} + 36129x^{28} + 2426572x^{26} + 97964688x^{24} + 2472946060x^{22} + 39660982534x^{20} + 406786378860x^{18} + 2661690956846x^{16} + 10978526899492x^{14} + 28015137621584x^{12} + 43436196420092x^{10} + 40842839881185x^{8} + 23029110624414x^{6} + 7468016201209x^{4} + 1257604575800x^{2} + 83926090000\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $...$ |
| 4 | $[4, 2, 2]$ | $...$ |
| 7 | $[7, 7, w + 3]$ | $...$ |
| 11 | $[11, 11, w + 3]$ | $...$ |
| 11 | $[11, 11, w + 7]$ | $...$ |
| 17 | $[17, 17, w + 8]$ | $\phantom{-}0$ |
| 23 | $[23, 23, w + 4]$ | $...$ |
| 23 | $[23, 23, w + 18]$ | $...$ |
| 25 | $[25, 5, 5]$ | $...$ |
| 29 | $[29, 29, w + 1]$ | $...$ |
| 29 | $[29, 29, w + 27]$ | $...$ |
| 31 | $[31, 31, w + 13]$ | $...$ |
| 31 | $[31, 31, w + 17]$ | $...$ |
| 43 | $[43, 43, -w - 11]$ | $...$ |
| 43 | $[43, 43, w - 12]$ | $...$ |
| 47 | $[47, 47, -w - 6]$ | $...$ |
| 47 | $[47, 47, w - 7]$ | $...$ |
| 59 | $[59, 59, -w - 5]$ | $...$ |
| 59 | $[59, 59, w - 6]$ | $...$ |
| 61 | $[61, 61, w + 16]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w + 3]$ | $\frac{35941963959315113566438318884089034390509495071}{104058010691351198565938959996268806716878162944384512000}e^{31} + \frac{10537365104842578044440806891995719316201045194349}{104058010691351198565938959996268806716878162944384512000}e^{29} + \frac{17914955960008246976552158086906896810269725709447}{1445250148490988868971374444392622315512196707560896000}e^{27} + \frac{21538586087285650303120622416485571958147636482412003}{26014502672837799641484739999067201679219540736096128000}e^{25} + \frac{862535195285897819566761882613212358371410397601012387}{26014502672837799641484739999067201679219540736096128000}e^{23} + \frac{1075534206553328002429457431198950763880885183778841157}{1300725133641889982074236999953360083960977036804806400}e^{21} + \frac{677327874855555787337604901665617533119098251898143153957}{52029005345675599282969479998134403358439081472192256000}e^{19} + \frac{150055995141866157217638886475360667159252768372095200119}{1156200118792791095177099555514097852409757366048716800}e^{17} + \frac{1761208014757316400703770217169082938908073563923076668767}{2167875222736483303457061666588933473268295061341344000}e^{15} + \frac{81217594843616414038827531596895887268441646920475560795883}{26014502672837799641484739999067201679219540736096128000}e^{13} + \frac{184658708887696675686440089851290028630256424463400044259291}{26014502672837799641484739999067201679219540736096128000}e^{11} + \frac{1236797595017675572041823572718997892963128390908237126399}{135492201421030206466066354161808342079268441333834000}e^{9} + \frac{135802410789098847587837445104639643592134354907719955081267}{20811602138270239713187791999253761343375632588876902400}e^{7} + \frac{260787093397130287414530983617163991425994339755550687437269}{104058010691351198565938959996268806716878162944384512000}e^{5} + \frac{6099833137795843947604265575824855881283303895433048479733}{13007251336418899820742369999533600839609770368048064000}e^{3} + \frac{895711997422720445679693113330547386401429149564047237}{28905002969819777379427488887852446310243934151217920}e$ |