Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [24,10,Mod(11,24)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(24, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("24.11");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.f (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: | \(12.3608600679\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
11.1 | −22.4402 | − | 2.90472i | −9.88844 | − | 139.947i | 495.125 | + | 130.365i | −1964.03 | −184.609 | + | 3169.17i | − | 5094.35i | −10732.0 | − | 4363.62i | −19487.4 | + | 2767.72i | 44073.2 | + | 5704.95i | |||
11.2 | −22.4402 | + | 2.90472i | −9.88844 | + | 139.947i | 495.125 | − | 130.365i | −1964.03 | −184.609 | − | 3169.17i | 5094.35i | −10732.0 | + | 4363.62i | −19487.4 | − | 2767.72i | 44073.2 | − | 5704.95i | ||||
11.3 | −22.1527 | − | 4.61075i | 103.462 | − | 94.7559i | 469.482 | + | 204.281i | 1830.99 | −2728.85 | + | 1622.06i | 9010.00i | −9458.39 | − | 6690.04i | 1725.65 | − | 19607.2i | −40561.4 | − | 8442.26i | ||||
11.4 | −22.1527 | + | 4.61075i | 103.462 | + | 94.7559i | 469.482 | − | 204.281i | 1830.99 | −2728.85 | − | 1622.06i | − | 9010.00i | −9458.39 | + | 6690.04i | 1725.65 | + | 19607.2i | −40561.4 | + | 8442.26i | |||
11.5 | −21.2599 | − | 7.74704i | −137.072 | + | 29.9043i | 391.967 | + | 329.403i | 546.341 | 3145.81 | + | 426.141i | − | 8986.35i | −5781.27 | − | 10039.7i | 17894.5 | − | 8198.08i | −11615.2 | − | 4232.53i | |||
11.6 | −21.2599 | + | 7.74704i | −137.072 | − | 29.9043i | 391.967 | − | 329.403i | 546.341 | 3145.81 | − | 426.141i | 8986.35i | −5781.27 | + | 10039.7i | 17894.5 | + | 8198.08i | −11615.2 | + | 4232.53i | ||||
11.7 | −17.0550 | − | 14.8703i | 139.823 | + | 11.5135i | 69.7466 | + | 507.227i | −1287.02 | −2213.47 | − | 2275.57i | − | 1676.19i | 6353.11 | − | 9687.92i | 19417.9 | + | 3219.69i | 21950.1 | + | 19138.4i | |||
11.8 | −17.0550 | + | 14.8703i | 139.823 | − | 11.5135i | 69.7466 | − | 507.227i | −1287.02 | −2213.47 | + | 2275.57i | 1676.19i | 6353.11 | + | 9687.92i | 19417.9 | − | 3219.69i | 21950.1 | − | 19138.4i | ||||
11.9 | −16.4606 | − | 15.5258i | −10.8849 | + | 139.873i | 29.9001 | + | 511.126i | 969.618 | 2350.81 | − | 2133.39i | 4447.25i | 7443.46 | − | 8877.65i | −19446.0 | − | 3045.02i | −15960.5 | − | 15054.1i | ||||
11.10 | −16.4606 | + | 15.5258i | −10.8849 | − | 139.873i | 29.9001 | − | 511.126i | 969.618 | 2350.81 | + | 2133.39i | − | 4447.25i | 7443.46 | + | 8877.65i | −19446.0 | + | 3045.02i | −15960.5 | + | 15054.1i | |||
11.11 | −12.5598 | − | 18.8216i | −90.7300 | − | 107.010i | −196.503 | + | 472.790i | 189.613 | −874.541 | + | 3051.70i | 5305.67i | 11366.7 | − | 2239.64i | −3219.13 | + | 19418.0i | −2381.50 | − | 3568.82i | ||||
11.12 | −12.5598 | + | 18.8216i | −90.7300 | + | 107.010i | −196.503 | − | 472.790i | 189.613 | −874.541 | − | 3051.70i | − | 5305.67i | 11366.7 | + | 2239.64i | −3219.13 | − | 19418.0i | −2381.50 | + | 3568.82i | |||
11.13 | −5.61849 | − | 21.9188i | 80.4694 | − | 114.925i | −448.865 | + | 246.301i | 1576.73 | −2971.12 | − | 1118.09i | − | 11117.7i | 7920.55 | + | 8454.74i | −6732.34 | − | 18495.8i | −8858.84 | − | 34560.0i | |||
11.14 | −5.61849 | + | 21.9188i | 80.4694 | + | 114.925i | −448.865 | − | 246.301i | 1576.73 | −2971.12 | + | 1118.09i | 11117.7i | 7920.55 | − | 8454.74i | −6732.34 | + | 18495.8i | −8858.84 | + | 34560.0i | ||||
11.15 | −4.59065 | − | 22.1568i | −123.179 | + | 67.1567i | −469.852 | + | 203.429i | −2552.17 | 2053.45 | + | 2420.96i | − | 3042.59i | 6664.26 | + | 9476.57i | 10663.0 | − | 16544.5i | 11716.1 | + | 56548.1i | |||
11.16 | −4.59065 | + | 22.1568i | −123.179 | − | 67.1567i | −469.852 | − | 203.429i | −2552.17 | 2053.45 | − | 2420.96i | 3042.59i | 6664.26 | − | 9476.57i | 10663.0 | + | 16544.5i | 11716.1 | − | 56548.1i | ||||
11.17 | 4.59065 | − | 22.1568i | −123.179 | + | 67.1567i | −469.852 | − | 203.429i | 2552.17 | 922.511 | + | 3037.54i | 3042.59i | −6664.26 | + | 9476.57i | 10663.0 | − | 16544.5i | 11716.1 | − | 56548.1i | ||||
11.18 | 4.59065 | + | 22.1568i | −123.179 | − | 67.1567i | −469.852 | + | 203.429i | 2552.17 | 922.511 | − | 3037.54i | − | 3042.59i | −6664.26 | − | 9476.57i | 10663.0 | + | 16544.5i | 11716.1 | + | 56548.1i | |||
11.19 | 5.61849 | − | 21.9188i | 80.4694 | − | 114.925i | −448.865 | − | 246.301i | −1576.73 | −2066.89 | − | 2409.49i | 11117.7i | −7920.55 | + | 8454.74i | −6732.34 | − | 18495.8i | −8858.84 | + | 34560.0i | ||||
11.20 | 5.61849 | + | 21.9188i | 80.4694 | + | 114.925i | −448.865 | + | 246.301i | −1576.73 | −2066.89 | + | 2409.49i | − | 11117.7i | −7920.55 | − | 8454.74i | −6732.34 | + | 18495.8i | −8858.84 | − | 34560.0i | |||
See all 32 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
3.b | odd | 2 | 1 | inner |
8.d | odd | 2 | 1 | inner |
24.f | even | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 24.10.f.b | ✓ | 32 |
3.b | odd | 2 | 1 | inner | 24.10.f.b | ✓ | 32 |
4.b | odd | 2 | 1 | 96.10.f.b | 32 | ||
8.b | even | 2 | 1 | 96.10.f.b | 32 | ||
8.d | odd | 2 | 1 | inner | 24.10.f.b | ✓ | 32 |
12.b | even | 2 | 1 | 96.10.f.b | 32 | ||
24.f | even | 2 | 1 | inner | 24.10.f.b | ✓ | 32 |
24.h | odd | 2 | 1 | 96.10.f.b | 32 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
24.10.f.b | ✓ | 32 | 1.a | even | 1 | 1 | trivial |
24.10.f.b | ✓ | 32 | 3.b | odd | 2 | 1 | inner |
24.10.f.b | ✓ | 32 | 8.d | odd | 2 | 1 | inner |
24.10.f.b | ✓ | 32 | 24.f | even | 2 | 1 | inner |
96.10.f.b | 32 | 4.b | odd | 2 | 1 | ||
96.10.f.b | 32 | 8.b | even | 2 | 1 | ||
96.10.f.b | 32 | 12.b | even | 2 | 1 | ||
96.10.f.b | 32 | 24.h | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{16} - 19140624 T_{5}^{14} + 143959473638496 T_{5}^{12} + \cdots + 34\!\cdots\!00 \) acting on \(S_{10}^{\mathrm{new}}(24, [\chi])\).