Newspace parameters
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.l (of order \(9\), degree \(6\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{9})\) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
101.1 | 0.766044 | − | 0.642788i | −2.74319 | − | 0.998438i | 0.173648 | − | 0.984808i | 0 | −2.74319 | + | 0.998438i | 0.366794 | − | 0.635305i | −0.500000 | − | 0.866025i | 4.23006 | + | 3.54944i | 0 | ||||
101.2 | 0.766044 | − | 0.642788i | −0.845354 | − | 0.307684i | 0.173648 | − | 0.984808i | 0 | −0.845354 | + | 0.307684i | −1.06731 | + | 1.84863i | −0.500000 | − | 0.866025i | −1.67818 | − | 1.40816i | 0 | ||||
101.3 | 0.766044 | − | 0.642788i | 0.0808150 | + | 0.0294142i | 0.173648 | − | 0.984808i | 0 | 0.0808150 | − | 0.0294142i | 1.91879 | − | 3.32344i | −0.500000 | − | 0.866025i | −2.29247 | − | 1.92361i | 0 | ||||
101.4 | 0.766044 | − | 0.642788i | 0.476729 | + | 0.173515i | 0.173648 | − | 0.984808i | 0 | 0.476729 | − | 0.173515i | −0.753583 | + | 1.30524i | −0.500000 | − | 0.866025i | −2.10097 | − | 1.76292i | 0 | ||||
101.5 | 0.766044 | − | 0.642788i | 3.03100 | + | 1.10319i | 0.173648 | − | 0.984808i | 0 | 3.03100 | − | 1.10319i | 1.36166 | − | 2.35847i | −0.500000 | − | 0.866025i | 5.67178 | + | 4.75918i | 0 | ||||
251.1 | −0.939693 | − | 0.342020i | −0.541196 | − | 3.06928i | 0.766044 | + | 0.642788i | 0 | −0.541196 | + | 3.06928i | 0.147073 | − | 0.254737i | −0.500000 | − | 0.866025i | −6.30849 | + | 2.29610i | 0 | ||||
251.2 | −0.939693 | − | 0.342020i | −0.237849 | − | 1.34891i | 0.766044 | + | 0.642788i | 0 | −0.237849 | + | 1.34891i | −0.816213 | + | 1.41372i | −0.500000 | − | 0.866025i | 1.05609 | − | 0.384387i | 0 | ||||
251.3 | −0.939693 | − | 0.342020i | 0.0989733 | + | 0.561305i | 0.766044 | + | 0.642788i | 0 | 0.0989733 | − | 0.561305i | 2.10163 | − | 3.64013i | −0.500000 | − | 0.866025i | 2.51381 | − | 0.914952i | 0 | ||||
251.4 | −0.939693 | − | 0.342020i | 0.260779 | + | 1.47895i | 0.766044 | + | 0.642788i | 0 | 0.260779 | − | 1.47895i | −1.51251 | + | 2.61975i | −0.500000 | − | 0.866025i | 0.699782 | − | 0.254700i | 0 | ||||
251.5 | −0.939693 | − | 0.342020i | 0.419293 | + | 2.37793i | 0.766044 | + | 0.642788i | 0 | 0.419293 | − | 2.37793i | 1.31398 | − | 2.27588i | −0.500000 | − | 0.866025i | −2.65966 | + | 0.968036i | 0 | ||||
301.1 | 0.766044 | + | 0.642788i | −2.74319 | + | 0.998438i | 0.173648 | + | 0.984808i | 0 | −2.74319 | − | 0.998438i | 0.366794 | + | 0.635305i | −0.500000 | + | 0.866025i | 4.23006 | − | 3.54944i | 0 | ||||
301.2 | 0.766044 | + | 0.642788i | −0.845354 | + | 0.307684i | 0.173648 | + | 0.984808i | 0 | −0.845354 | − | 0.307684i | −1.06731 | − | 1.84863i | −0.500000 | + | 0.866025i | −1.67818 | + | 1.40816i | 0 | ||||
301.3 | 0.766044 | + | 0.642788i | 0.0808150 | − | 0.0294142i | 0.173648 | + | 0.984808i | 0 | 0.0808150 | + | 0.0294142i | 1.91879 | + | 3.32344i | −0.500000 | + | 0.866025i | −2.29247 | + | 1.92361i | 0 | ||||
301.4 | 0.766044 | + | 0.642788i | 0.476729 | − | 0.173515i | 0.173648 | + | 0.984808i | 0 | 0.476729 | + | 0.173515i | −0.753583 | − | 1.30524i | −0.500000 | + | 0.866025i | −2.10097 | + | 1.76292i | 0 | ||||
301.5 | 0.766044 | + | 0.642788i | 3.03100 | − | 1.10319i | 0.173648 | + | 0.984808i | 0 | 3.03100 | + | 1.10319i | 1.36166 | + | 2.35847i | −0.500000 | + | 0.866025i | 5.67178 | − | 4.75918i | 0 | ||||
351.1 | 0.173648 | + | 0.984808i | −1.79775 | + | 1.50849i | −0.939693 | + | 0.342020i | 0 | −1.79775 | − | 1.50849i | 0.273873 | − | 0.474362i | −0.500000 | − | 0.866025i | 0.435412 | − | 2.46935i | 0 | ||||
351.2 | 0.173648 | + | 0.984808i | −1.52559 | + | 1.28013i | −0.939693 | + | 0.342020i | 0 | −1.52559 | − | 1.28013i | 1.97239 | − | 3.41629i | −0.500000 | − | 0.866025i | 0.167771 | − | 0.951479i | 0 | ||||
351.3 | 0.173648 | + | 0.984808i | −0.0864812 | + | 0.0725664i | −0.939693 | + | 0.342020i | 0 | −0.0864812 | − | 0.0725664i | −0.772138 | + | 1.33738i | −0.500000 | − | 0.866025i | −0.518731 | + | 2.94187i | 0 | ||||
351.4 | 0.173648 | + | 0.984808i | 1.28288 | − | 1.07646i | −0.939693 | + | 0.342020i | 0 | 1.28288 | + | 1.07646i | 1.16183 | − | 2.01234i | −0.500000 | − | 0.866025i | −0.0339381 | + | 0.192472i | 0 | ||||
351.5 | 0.173648 | + | 0.984808i | 2.12694 | − | 1.78472i | −0.939693 | + | 0.342020i | 0 | 2.12694 | + | 1.78472i | 0.303737 | − | 0.526088i | −0.500000 | − | 0.866025i | 0.817727 | − | 4.63756i | 0 | ||||
See all 30 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
19.e | even | 9 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 950.2.l.m | 30 | |
5.b | even | 2 | 1 | 950.2.l.l | 30 | ||
5.c | odd | 4 | 2 | 190.2.p.a | ✓ | 60 | |
19.e | even | 9 | 1 | inner | 950.2.l.m | 30 | |
95.p | even | 18 | 1 | 950.2.l.l | 30 | ||
95.q | odd | 36 | 2 | 190.2.p.a | ✓ | 60 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
190.2.p.a | ✓ | 60 | 5.c | odd | 4 | 2 | |
190.2.p.a | ✓ | 60 | 95.q | odd | 36 | 2 | |
950.2.l.l | 30 | 5.b | even | 2 | 1 | ||
950.2.l.l | 30 | 95.p | even | 18 | 1 | ||
950.2.l.m | 30 | 1.a | even | 1 | 1 | trivial | |
950.2.l.m | 30 | 19.e | even | 9 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{30} - 6 T_{3}^{27} - 15 T_{3}^{26} + 102 T_{3}^{25} + 616 T_{3}^{24} - 186 T_{3}^{23} + 2142 T_{3}^{22} + 3750 T_{3}^{21} + 20610 T_{3}^{20} + 41724 T_{3}^{19} + 308104 T_{3}^{18} + 313020 T_{3}^{17} + 791652 T_{3}^{16} + \cdots + 64 \)
acting on \(S_{2}^{\mathrm{new}}(950, [\chi])\).