Newspace parameters
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.q (of order \(11\), degree \(10\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(4.40774219157\) |
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
25.1 | 0 | 0.142315 | + | 0.989821i | 0 | −2.56277 | − | 0.752498i | 0 | 1.17327 | − | 1.35403i | 0 | −0.959493 | + | 0.281733i | 0 | ||||||||||
25.2 | 0 | 0.142315 | + | 0.989821i | 0 | 0.832695 | + | 0.244501i | 0 | 1.47208 | − | 1.69888i | 0 | −0.959493 | + | 0.281733i | 0 | ||||||||||
25.3 | 0 | 0.142315 | + | 0.989821i | 0 | 2.52725 | + | 0.742069i | 0 | −1.72994 | + | 1.99646i | 0 | −0.959493 | + | 0.281733i | 0 | ||||||||||
49.1 | 0 | −0.415415 | + | 0.909632i | 0 | −2.35936 | + | 2.72285i | 0 | 1.95097 | − | 1.25381i | 0 | −0.654861 | − | 0.755750i | 0 | ||||||||||
49.2 | 0 | −0.415415 | + | 0.909632i | 0 | 0.182341 | − | 0.210432i | 0 | 1.45078 | − | 0.932358i | 0 | −0.654861 | − | 0.755750i | 0 | ||||||||||
49.3 | 0 | −0.415415 | + | 0.909632i | 0 | 0.920354 | − | 1.06214i | 0 | −3.86124 | + | 2.48147i | 0 | −0.654861 | − | 0.755750i | 0 | ||||||||||
73.1 | 0 | 0.959493 | − | 0.281733i | 0 | −0.776140 | − | 0.498795i | 0 | 0.172807 | + | 1.20190i | 0 | 0.841254 | − | 0.540641i | 0 | ||||||||||
73.2 | 0 | 0.959493 | − | 0.281733i | 0 | −0.0432483 | − | 0.0277940i | 0 | −0.706094 | − | 4.91099i | 0 | 0.841254 | − | 0.540641i | 0 | ||||||||||
73.3 | 0 | 0.959493 | − | 0.281733i | 0 | 1.92120 | + | 1.23468i | 0 | 0.378426 | + | 2.63201i | 0 | 0.841254 | − | 0.540641i | 0 | ||||||||||
121.1 | 0 | 0.959493 | + | 0.281733i | 0 | −0.776140 | + | 0.498795i | 0 | 0.172807 | − | 1.20190i | 0 | 0.841254 | + | 0.540641i | 0 | ||||||||||
121.2 | 0 | 0.959493 | + | 0.281733i | 0 | −0.0432483 | + | 0.0277940i | 0 | −0.706094 | + | 4.91099i | 0 | 0.841254 | + | 0.540641i | 0 | ||||||||||
121.3 | 0 | 0.959493 | + | 0.281733i | 0 | 1.92120 | − | 1.23468i | 0 | 0.378426 | − | 2.63201i | 0 | 0.841254 | + | 0.540641i | 0 | ||||||||||
169.1 | 0 | −0.415415 | − | 0.909632i | 0 | −2.35936 | − | 2.72285i | 0 | 1.95097 | + | 1.25381i | 0 | −0.654861 | + | 0.755750i | 0 | ||||||||||
169.2 | 0 | −0.415415 | − | 0.909632i | 0 | 0.182341 | + | 0.210432i | 0 | 1.45078 | + | 0.932358i | 0 | −0.654861 | + | 0.755750i | 0 | ||||||||||
169.3 | 0 | −0.415415 | − | 0.909632i | 0 | 0.920354 | + | 1.06214i | 0 | −3.86124 | − | 2.48147i | 0 | −0.654861 | + | 0.755750i | 0 | ||||||||||
193.1 | 0 | 0.654861 | + | 0.755750i | 0 | −0.280570 | − | 1.95141i | 0 | 1.41601 | − | 3.10064i | 0 | −0.142315 | + | 0.989821i | 0 | ||||||||||
193.2 | 0 | 0.654861 | + | 0.755750i | 0 | −0.0891792 | − | 0.620255i | 0 | 0.0603595 | − | 0.132169i | 0 | −0.142315 | + | 0.989821i | 0 | ||||||||||
193.3 | 0 | 0.654861 | + | 0.755750i | 0 | 0.609195 | + | 4.23705i | 0 | −0.135120 | + | 0.295872i | 0 | −0.142315 | + | 0.989821i | 0 | ||||||||||
265.1 | 0 | 0.142315 | − | 0.989821i | 0 | −2.56277 | + | 0.752498i | 0 | 1.17327 | + | 1.35403i | 0 | −0.959493 | − | 0.281733i | 0 | ||||||||||
265.2 | 0 | 0.142315 | − | 0.989821i | 0 | 0.832695 | − | 0.244501i | 0 | 1.47208 | + | 1.69888i | 0 | −0.959493 | − | 0.281733i | 0 | ||||||||||
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 | 552.2.q.d | ✓ | 30 |
23.c | even | 11 | 1 | inner | 552.2.q.d | ✓ | 30 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
552.2.q.d | ✓ | 30 | 1.a | even | 1 | 1 | trivial |
552.2.q.d | ✓ | 30 | 23.c | even | 11 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{30} - 2 T_{5}^{29} + 19 T_{5}^{28} - 27 T_{5}^{27} + 92 T_{5}^{26} - 525 T_{5}^{25} + 1488 T_{5}^{24} - 1546 T_{5}^{23} - 6640 T_{5}^{22} + 29978 T_{5}^{21} - 1490 T_{5}^{20} - 68430 T_{5}^{19} + 353531 T_{5}^{18} - 1389483 T_{5}^{17} + \cdots + 529 \)
acting on \(S_{2}^{\mathrm{new}}(552, [\chi])\).