Newspace parameters
Level: | |||
Weight: | |||
Character orbit: | 890.o (of order , degree , minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Twist minimal: | yes |
Sato-Tate group: |
-expansion
The algebraic -expansion of this newform has not been computed, but we have computed the trace expansion.
Embeddings
For each embedding of the coefficient field, the values are shown below.
For more information on an embedded modular form you can click on its label.
Label | |||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
91.1 | −0.959493 | + | 0.281733i | −2.15610 | − | 1.38564i | 0.841254 | − | 0.540641i | −0.654861 | + | 0.755750i | 2.45914 | + | 0.722068i | −2.60674 | + | 3.00834i | −0.654861 | + | 0.755750i | 1.48251 | + | 3.24625i | 0.415415 | − | 0.909632i |
91.2 | −0.959493 | + | 0.281733i | −0.970228 | − | 0.623528i | 0.841254 | − | 0.540641i | −0.654861 | + | 0.755750i | 1.10660 | + | 0.324926i | 1.95889 | − | 2.26068i | −0.654861 | + | 0.755750i | −0.693689 | − | 1.51897i | 0.415415 | − | 0.909632i |
91.3 | −0.959493 | + | 0.281733i | −0.0785546 | − | 0.0504840i | 0.841254 | − | 0.540641i | −0.654861 | + | 0.755750i | 0.0895956 | + | 0.0263076i | −0.739256 | + | 0.853147i | −0.654861 | + | 0.755750i | −1.24262 | − | 2.72096i | 0.415415 | − | 0.909632i |
91.4 | −0.959493 | + | 0.281733i | 1.09596 | + | 0.704333i | 0.841254 | − | 0.540641i | −0.654861 | + | 0.755750i | −1.25000 | − | 0.367034i | 0.906125 | − | 1.04572i | −0.654861 | + | 0.755750i | −0.541194 | − | 1.18505i | 0.415415 | − | 0.909632i |
91.5 | −0.959493 | + | 0.281733i | 1.18519 | + | 0.761672i | 0.841254 | − | 0.540641i | −0.654861 | + | 0.755750i | −1.35177 | − | 0.396914i | −0.694605 | + | 0.801617i | −0.654861 | + | 0.755750i | −0.421725 | − | 0.923450i | 0.415415 | − | 0.909632i |
91.6 | −0.959493 | + | 0.281733i | 2.26498 | + | 1.45562i | 0.841254 | − | 0.540641i | −0.654861 | + | 0.755750i | −2.58333 | − | 0.758534i | −0.453862 | + | 0.523785i | −0.654861 | + | 0.755750i | 1.76509 | + | 3.86500i | 0.415415 | − | 0.909632i |
121.1 | −0.142315 | + | 0.989821i | −2.59272 | + | 0.761291i | −0.959493 | − | 0.281733i | 0.415415 | − | 0.909632i | −0.384560 | − | 2.67467i | −1.47545 | + | 3.23078i | 0.415415 | − | 0.909632i | 3.61886 | − | 2.32570i | 0.841254 | + | 0.540641i |
121.2 | −0.142315 | + | 0.989821i | −2.13119 | + | 0.625774i | −0.959493 | − | 0.281733i | 0.415415 | − | 0.909632i | −0.316104 | − | 2.19855i | 1.98779 | − | 4.35266i | 0.415415 | − | 0.909632i | 1.62662 | − | 1.04536i | 0.841254 | + | 0.540641i |
121.3 | −0.142315 | + | 0.989821i | −0.724740 | + | 0.212803i | −0.959493 | − | 0.281733i | 0.415415 | − | 0.909632i | −0.107496 | − | 0.747649i | −0.0604032 | + | 0.132265i | 0.415415 | − | 0.909632i | −2.04380 | + | 1.31347i | 0.841254 | + | 0.540641i |
121.4 | −0.142315 | + | 0.989821i | 0.707712 | − | 0.207803i | −0.959493 | − | 0.281733i | 0.415415 | − | 0.909632i | 0.104970 | + | 0.730082i | 1.04299 | − | 2.28383i | 0.415415 | − | 0.909632i | −2.06609 | + | 1.32779i | 0.841254 | + | 0.540641i |
121.5 | −0.142315 | + | 0.989821i | 1.15127 | − | 0.338042i | −0.959493 | − | 0.281733i | 0.415415 | − | 0.909632i | 0.170759 | + | 1.18766i | −0.834221 | + | 1.82669i | 0.415415 | − | 0.909632i | −1.31262 | + | 0.843570i | 0.841254 | + | 0.540641i |
121.6 | −0.142315 | + | 0.989821i | 3.13018 | − | 0.919103i | −0.959493 | − | 0.281733i | 0.415415 | − | 0.909632i | 0.464277 | + | 3.22912i | 0.545687 | − | 1.19489i | 0.415415 | − | 0.909632i | 6.42950 | − | 4.13199i | 0.841254 | + | 0.540641i |
271.1 | 0.841254 | − | 0.540641i | −0.881612 | − | 1.93046i | 0.415415 | − | 0.909632i | −0.142315 | − | 0.989821i | −1.78534 | − | 1.14737i | −0.00872159 | − | 0.0606600i | −0.142315 | − | 0.989821i | −0.984857 | + | 1.13659i | −0.654861 | − | 0.755750i |
271.2 | 0.841254 | − | 0.540641i | −0.608481 | − | 1.33239i | 0.415415 | − | 0.909632i | −0.142315 | − | 0.989821i | −1.23223 | − | 0.791906i | −0.345110 | − | 2.40030i | −0.142315 | − | 0.989821i | 0.559573 | − | 0.645782i | −0.654861 | − | 0.755750i |
271.3 | 0.841254 | − | 0.540641i | 0.249407 | + | 0.546126i | 0.415415 | − | 0.909632i | −0.142315 | − | 0.989821i | 0.505073 | + | 0.324591i | −0.576031 | − | 4.00638i | −0.142315 | − | 0.989821i | 1.72853 | − | 1.99483i | −0.654861 | − | 0.755750i |
271.4 | 0.841254 | − | 0.540641i | 0.312407 | + | 0.684075i | 0.415415 | − | 0.909632i | −0.142315 | − | 0.989821i | 0.632652 | + | 0.406581i | 0.110561 | + | 0.768972i | −0.142315 | − | 0.989821i | 1.59422 | − | 1.83983i | −0.654861 | − | 0.755750i |
271.5 | 0.841254 | − | 0.540641i | 0.606764 | + | 1.32863i | 0.415415 | − | 0.909632i | −0.142315 | − | 0.989821i | 1.22875 | + | 0.789671i | 0.0430450 | + | 0.299384i | −0.142315 | − | 0.989821i | 0.567494 | − | 0.654923i | −0.654861 | − | 0.755750i |
271.6 | 0.841254 | − | 0.540641i | 1.23693 | + | 2.70850i | 0.415415 | − | 0.909632i | −0.142315 | − | 0.989821i | 2.50490 | + | 1.60980i | 0.469502 | + | 3.26546i | −0.142315 | − | 0.989821i | −3.84139 | + | 4.43320i | −0.654861 | − | 0.755750i |
331.1 | −0.142315 | − | 0.989821i | −2.59272 | − | 0.761291i | −0.959493 | + | 0.281733i | 0.415415 | + | 0.909632i | −0.384560 | + | 2.67467i | −1.47545 | − | 3.23078i | 0.415415 | + | 0.909632i | 3.61886 | + | 2.32570i | 0.841254 | − | 0.540641i |
331.2 | −0.142315 | − | 0.989821i | −2.13119 | − | 0.625774i | −0.959493 | + | 0.281733i | 0.415415 | + | 0.909632i | −0.316104 | + | 2.19855i | 1.98779 | + | 4.35266i | 0.415415 | + | 0.909632i | 1.62662 | + | 1.04536i | 0.841254 | − | 0.540641i |
See all 60 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
89.e | even | 11 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 890.2.o.a | ✓ | 60 |
89.e | even | 11 | 1 | inner | 890.2.o.a | ✓ | 60 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
890.2.o.a | ✓ | 60 | 1.a | even | 1 | 1 | trivial |
890.2.o.a | ✓ | 60 | 89.e | even | 11 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
acting on .