Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [92,10,Mod(91,92)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(92, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("92.91");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 92 = 2^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 92.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(47.3832969271\) |
Analytic rank: | \(0\) |
Dimension: | \(100\) |
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.
comment: embeddings in the coefficient field
gp: mfembed(f)
Label | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
91.1 | −22.5638 | − | 1.69576i | − | 66.5026i | 506.249 | + | 76.5257i | − | 1801.05i | −112.773 | + | 1500.55i | 4087.65 | −11293.1 | − | 2585.19i | 15260.4 | −3054.15 | + | 40638.4i | ||||||
91.2 | −22.5638 | − | 1.69576i | − | 66.5026i | 506.249 | + | 76.5257i | 1801.05i | −112.773 | + | 1500.55i | −4087.65 | −11293.1 | − | 2585.19i | 15260.4 | 3054.15 | − | 40638.4i | |||||||
91.3 | −22.5638 | + | 1.69576i | 66.5026i | 506.249 | − | 76.5257i | − | 1801.05i | −112.773 | − | 1500.55i | −4087.65 | −11293.1 | + | 2585.19i | 15260.4 | 3054.15 | + | 40638.4i | |||||||
91.4 | −22.5638 | + | 1.69576i | 66.5026i | 506.249 | − | 76.5257i | 1801.05i | −112.773 | − | 1500.55i | 4087.65 | −11293.1 | + | 2585.19i | 15260.4 | −3054.15 | − | 40638.4i | ||||||||
91.5 | −22.5102 | − | 2.30032i | 230.553i | 501.417 | + | 103.561i | − | 660.081i | 530.348 | − | 5189.80i | −9465.28 | −11048.8 | − | 3484.61i | −33471.9 | −1518.40 | + | 14858.6i | |||||||
91.6 | −22.5102 | − | 2.30032i | 230.553i | 501.417 | + | 103.561i | 660.081i | 530.348 | − | 5189.80i | 9465.28 | −11048.8 | − | 3484.61i | −33471.9 | 1518.40 | − | 14858.6i | ||||||||
91.7 | −22.5102 | + | 2.30032i | − | 230.553i | 501.417 | − | 103.561i | − | 660.081i | 530.348 | + | 5189.80i | 9465.28 | −11048.8 | + | 3484.61i | −33471.9 | 1518.40 | + | 14858.6i | ||||||
91.8 | −22.5102 | + | 2.30032i | − | 230.553i | 501.417 | − | 103.561i | 660.081i | 530.348 | + | 5189.80i | −9465.28 | −11048.8 | + | 3484.61i | −33471.9 | −1518.40 | − | 14858.6i | |||||||
91.9 | −20.8820 | − | 8.71446i | 73.2819i | 360.116 | + | 363.951i | − | 1060.89i | 638.612 | − | 1530.27i | 7324.58 | −4348.32 | − | 10738.2i | 14312.8 | −9245.13 | + | 22153.6i | |||||||
91.10 | −20.8820 | − | 8.71446i | 73.2819i | 360.116 | + | 363.951i | 1060.89i | 638.612 | − | 1530.27i | −7324.58 | −4348.32 | − | 10738.2i | 14312.8 | 9245.13 | − | 22153.6i | ||||||||
91.11 | −20.8820 | + | 8.71446i | − | 73.2819i | 360.116 | − | 363.951i | − | 1060.89i | 638.612 | + | 1530.27i | −7324.58 | −4348.32 | + | 10738.2i | 14312.8 | 9245.13 | + | 22153.6i | ||||||
91.12 | −20.8820 | + | 8.71446i | − | 73.2819i | 360.116 | − | 363.951i | 1060.89i | 638.612 | + | 1530.27i | 7324.58 | −4348.32 | + | 10738.2i | 14312.8 | −9245.13 | − | 22153.6i | |||||||
91.13 | −20.1734 | − | 10.2486i | − | 108.291i | 301.934 | + | 413.497i | − | 580.393i | −1109.82 | + | 2184.60i | −6232.00 | −1853.30 | − | 11436.0i | 7956.11 | −5948.19 | + | 11708.5i | ||||||
91.14 | −20.1734 | − | 10.2486i | − | 108.291i | 301.934 | + | 413.497i | 580.393i | −1109.82 | + | 2184.60i | 6232.00 | −1853.30 | − | 11436.0i | 7956.11 | 5948.19 | − | 11708.5i | |||||||
91.15 | −20.1734 | + | 10.2486i | 108.291i | 301.934 | − | 413.497i | − | 580.393i | −1109.82 | − | 2184.60i | 6232.00 | −1853.30 | + | 11436.0i | 7956.11 | 5948.19 | + | 11708.5i | |||||||
91.16 | −20.1734 | + | 10.2486i | 108.291i | 301.934 | − | 413.497i | 580.393i | −1109.82 | − | 2184.60i | −6232.00 | −1853.30 | + | 11436.0i | 7956.11 | −5948.19 | − | 11708.5i | ||||||||
91.17 | −19.9692 | − | 10.6410i | − | 226.780i | 285.537 | + | 424.985i | − | 2286.72i | −2413.17 | + | 4528.61i | −4221.06 | −1179.68 | − | 11525.0i | −31746.2 | −24333.0 | + | 45663.9i | ||||||
91.18 | −19.9692 | − | 10.6410i | − | 226.780i | 285.537 | + | 424.985i | 2286.72i | −2413.17 | + | 4528.61i | 4221.06 | −1179.68 | − | 11525.0i | −31746.2 | 24333.0 | − | 45663.9i | |||||||
91.19 | −19.9692 | + | 10.6410i | 226.780i | 285.537 | − | 424.985i | − | 2286.72i | −2413.17 | − | 4528.61i | 4221.06 | −1179.68 | + | 11525.0i | −31746.2 | 24333.0 | + | 45663.9i | |||||||
91.20 | −19.9692 | + | 10.6410i | 226.780i | 285.537 | − | 424.985i | 2286.72i | −2413.17 | − | 4528.61i | −4221.06 | −1179.68 | + | 11525.0i | −31746.2 | −24333.0 | − | 45663.9i | ||||||||
See all 100 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
4.b | odd | 2 | 1 | inner |
23.b | odd | 2 | 1 | inner |
92.b | even | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 92.10.b.c | ✓ | 100 |
4.b | odd | 2 | 1 | inner | 92.10.b.c | ✓ | 100 |
23.b | odd | 2 | 1 | inner | 92.10.b.c | ✓ | 100 |
92.b | even | 2 | 1 | inner | 92.10.b.c | ✓ | 100 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
92.10.b.c | ✓ | 100 | 1.a | even | 1 | 1 | trivial |
92.10.b.c | ✓ | 100 | 4.b | odd | 2 | 1 | inner |
92.10.b.c | ✓ | 100 | 23.b | odd | 2 | 1 | inner |
92.10.b.c | ✓ | 100 | 92.b | even | 2 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{50} + 629857 T_{3}^{48} + 184238593368 T_{3}^{46} + \cdots + 42\!\cdots\!04 \)
acting on \(S_{10}^{\mathrm{new}}(92, [\chi])\).