Base field 4.4.17609.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 10x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11, 11, -w^{3} + 6w - 4]$ |
| Dimension: | $13$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{13} + 4x^{12} - 11x^{11} - 56x^{10} + 31x^{9} + 282x^{8} + 27x^{7} - 622x^{6} - 214x^{5} + 579x^{4} + 250x^{3} - 175x^{2} - 81x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{3} + w^{2} - 4w + 1]$ | $-\frac{503}{3809}e^{12} - \frac{1516}{3809}e^{11} + \frac{6725}{3809}e^{10} + \frac{21423}{3809}e^{9} - \frac{2380}{293}e^{8} - \frac{109398}{3809}e^{7} + \frac{55311}{3809}e^{6} + \frac{247708}{3809}e^{5} - \frac{24825}{3809}e^{4} - \frac{244532}{3809}e^{3} - \frac{12976}{3809}e^{2} + \frac{81836}{3809}e + \frac{5663}{3809}$ |
| 7 | $[7, 7, -w^{3} + 6w - 2]$ | $\phantom{-}\frac{154}{3809}e^{12} - \frac{490}{3809}e^{11} - \frac{3369}{3809}e^{10} + \frac{7261}{3809}e^{9} + \frac{1843}{293}e^{8} - \frac{38264}{3809}e^{7} - \frac{65232}{3809}e^{6} + \frac{85290}{3809}e^{5} + \frac{51900}{3809}e^{4} - \frac{76153}{3809}e^{3} + \frac{10258}{3809}e^{2} + \frac{30270}{3809}e - \frac{6868}{3809}$ |
| 8 | $[8, 2, w^{3} - 7w + 3]$ | $-\frac{131}{3809}e^{12} - \frac{622}{3809}e^{11} + \frac{714}{3809}e^{10} + \frac{7056}{3809}e^{9} + \frac{371}{293}e^{8} - \frac{23448}{3809}e^{7} - \frac{41170}{3809}e^{6} + \frac{12186}{3809}e^{5} + \frac{94954}{3809}e^{4} + \frac{43830}{3809}e^{3} - \frac{75705}{3809}e^{2} - \frac{35890}{3809}e + \frac{6238}{3809}$ |
| 11 | $[11, 11, -w^{3} + 6w - 4]$ | $\phantom{-}1$ |
| 17 | $[17, 17, w^{3} + w^{2} - 6w - 1]$ | $-\frac{721}{3809}e^{12} - \frac{2900}{3809}e^{11} + \frac{9367}{3809}e^{10} + \frac{43051}{3809}e^{9} - \frac{3288}{293}e^{8} - \frac{233612}{3809}e^{7} + \frac{82751}{3809}e^{6} + \frac{564711}{3809}e^{5} - \frac{58423}{3809}e^{4} - \frac{586193}{3809}e^{3} - \frac{19978}{3809}e^{2} + \frac{203169}{3809}e + \frac{28692}{3809}$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $\phantom{-}\frac{131}{3809}e^{12} + \frac{622}{3809}e^{11} - \frac{714}{3809}e^{10} - \frac{7056}{3809}e^{9} - \frac{371}{293}e^{8} + \frac{23448}{3809}e^{7} + \frac{41170}{3809}e^{6} - \frac{12186}{3809}e^{5} - \frac{94954}{3809}e^{4} - \frac{43830}{3809}e^{3} + \frac{75705}{3809}e^{2} + \frac{35890}{3809}e - \frac{17665}{3809}$ |
| 31 | $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ | $\phantom{-}\frac{503}{3809}e^{12} + \frac{1516}{3809}e^{11} - \frac{6725}{3809}e^{10} - \frac{21423}{3809}e^{9} + \frac{2380}{293}e^{8} + \frac{109398}{3809}e^{7} - \frac{55311}{3809}e^{6} - \frac{251517}{3809}e^{5} + \frac{21016}{3809}e^{4} + \frac{271195}{3809}e^{3} + \frac{32021}{3809}e^{2} - \frac{116117}{3809}e - \frac{24708}{3809}$ |
| 37 | $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ | $\phantom{-}\frac{912}{3809}e^{12} + \frac{1946}{3809}e^{11} - \frac{11542}{3809}e^{10} - \frac{22198}{3809}e^{9} + \frac{3597}{293}e^{8} + \frac{73715}{3809}e^{7} - \frac{55668}{3809}e^{6} - \frac{37268}{3809}e^{5} - \frac{30359}{3809}e^{4} - \frac{134837}{3809}e^{3} + \frac{37400}{3809}e^{2} + \frac{116487}{3809}e + \frac{3007}{3809}$ |
| 41 | $[41, 41, w^{2} + 2w - 4]$ | $-\frac{1210}{3809}e^{12} - \frac{3768}{3809}e^{11} + \frac{16132}{3809}e^{10} + \frac{52322}{3809}e^{9} - \frac{5900}{293}e^{8} - \frac{258189}{3809}e^{7} + \frac{161565}{3809}e^{6} + \frac{540038}{3809}e^{5} - \frac{161289}{3809}e^{4} - \frac{433894}{3809}e^{3} + \frac{92983}{3809}e^{2} + \frac{84841}{3809}e - \frac{36909}{3809}$ |
| 47 | $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ | $-\frac{1821}{3809}e^{12} - \frac{3209}{3809}e^{11} + \frac{28534}{3809}e^{10} + \frac{45601}{3809}e^{9} - \frac{12727}{293}e^{8} - \frac{239443}{3809}e^{7} + \frac{434968}{3809}e^{6} + \frac{581261}{3809}e^{5} - \frac{504229}{3809}e^{4} - \frac{647874}{3809}e^{3} + \frac{194058}{3809}e^{2} + \frac{231819}{3809}e + \frac{12452}{3809}$ |
| 47 | $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ | $\phantom{-}\frac{882}{3809}e^{12} + \frac{2734}{3809}e^{11} - \frac{8907}{3809}e^{10} - \frac{34248}{3809}e^{9} + \frac{1206}{293}e^{8} + \frac{148247}{3809}e^{7} + \frac{82786}{3809}e^{6} - \frac{270897}{3809}e^{5} - \frac{300075}{3809}e^{4} + \frac{218999}{3809}e^{3} + \frac{258896}{3809}e^{2} - \frac{78722}{3809}e - \frac{52147}{3809}$ |
| 59 | $[59, 59, -2w^{3} + 13w - 6]$ | $\phantom{-}\frac{2378}{3809}e^{12} + \frac{5592}{3809}e^{11} - \frac{36193}{3809}e^{10} - \frac{79615}{3809}e^{9} + \frac{16012}{293}e^{8} + \frac{410466}{3809}e^{7} - \frac{568853}{3809}e^{6} - \frac{937126}{3809}e^{5} + \frac{743342}{3809}e^{4} + \frac{922838}{3809}e^{3} - \frac{373327}{3809}e^{2} - \frac{308136}{3809}e + \frac{20980}{3809}$ |
| 59 | $[59, 59, -w^{3} - w^{2} + 5w + 2]$ | $\phantom{-}\frac{972}{3809}e^{12} + \frac{370}{3809}e^{11} - \frac{16812}{3809}e^{10} - \frac{1907}{3809}e^{9} + \frac{8379}{293}e^{8} - \frac{10596}{3809}e^{7} - \frac{321149}{3809}e^{6} + \frac{71944}{3809}e^{5} + \frac{406230}{3809}e^{4} - \frac{103563}{3809}e^{3} - \frac{158007}{3809}e^{2} + \frac{38398}{3809}e + \frac{14281}{3809}$ |
| 59 | $[59, 59, w^{2} + w - 1]$ | $-\frac{48}{293}e^{12} - \frac{87}{293}e^{11} + \frac{700}{293}e^{10} + \frac{1230}{293}e^{9} - \frac{3556}{293}e^{8} - \frac{6563}{293}e^{7} + \frac{6816}{293}e^{6} + \frac{16704}{293}e^{5} - \frac{777}{293}e^{4} - \frac{19628}{293}e^{3} - \frac{9571}{293}e^{2} + \frac{7270}{293}e + \frac{3990}{293}$ |
| 59 | $[59, 59, w^{2} + 2w - 6]$ | $-\frac{1822}{3809}e^{12} - \frac{2167}{3809}e^{11} + \frac{31796}{3809}e^{10} + \frac{31233}{3809}e^{9} - \frac{16059}{293}e^{8} - \frac{163064}{3809}e^{7} + \frac{634350}{3809}e^{6} + \frac{376802}{3809}e^{5} - \frac{877106}{3809}e^{4} - \frac{375036}{3809}e^{3} + \frac{453597}{3809}e^{2} + \frac{126405}{3809}e - \frac{33063}{3809}$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 8w - 7]$ | $-\frac{2438}{3809}e^{12} - \frac{7825}{3809}e^{11} + \frac{30036}{3809}e^{10} + \frac{105032}{3809}e^{9} - \frac{9367}{293}e^{8} - \frac{493751}{3809}e^{7} + \frac{179186}{3809}e^{6} + \frac{965038}{3809}e^{5} - \frac{75321}{3809}e^{4} - \frac{706527}{3809}e^{3} + \frac{35474}{3809}e^{2} + \frac{108168}{3809}e - \frac{13209}{3809}$ |
| 67 | $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ | $-\frac{242}{3809}e^{12} - \frac{3039}{3809}e^{11} + \frac{941}{3809}e^{10} + \frac{46269}{3809}e^{9} + \frac{871}{293}e^{8} - \frac{252753}{3809}e^{7} - \frac{70530}{3809}e^{6} + \frac{582609}{3809}e^{5} + \frac{124673}{3809}e^{4} - \frac{485962}{3809}e^{3} - \frac{81961}{3809}e^{2} + \frac{59629}{3809}e + \frac{12425}{3809}$ |
| 73 | $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ | $\phantom{-}\frac{834}{3809}e^{12} + \frac{3233}{3809}e^{11} - \frac{12309}{3809}e^{10} - \frac{49719}{3809}e^{9} + \frac{5350}{293}e^{8} + \frac{279687}{3809}e^{7} - \frac{189334}{3809}e^{6} - \frac{695744}{3809}e^{5} + \frac{237389}{3809}e^{4} + \frac{726478}{3809}e^{3} - \frac{66236}{3809}e^{2} - \frac{247838}{3809}e - \frac{58119}{3809}$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{120}{293}e^{12} + \frac{364}{293}e^{11} - \frac{1750}{293}e^{10} - \frac{5126}{293}e^{9} + \frac{10062}{293}e^{8} + \frac{25930}{293}e^{7} - \frac{30225}{293}e^{6} - \frac{56996}{293}e^{5} + \frac{49555}{293}e^{4} + \frac{51707}{293}e^{3} - \frac{35405}{293}e^{2} - \frac{15538}{293}e + \frac{4382}{293}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -w^{3} + 6w - 4]$ | $-1$ |