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: | \(40\) |
Relative dimension: | \(4\) 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 | −1.70670 | − | 3.73716i | −0.142315 | + | 0.989821i | −0.959493 | + | 0.281733i | 0.841254 | + | 0.540641i | 0.415415 | − | 0.909632i | 3.94201 | + | 1.15748i |
85.2 | −0.654861 | + | 0.755750i | 0.841254 | − | 0.540641i | −0.142315 | − | 0.989821i | −0.446804 | − | 0.978364i | −0.142315 | + | 0.989821i | −0.959493 | + | 0.281733i | 0.841254 | + | 0.540641i | 0.415415 | − | 0.909632i | 1.03199 | + | 0.303020i |
85.3 | −0.654861 | + | 0.755750i | 0.841254 | − | 0.540641i | −0.142315 | − | 0.989821i | 0.431857 | + | 0.945634i | −0.142315 | + | 0.989821i | −0.959493 | + | 0.281733i | 0.841254 | + | 0.540641i | 0.415415 | − | 0.909632i | −0.997469 | − | 0.292883i |
85.4 | −0.654861 | + | 0.755750i | 0.841254 | − | 0.540641i | −0.142315 | − | 0.989821i | 1.56679 | + | 3.43079i | −0.142315 | + | 0.989821i | −0.959493 | + | 0.281733i | 0.841254 | + | 0.540641i | 0.415415 | − | 0.909632i | −3.61885 | − | 1.06259i |
127.1 | 0.841254 | − | 0.540641i | −0.142315 | + | 0.989821i | 0.415415 | − | 0.909632i | −2.99676 | + | 0.879928i | 0.415415 | + | 0.909632i | −0.654861 | − | 0.755750i | −0.142315 | − | 0.989821i | −0.959493 | − | 0.281733i | −2.04531 | + | 2.36041i |
127.2 | 0.841254 | − | 0.540641i | −0.142315 | + | 0.989821i | 0.415415 | − | 0.909632i | −1.32090 | + | 0.387851i | 0.415415 | + | 0.909632i | −0.654861 | − | 0.755750i | −0.142315 | − | 0.989821i | −0.959493 | − | 0.281733i | −0.901523 | + | 1.04041i |
127.3 | 0.841254 | − | 0.540641i | −0.142315 | + | 0.989821i | 0.415415 | − | 0.909632i | 2.16398 | − | 0.635401i | 0.415415 | + | 0.909632i | −0.654861 | − | 0.755750i | −0.142315 | − | 0.989821i | −0.959493 | − | 0.281733i | 1.47693 | − | 1.70447i |
127.4 | 0.841254 | − | 0.540641i | −0.142315 | + | 0.989821i | 0.415415 | − | 0.909632i | 3.49494 | − | 1.02621i | 0.415415 | + | 0.909632i | −0.654861 | − | 0.755750i | −0.142315 | − | 0.989821i | −0.959493 | − | 0.281733i | 2.38532 | − | 2.75280i |
169.1 | −0.142315 | + | 0.989821i | 0.415415 | + | 0.909632i | −0.959493 | − | 0.281733i | −1.80470 | − | 2.08274i | −0.959493 | + | 0.281733i | 0.841254 | + | 0.540641i | 0.415415 | − | 0.909632i | −0.654861 | + | 0.755750i | 2.31838 | − | 1.48993i |
169.2 | −0.142315 | + | 0.989821i | 0.415415 | + | 0.909632i | −0.959493 | − | 0.281733i | −0.987362 | − | 1.13948i | −0.959493 | + | 0.281733i | 0.841254 | + | 0.540641i | 0.415415 | − | 0.909632i | −0.654861 | + | 0.755750i | 1.26839 | − | 0.815148i |
169.3 | −0.142315 | + | 0.989821i | 0.415415 | + | 0.909632i | −0.959493 | − | 0.281733i | 0.751750 | + | 0.867566i | −0.959493 | + | 0.281733i | 0.841254 | + | 0.540641i | 0.415415 | − | 0.909632i | −0.654861 | + | 0.755750i | −0.965721 | + | 0.620631i |
169.4 | −0.142315 | + | 0.989821i | 0.415415 | + | 0.909632i | −0.959493 | − | 0.281733i | 2.39800 | + | 2.76744i | −0.959493 | + | 0.281733i | 0.841254 | + | 0.540641i | 0.415415 | − | 0.909632i | −0.654861 | + | 0.755750i | −3.08054 | + | 1.97974i |
211.1 | 0.415415 | + | 0.909632i | −0.959493 | + | 0.281733i | −0.654861 | + | 0.755750i | −2.63117 | − | 1.69095i | −0.654861 | − | 0.755750i | −0.142315 | − | 0.989821i | −0.959493 | − | 0.281733i | 0.841254 | − | 0.540641i | 0.445115 | − | 3.09584i |
211.2 | 0.415415 | + | 0.909632i | −0.959493 | + | 0.281733i | −0.654861 | + | 0.755750i | −0.627520 | − | 0.403283i | −0.654861 | − | 0.755750i | −0.142315 | − | 0.989821i | −0.959493 | − | 0.281733i | 0.841254 | − | 0.540641i | 0.106158 | − | 0.738342i |
211.3 | 0.415415 | + | 0.909632i | −0.959493 | + | 0.281733i | −0.654861 | + | 0.755750i | 1.41748 | + | 0.910960i | −0.654861 | − | 0.755750i | −0.142315 | − | 0.989821i | −0.959493 | − | 0.281733i | 0.841254 | − | 0.540641i | −0.239795 | + | 1.66781i |
211.4 | 0.415415 | + | 0.909632i | −0.959493 | + | 0.281733i | −0.654861 | + | 0.755750i | 2.75663 | + | 1.77158i | −0.654861 | − | 0.755750i | −0.142315 | − | 0.989821i | −0.959493 | − | 0.281733i | 0.841254 | − | 0.540641i | −0.466338 | + | 3.24345i |
463.1 | −0.142315 | − | 0.989821i | 0.415415 | − | 0.909632i | −0.959493 | + | 0.281733i | −1.80470 | + | 2.08274i | −0.959493 | − | 0.281733i | 0.841254 | − | 0.540641i | 0.415415 | + | 0.909632i | −0.654861 | − | 0.755750i | 2.31838 | + | 1.48993i |
463.2 | −0.142315 | − | 0.989821i | 0.415415 | − | 0.909632i | −0.959493 | + | 0.281733i | −0.987362 | + | 1.13948i | −0.959493 | − | 0.281733i | 0.841254 | − | 0.540641i | 0.415415 | + | 0.909632i | −0.654861 | − | 0.755750i | 1.26839 | + | 0.815148i |
463.3 | −0.142315 | − | 0.989821i | 0.415415 | − | 0.909632i | −0.959493 | + | 0.281733i | 0.751750 | − | 0.867566i | −0.959493 | − | 0.281733i | 0.841254 | − | 0.540641i | 0.415415 | + | 0.909632i | −0.654861 | − | 0.755750i | −0.965721 | − | 0.620631i |
463.4 | −0.142315 | − | 0.989821i | 0.415415 | − | 0.909632i | −0.959493 | + | 0.281733i | 2.39800 | − | 2.76744i | −0.959493 | − | 0.281733i | 0.841254 | − | 0.540641i | 0.415415 | + | 0.909632i | −0.654861 | − | 0.755750i | −3.08054 | − | 1.97974i |
See all 40 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.i | ✓ | 40 |
23.c | even | 11 | 1 | inner | 966.2.q.i | ✓ | 40 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
966.2.q.i | ✓ | 40 | 1.a | even | 1 | 1 | trivial |
966.2.q.i | ✓ | 40 | 23.c | even | 11 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{40} - 4 T_{5}^{39} + 29 T_{5}^{38} - 118 T_{5}^{37} + 490 T_{5}^{36} - 1276 T_{5}^{35} + 3416 T_{5}^{34} - 7890 T_{5}^{33} + 25074 T_{5}^{32} - 51327 T_{5}^{31} + 482723 T_{5}^{30} - 1600581 T_{5}^{29} + \cdots + 6847307293696 \)
acting on \(S_{2}^{\mathrm{new}}(966, [\chi])\).