↑

Properties

Label 24.10.f.b
Level $24$
Weight $10$
Character orbit 24.f
Analytic conductor $12.361$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 192 q^{3} + 1364 q^{4} - 5256 q^{6} + 3264 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q - 192 q^{3} + 1364 q^{4} - 5256 q^{6} + 3264 q^{9} - 6552 q^{10} + 155844 q^{12} + 297896 q^{16} - 2207112 q^{18} - 2461184 q^{19} - 4404320 q^{22} + 2017992 q^{24} + 14062496 q^{25} - 1964736 q^{27} + 4838256 q^{28} - 6949488 q^{30} + 14722656 q^{33} - 19509200 q^{34} - 9628644 q^{36} - 10890144 q^{40} + 1569768 q^{42} + 143476480 q^{43} + 9112608 q^{46} - 65606472 q^{48} - 194625760 q^{49} + 188122368 q^{51} - 106097184 q^{52} - 9718776 q^{54} - 133315104 q^{57} + 36812808 q^{58} + 86058096 q^{60} + 266450288 q^{64} - 296675928 q^{66} - 528472448 q^{67} - 108471888 q^{70} + 637640400 q^{72} - 622799936 q^{73} - 90490560 q^{75} + 1886230072 q^{76} - 449212272 q^{78} + 622852128 q^{81} - 673950464 q^{82} - 349697568 q^{84} + 3011704624 q^{88} - 831547512 q^{90} + 707197824 q^{91} + 582965568 q^{94} - 2841493680 q^{96} - 4588539776 q^{97} + 4346671488 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 11.32
Significant digits:
Format:

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 \(S_{10}^{\mathrm{new}}(24, [\chi])\). Copy content Toggle raw display