Base field 3.3.761.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[23, 23, -w + 4]$ |
| Dimension: | $18$ |
| 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:
| \(x^{18} - 44x^{16} + 791x^{14} - 7461x^{12} + 39425x^{10} - 115322x^{8} + 173000x^{6} - 116288x^{4} + 34960x^{2} - 3872\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 1]$ | $\phantom{-}\frac{2371}{10016}e^{16} - \frac{51701}{5008}e^{14} + \frac{1835185}{10016}e^{12} - \frac{16974321}{10016}e^{10} + \frac{86851437}{10016}e^{8} - \frac{7484880}{313}e^{6} + \frac{19790787}{626}e^{4} - \frac{9503825}{626}e^{2} + \frac{1468311}{626}$ |
| 8 | $[8, 2, 2]$ | $-\frac{2815}{5008}e^{16} + \frac{122813}{5008}e^{14} - \frac{2181025}{5008}e^{12} + \frac{10096347}{2504}e^{10} - \frac{6467786}{313}e^{8} + \frac{286215695}{5008}e^{6} - \frac{190370381}{2504}e^{4} + \frac{46500655}{1252}e^{2} - \frac{3671079}{626}$ |
| 9 | $[9, 3, -w^{2} + 2w + 4]$ | $-\frac{61761}{220352}e^{17} + \frac{122487}{10016}e^{15} - \frac{47860971}{220352}e^{13} + \frac{443207071}{220352}e^{11} - \frac{2272267499}{220352}e^{9} + \frac{1572412855}{55088}e^{7} - \frac{1047800835}{27544}e^{5} + \frac{64314660}{3443}e^{3} - \frac{40827979}{13772}e$ |
| 11 | $[11, 11, -w^{2} + 2w + 2]$ | $\phantom{-}\frac{55205}{55088}e^{17} - \frac{437923}{10016}e^{15} + \frac{42775781}{55088}e^{13} - \frac{792127653}{110176}e^{11} + \frac{4060123983}{110176}e^{9} - \frac{11232865297}{110176}e^{7} + \frac{7476885987}{55088}e^{5} - \frac{1830332611}{27544}e^{3} + \frac{144948307}{13772}e$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $-\frac{4777}{110176}e^{17} + \frac{18913}{10016}e^{15} - \frac{3685459}{110176}e^{13} + \frac{16998189}{55088}e^{11} - \frac{43303269}{27544}e^{9} + \frac{474113381}{110176}e^{7} - \frac{308367201}{55088}e^{5} + \frac{70595863}{27544}e^{3} - \frac{5051143}{13772}e$ |
| 19 | $[19, 19, w + 3]$ | $-\frac{17017}{20032}e^{16} + \frac{371219}{10016}e^{14} - \frac{13185115}{20032}e^{12} + \frac{122073611}{20032}e^{10} - \frac{625616327}{20032}e^{8} + \frac{108149519}{1252}e^{6} - \frac{287782913}{2504}e^{4} + \frac{70340639}{1252}e^{2} - \frac{11116039}{1252}$ |
| 19 | $[19, 19, -w^{2} + 2w + 5]$ | $-\frac{8951}{27544}e^{17} + \frac{17735}{1252}e^{15} - \frac{6919883}{27544}e^{13} + \frac{63935621}{27544}e^{11} - \frac{326546283}{27544}e^{9} + \frac{448749799}{13772}e^{7} - \frac{588817175}{13772}e^{5} + \frac{138334969}{6886}e^{3} - \frac{10371341}{3443}e$ |
| 19 | $[19, 19, -w^{2} + 3w + 2]$ | $-\frac{411681}{220352}e^{17} + \frac{816431}{10016}e^{15} - \frac{318987179}{220352}e^{13} + \frac{2953411919}{220352}e^{11} - \frac{15136747643}{220352}e^{9} + \frac{10467582155}{55088}e^{7} - \frac{6964465623}{27544}e^{5} + \frac{851327765}{6886}e^{3} - \frac{269139539}{13772}e$ |
| 23 | $[23, 23, w^{2} - w - 3]$ | $\phantom{-}\frac{48649}{110176}e^{17} - \frac{192949}{10016}e^{15} + \frac{37690591}{110176}e^{13} - \frac{174460291}{55088}e^{11} + \frac{446964121}{27544}e^{9} - \frac{4943213877}{110176}e^{7} + \frac{3285682647}{55088}e^{5} - \frac{801298051}{27544}e^{3} + \frac{63264805}{13772}e$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $\phantom{-}\frac{81207}{220352}e^{17} - \frac{160965}{10016}e^{15} + \frac{62845965}{220352}e^{13} - \frac{581256977}{220352}e^{11} + \frac{2973906149}{220352}e^{9} - \frac{2050073171}{55088}e^{7} + \frac{1354640557}{27544}e^{5} - \frac{81214550}{3443}e^{3} + \frac{50148221}{13772}e$ |
| 23 | $[23, 23, -w + 4]$ | $\phantom{-}1$ |
| 31 | $[31, 31, w^{2} - 5]$ | $-\frac{19715}{20032}e^{16} + \frac{430179}{10016}e^{14} - \frac{15284185}{20032}e^{12} + \frac{141572341}{20032}e^{10} - \frac{726061185}{20032}e^{8} + \frac{502677709}{5008}e^{6} - \frac{41908178}{313}e^{4} + \frac{20625972}{313}e^{2} - \frac{13141207}{1252}$ |
| 43 | $[43, 43, w^{2} - 3w - 3]$ | $\phantom{-}\frac{688207}{220352}e^{17} - \frac{1365035}{10016}e^{15} + \frac{533445349}{220352}e^{13} - \frac{4940573845}{220352}e^{11} + \frac{25334018097}{220352}e^{9} - \frac{4383761361}{13772}e^{7} + \frac{2922217047}{6886}e^{5} - \frac{2872421323}{13772}e^{3} + \frac{456866299}{13772}e$ |
| 49 | $[49, 7, w^{2} - 6]$ | $\phantom{-}\frac{38941}{20032}e^{16} - \frac{849543}{10016}e^{14} + \frac{30177911}{20032}e^{12} - \frac{279453831}{20032}e^{10} + \frac{1432649411}{20032}e^{8} - \frac{247812369}{1252}e^{6} + \frac{660276579}{2504}e^{4} - \frac{161932127}{1252}e^{2} + \frac{25694983}{1252}$ |
| 53 | $[53, 53, 2w - 5]$ | $\phantom{-}\frac{8773}{10016}e^{16} - \frac{191371}{5008}e^{14} + \frac{6796767}{10016}e^{12} - \frac{62921671}{10016}e^{10} + \frac{322421795}{10016}e^{8} - \frac{111444799}{1252}e^{6} + \frac{148189235}{1252}e^{4} - \frac{36155861}{626}e^{2} + \frac{5705115}{626}$ |
| 61 | $[61, 61, 2w^{2} - 2w - 9]$ | $-\frac{289073}{220352}e^{17} + \frac{573309}{10016}e^{15} - \frac{224012411}{220352}e^{13} + \frac{2074274555}{220352}e^{11} - \frac{10632786399}{220352}e^{9} + \frac{459706581}{3443}e^{7} - \frac{1224359597}{6886}e^{5} + \frac{1200041281}{13772}e^{3} - \frac{190381505}{13772}e$ |
| 71 | $[71, 71, 2w - 3]$ | $-\frac{42235}{20032}e^{16} + \frac{921431}{10016}e^{14} - \frac{32732385}{20032}e^{12} + \frac{303113893}{20032}e^{10} - \frac{1553937793}{20032}e^{8} + \frac{1075109099}{5008}e^{6} - \frac{358003093}{1252}e^{4} + \frac{87753851}{626}e^{2} - \frac{27838043}{1252}$ |
| 73 | $[73, 73, 2w^{2} - 5w - 5]$ | $\phantom{-}\frac{307267}{220352}e^{17} - \frac{609283}{10016}e^{15} + \frac{238007073}{220352}e^{13} - \frac{2202983289}{220352}e^{11} + \frac{11285064949}{220352}e^{9} - \frac{3898434913}{27544}e^{7} + \frac{2588615577}{13772}e^{5} - \frac{1258734113}{13772}e^{3} + \frac{197558323}{13772}e$ |
| 83 | $[83, 83, w^{2} - w - 9]$ | $\phantom{-}\frac{9499}{5008}e^{16} - \frac{103613}{1252}e^{14} + \frac{7360621}{5008}e^{12} - \frac{68149407}{5008}e^{10} + \frac{349253899}{5008}e^{8} - \frac{482943403}{2504}e^{6} + \frac{80284897}{313}e^{4} - \frac{78377717}{626}e^{2} + \frac{6181447}{313}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, -w + 4]$ | $-1$ |