Newspace parameters
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.u (of order \(18\), degree \(6\), not minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
99.1 | −0.342020 | + | 0.939693i | −3.16698 | + | 0.558424i | −0.766044 | − | 0.642788i | 0 | 0.558424 | − | 3.16698i | 0.0202608 | + | 0.0116976i | 0.866025 | − | 0.500000i | 6.89886 | − | 2.51098i | 0 | ||||
99.2 | −0.342020 | + | 0.939693i | 0.0355948 | − | 0.00627632i | −0.766044 | − | 0.642788i | 0 | −0.00627632 | + | 0.0355948i | −1.59124 | − | 0.918706i | 0.866025 | − | 0.500000i | −2.81785 | + | 1.02561i | 0 | ||||
99.3 | −0.342020 | + | 0.939693i | 3.13139 | − | 0.552148i | −0.766044 | − | 0.642788i | 0 | −0.552148 | + | 3.13139i | 2.89781 | + | 1.67305i | 0.866025 | − | 0.500000i | 6.68164 | − | 2.43192i | 0 | ||||
99.4 | 0.342020 | − | 0.939693i | −3.13139 | + | 0.552148i | −0.766044 | − | 0.642788i | 0 | −0.552148 | + | 3.13139i | −2.89781 | − | 1.67305i | −0.866025 | + | 0.500000i | 6.68164 | − | 2.43192i | 0 | ||||
99.5 | 0.342020 | − | 0.939693i | −0.0355948 | + | 0.00627632i | −0.766044 | − | 0.642788i | 0 | −0.00627632 | + | 0.0355948i | 1.59124 | + | 0.918706i | −0.866025 | + | 0.500000i | −2.81785 | + | 1.02561i | 0 | ||||
99.6 | 0.342020 | − | 0.939693i | 3.16698 | − | 0.558424i | −0.766044 | − | 0.642788i | 0 | 0.558424 | − | 3.16698i | −0.0202608 | − | 0.0116976i | −0.866025 | + | 0.500000i | 6.89886 | − | 2.51098i | 0 | ||||
149.1 | −0.642788 | + | 0.766044i | −0.613893 | − | 1.68666i | −0.173648 | − | 0.984808i | 0 | 1.68666 | + | 0.613893i | −1.17907 | + | 0.680736i | 0.866025 | + | 0.500000i | −0.169813 | + | 0.142490i | 0 | ||||
149.2 | −0.642788 | + | 0.766044i | −0.197144 | − | 0.541649i | −0.173648 | − | 0.984808i | 0 | 0.541649 | + | 0.197144i | 4.21251 | − | 2.43209i | 0.866025 | + | 0.500000i | 2.04362 | − | 1.71480i | 0 | ||||
149.3 | −0.642788 | + | 0.766044i | 0.811037 | + | 2.22831i | −0.173648 | − | 0.984808i | 0 | −2.22831 | − | 0.811037i | −2.73267 | + | 1.57771i | 0.866025 | + | 0.500000i | −2.00943 | + | 1.68611i | 0 | ||||
149.4 | 0.642788 | − | 0.766044i | −0.811037 | − | 2.22831i | −0.173648 | − | 0.984808i | 0 | −2.22831 | − | 0.811037i | 2.73267 | − | 1.57771i | −0.866025 | − | 0.500000i | −2.00943 | + | 1.68611i | 0 | ||||
149.5 | 0.642788 | − | 0.766044i | 0.197144 | + | 0.541649i | −0.173648 | − | 0.984808i | 0 | 0.541649 | + | 0.197144i | −4.21251 | + | 2.43209i | −0.866025 | − | 0.500000i | 2.04362 | − | 1.71480i | 0 | ||||
149.6 | 0.642788 | − | 0.766044i | 0.613893 | + | 1.68666i | −0.173648 | − | 0.984808i | 0 | 1.68666 | + | 0.613893i | 1.17907 | − | 0.680736i | −0.866025 | − | 0.500000i | −0.169813 | + | 0.142490i | 0 | ||||
199.1 | −0.984808 | + | 0.173648i | −1.49114 | − | 1.77707i | 0.939693 | − | 0.342020i | 0 | 1.77707 | + | 1.49114i | −4.25802 | − | 2.45837i | −0.866025 | + | 0.500000i | −0.413538 | + | 2.34529i | 0 | ||||
199.2 | −0.984808 | + | 0.173648i | −0.712963 | − | 0.849676i | 0.939693 | − | 0.342020i | 0 | 0.849676 | + | 0.712963i | 4.26875 | + | 2.46456i | −0.866025 | + | 0.500000i | 0.307311 | − | 1.74285i | 0 | ||||
199.3 | −0.984808 | + | 0.173648i | 2.20410 | + | 2.62675i | 0.939693 | − | 0.342020i | 0 | −2.62675 | − | 2.20410i | 1.61687 | + | 0.933500i | −0.866025 | + | 0.500000i | −1.52078 | + | 8.62480i | 0 | ||||
199.4 | 0.984808 | − | 0.173648i | −2.20410 | − | 2.62675i | 0.939693 | − | 0.342020i | 0 | −2.62675 | − | 2.20410i | −1.61687 | − | 0.933500i | 0.866025 | − | 0.500000i | −1.52078 | + | 8.62480i | 0 | ||||
199.5 | 0.984808 | − | 0.173648i | 0.712963 | + | 0.849676i | 0.939693 | − | 0.342020i | 0 | 0.849676 | + | 0.712963i | −4.26875 | − | 2.46456i | 0.866025 | − | 0.500000i | 0.307311 | − | 1.74285i | 0 | ||||
199.6 | 0.984808 | − | 0.173648i | 1.49114 | + | 1.77707i | 0.939693 | − | 0.342020i | 0 | 1.77707 | + | 1.49114i | 4.25802 | + | 2.45837i | 0.866025 | − | 0.500000i | −0.413538 | + | 2.34529i | 0 | ||||
499.1 | −0.342020 | − | 0.939693i | −3.16698 | − | 0.558424i | −0.766044 | + | 0.642788i | 0 | 0.558424 | + | 3.16698i | 0.0202608 | − | 0.0116976i | 0.866025 | + | 0.500000i | 6.89886 | + | 2.51098i | 0 | ||||
499.2 | −0.342020 | − | 0.939693i | 0.0355948 | + | 0.00627632i | −0.766044 | + | 0.642788i | 0 | −0.00627632 | − | 0.0355948i | −1.59124 | + | 0.918706i | 0.866025 | + | 0.500000i | −2.81785 | − | 1.02561i | 0 | ||||
See all 36 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
5.b | even | 2 | 1 | inner |
19.e | even | 9 | 1 | inner |
95.p | even | 18 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 950.2.u.g | 36 | |
5.b | even | 2 | 1 | inner | 950.2.u.g | 36 | |
5.c | odd | 4 | 1 | 190.2.k.d | ✓ | 18 | |
5.c | odd | 4 | 1 | 950.2.l.i | 18 | ||
19.e | even | 9 | 1 | inner | 950.2.u.g | 36 | |
95.p | even | 18 | 1 | inner | 950.2.u.g | 36 | |
95.q | odd | 36 | 1 | 190.2.k.d | ✓ | 18 | |
95.q | odd | 36 | 1 | 950.2.l.i | 18 | ||
95.q | odd | 36 | 1 | 3610.2.a.bi | 9 | ||
95.r | even | 36 | 1 | 3610.2.a.bj | 9 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
190.2.k.d | ✓ | 18 | 5.c | odd | 4 | 1 | |
190.2.k.d | ✓ | 18 | 95.q | odd | 36 | 1 | |
950.2.l.i | 18 | 5.c | odd | 4 | 1 | ||
950.2.l.i | 18 | 95.q | odd | 36 | 1 | ||
950.2.u.g | 36 | 1.a | even | 1 | 1 | trivial | |
950.2.u.g | 36 | 5.b | even | 2 | 1 | inner | |
950.2.u.g | 36 | 19.e | even | 9 | 1 | inner | |
950.2.u.g | 36 | 95.p | even | 18 | 1 | inner | |
3610.2.a.bi | 9 | 95.q | odd | 36 | 1 | ||
3610.2.a.bj | 9 | 95.r | even | 36 | 1 |
Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(950, [\chi])\):
\(T_{3}^{36} - \cdots\) |
\(32\!\cdots\!84\)\( T_{7}^{18} + \)\(20\!\cdots\!72\)\( T_{7}^{16} - \)\(93\!\cdots\!60\)\( T_{7}^{14} + \)\(32\!\cdots\!32\)\( T_{7}^{12} - \)\(80\!\cdots\!48\)\( T_{7}^{10} + \)\(14\!\cdots\!80\)\( T_{7}^{8} - \)\(16\!\cdots\!12\)\( T_{7}^{6} + \)\(11\!\cdots\!68\)\( T_{7}^{4} - 625528209408 T_{7}^{2} + 342102016 \)">\(T_{7}^{36} - \cdots\) |