Newspace parameters
Level: | \( N \) | \(=\) | \( 935 = 5 \cdot 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 935.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(7.46601258899\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
441.1 | −2.71357 | − | 1.88783i | 5.36347 | − | 1.00000i | 5.12275i | − | 1.94701i | −9.12702 | −0.563885 | 2.71357i | |||||||||||||||
441.2 | −2.71357 | 1.88783i | 5.36347 | 1.00000i | − | 5.12275i | 1.94701i | −9.12702 | −0.563885 | − | 2.71357i | ||||||||||||||||
441.3 | −2.66544 | − | 3.36068i | 5.10456 | 1.00000i | 8.95769i | − | 3.62292i | −8.27500 | −8.29419 | − | 2.66544i | |||||||||||||||
441.4 | −2.66544 | 3.36068i | 5.10456 | − | 1.00000i | − | 8.95769i | 3.62292i | −8.27500 | −8.29419 | 2.66544i | ||||||||||||||||
441.5 | −2.21920 | − | 3.15959i | 2.92486 | − | 1.00000i | 7.01176i | 3.92482i | −2.05244 | −6.98299 | 2.21920i | ||||||||||||||||
441.6 | −2.21920 | 3.15959i | 2.92486 | 1.00000i | − | 7.01176i | − | 3.92482i | −2.05244 | −6.98299 | − | 2.21920i | |||||||||||||||
441.7 | −2.06277 | − | 0.620881i | 2.25501 | 1.00000i | 1.28073i | 0.540632i | −0.526032 | 2.61451 | − | 2.06277i | ||||||||||||||||
441.8 | −2.06277 | 0.620881i | 2.25501 | − | 1.00000i | − | 1.28073i | − | 0.540632i | −0.526032 | 2.61451 | 2.06277i | |||||||||||||||
441.9 | −1.83110 | − | 2.66006i | 1.35293 | 1.00000i | 4.87084i | 2.65496i | 1.18486 | −4.07594 | − | 1.83110i | ||||||||||||||||
441.10 | −1.83110 | 2.66006i | 1.35293 | − | 1.00000i | − | 4.87084i | − | 2.65496i | 1.18486 | −4.07594 | 1.83110i | |||||||||||||||
441.11 | −1.70389 | − | 1.74029i | 0.903257 | − | 1.00000i | 2.96527i | − | 0.100972i | 1.86873 | −0.0286124 | 1.70389i | |||||||||||||||
441.12 | −1.70389 | 1.74029i | 0.903257 | 1.00000i | − | 2.96527i | 0.100972i | 1.86873 | −0.0286124 | − | 1.70389i | ||||||||||||||||
441.13 | −1.02257 | − | 1.44697i | −0.954349 | 1.00000i | 1.47963i | − | 1.42982i | 3.02103 | 0.906284 | − | 1.02257i | |||||||||||||||
441.14 | −1.02257 | 1.44697i | −0.954349 | − | 1.00000i | − | 1.47963i | 1.42982i | 3.02103 | 0.906284 | 1.02257i | ||||||||||||||||
441.15 | −0.478851 | − | 1.89263i | −1.77070 | 1.00000i | 0.906287i | − | 1.08857i | 1.80560 | −0.582043 | − | 0.478851i | |||||||||||||||
441.16 | −0.478851 | 1.89263i | −1.77070 | − | 1.00000i | − | 0.906287i | 1.08857i | 1.80560 | −0.582043 | 0.478851i | ||||||||||||||||
441.17 | −0.368204 | − | 1.85231i | −1.86443 | − | 1.00000i | 0.682030i | 2.84540i | 1.42290 | −0.431060 | 0.368204i | ||||||||||||||||
441.18 | −0.368204 | 1.85231i | −1.86443 | 1.00000i | − | 0.682030i | − | 2.84540i | 1.42290 | −0.431060 | − | 0.368204i | |||||||||||||||
441.19 | −0.0999015 | − | 0.941658i | −1.99002 | − | 1.00000i | 0.0940730i | − | 4.23923i | 0.398609 | 2.11328 | 0.0999015i | |||||||||||||||
441.20 | −0.0999015 | 0.941658i | −1.99002 | 1.00000i | − | 0.0940730i | 4.23923i | 0.398609 | 2.11328 | − | 0.0999015i | ||||||||||||||||
See all 34 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
17.b | even | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 935.2.f.b | ✓ | 34 |
17.b | even | 2 | 1 | inner | 935.2.f.b | ✓ | 34 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
935.2.f.b | ✓ | 34 | 1.a | even | 1 | 1 | trivial |
935.2.f.b | ✓ | 34 | 17.b | even | 2 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{17} + 3 T_{2}^{16} - 23 T_{2}^{15} - 71 T_{2}^{14} + 209 T_{2}^{13} + 673 T_{2}^{12} - 952 T_{2}^{11} - 3275 T_{2}^{10} + 2258 T_{2}^{9} + 8718 T_{2}^{8} - 2491 T_{2}^{7} - 12469 T_{2}^{6} + 427 T_{2}^{5} + 8660 T_{2}^{4} + \cdots - 56 \)
acting on \(S_{2}^{\mathrm{new}}(935, [\chi])\).