Newspace parameters
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.q (of order \(11\), degree \(10\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{11})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{11}]$ |
$q$-expansion
The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.
Embeddings
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
Label | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
85.1 | 0.654861 | − | 0.755750i | 0.841254 | − | 0.540641i | −0.142315 | − | 0.989821i | −1.82570 | − | 3.99772i | 0.142315 | − | 0.989821i | 0.959493 | − | 0.281733i | −0.841254 | − | 0.540641i | 0.415415 | − | 0.909632i | −4.21685 | − | 1.23818i |
85.2 | 0.654861 | − | 0.755750i | 0.841254 | − | 0.540641i | −0.142315 | − | 0.989821i | −0.454603 | − | 0.995441i | 0.142315 | − | 0.989821i | 0.959493 | − | 0.281733i | −0.841254 | − | 0.540641i | 0.415415 | − | 0.909632i | −1.05001 | − | 0.308309i |
85.3 | 0.654861 | − | 0.755750i | 0.841254 | − | 0.540641i | −0.142315 | − | 0.989821i | 0.722570 | + | 1.58221i | 0.142315 | − | 0.989821i | 0.959493 | − | 0.281733i | −0.841254 | − | 0.540641i | 0.415415 | − | 0.909632i | 1.66893 | + | 0.490044i |
127.1 | −0.841254 | + | 0.540641i | −0.142315 | + | 0.989821i | 0.415415 | − | 0.909632i | −1.76124 | + | 0.517147i | −0.415415 | − | 0.909632i | 0.654861 | + | 0.755750i | 0.142315 | + | 0.989821i | −0.959493 | − | 0.281733i | 1.20206 | − | 1.38725i |
127.2 | −0.841254 | + | 0.540641i | −0.142315 | + | 0.989821i | 0.415415 | − | 0.909632i | −0.421404 | + | 0.123735i | −0.415415 | − | 0.909632i | 0.654861 | + | 0.755750i | 0.142315 | + | 0.989821i | −0.959493 | − | 0.281733i | 0.287611 | − | 0.331921i |
127.3 | −0.841254 | + | 0.540641i | −0.142315 | + | 0.989821i | 0.415415 | − | 0.909632i | 2.55755 | − | 0.750965i | −0.415415 | − | 0.909632i | 0.654861 | + | 0.755750i | 0.142315 | + | 0.989821i | −0.959493 | − | 0.281733i | −1.74555 | + | 2.01447i |
169.1 | 0.142315 | − | 0.989821i | 0.415415 | + | 0.909632i | −0.959493 | − | 0.281733i | −2.78120 | − | 3.20968i | 0.959493 | − | 0.281733i | −0.841254 | − | 0.540641i | −0.415415 | + | 0.909632i | −0.654861 | + | 0.755750i | −3.57281 | + | 2.29611i |
169.2 | 0.142315 | − | 0.989821i | 0.415415 | + | 0.909632i | −0.959493 | − | 0.281733i | −0.150642 | − | 0.173850i | 0.959493 | − | 0.281733i | −0.841254 | − | 0.540641i | −0.415415 | + | 0.909632i | −0.654861 | + | 0.755750i | −0.193519 | + | 0.124367i |
169.3 | 0.142315 | − | 0.989821i | 0.415415 | + | 0.909632i | −0.959493 | − | 0.281733i | 1.62721 | + | 1.87790i | 0.959493 | − | 0.281733i | −0.841254 | − | 0.540641i | −0.415415 | + | 0.909632i | −0.654861 | + | 0.755750i | 2.09036 | − | 1.34340i |
211.1 | −0.415415 | − | 0.909632i | −0.959493 | + | 0.281733i | −0.654861 | + | 0.755750i | −2.44943 | − | 1.57415i | 0.654861 | + | 0.755750i | 0.142315 | + | 0.989821i | 0.959493 | + | 0.281733i | 0.841254 | − | 0.540641i | −0.414370 | + | 2.88200i |
211.2 | −0.415415 | − | 0.909632i | −0.959493 | + | 0.281733i | −0.654861 | + | 0.755750i | −2.10097 | − | 1.35021i | 0.654861 | + | 0.755750i | 0.142315 | + | 0.989821i | 0.959493 | + | 0.281733i | 0.841254 | − | 0.540641i | −0.355420 | + | 2.47200i |
211.3 | −0.415415 | − | 0.909632i | −0.959493 | + | 0.281733i | −0.654861 | + | 0.755750i | 2.05428 | + | 1.32020i | 0.654861 | + | 0.755750i | 0.142315 | + | 0.989821i | 0.959493 | + | 0.281733i | 0.841254 | − | 0.540641i | 0.347522 | − | 2.41707i |
463.1 | 0.142315 | + | 0.989821i | 0.415415 | − | 0.909632i | −0.959493 | + | 0.281733i | −2.78120 | + | 3.20968i | 0.959493 | + | 0.281733i | −0.841254 | + | 0.540641i | −0.415415 | − | 0.909632i | −0.654861 | − | 0.755750i | −3.57281 | − | 2.29611i |
463.2 | 0.142315 | + | 0.989821i | 0.415415 | − | 0.909632i | −0.959493 | + | 0.281733i | −0.150642 | + | 0.173850i | 0.959493 | + | 0.281733i | −0.841254 | + | 0.540641i | −0.415415 | − | 0.909632i | −0.654861 | − | 0.755750i | −0.193519 | − | 0.124367i |
463.3 | 0.142315 | + | 0.989821i | 0.415415 | − | 0.909632i | −0.959493 | + | 0.281733i | 1.62721 | − | 1.87790i | 0.959493 | + | 0.281733i | −0.841254 | + | 0.540641i | −0.415415 | − | 0.909632i | −0.654861 | − | 0.755750i | 2.09036 | + | 1.34340i |
547.1 | 0.959493 | + | 0.281733i | −0.654861 | + | 0.755750i | 0.841254 | + | 0.540641i | −0.220101 | + | 1.53083i | −0.841254 | + | 0.540641i | −0.415415 | − | 0.909632i | 0.654861 | + | 0.755750i | −0.142315 | − | 0.989821i | −0.642471 | + | 1.40681i |
547.2 | 0.959493 | + | 0.281733i | −0.654861 | + | 0.755750i | 0.841254 | + | 0.540641i | 0.0353399 | − | 0.245794i | −0.841254 | + | 0.540641i | −0.415415 | − | 0.909632i | 0.654861 | + | 0.755750i | −0.142315 | − | 0.989821i | 0.103157 | − | 0.225881i |
547.3 | 0.959493 | + | 0.281733i | −0.654861 | + | 0.755750i | 0.841254 | + | 0.540641i | 0.168329 | − | 1.17076i | −0.841254 | + | 0.540641i | −0.415415 | − | 0.909632i | 0.654861 | + | 0.755750i | −0.142315 | − | 0.989821i | 0.491350 | − | 1.07591i |
673.1 | −0.415415 | + | 0.909632i | −0.959493 | − | 0.281733i | −0.654861 | − | 0.755750i | −2.44943 | + | 1.57415i | 0.654861 | − | 0.755750i | 0.142315 | − | 0.989821i | 0.959493 | − | 0.281733i | 0.841254 | + | 0.540641i | −0.414370 | − | 2.88200i |
673.2 | −0.415415 | + | 0.909632i | −0.959493 | − | 0.281733i | −0.654861 | − | 0.755750i | −2.10097 | + | 1.35021i | 0.654861 | − | 0.755750i | 0.142315 | − | 0.989821i | 0.959493 | − | 0.281733i | 0.841254 | + | 0.540641i | −0.355420 | − | 2.47200i |
See all 30 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
23.c | even | 11 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 966.2.q.f | ✓ | 30 |
23.c | even | 11 | 1 | inner | 966.2.q.f | ✓ | 30 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
966.2.q.f | ✓ | 30 | 1.a | even | 1 | 1 | trivial |
966.2.q.f | ✓ | 30 | 23.c | even | 11 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{30} + 10 T_{5}^{29} + 55 T_{5}^{28} + 122 T_{5}^{27} - 34 T_{5}^{26} - 836 T_{5}^{25} + 859 T_{5}^{24} + 10889 T_{5}^{23} + 11924 T_{5}^{22} - 47046 T_{5}^{21} + 3783 T_{5}^{20} + 386123 T_{5}^{19} + 628892 T_{5}^{18} + \cdots + 123904 \)
acting on \(S_{2}^{\mathrm{new}}(966, [\chi])\).