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Properties

Label 46.4.c.b
Level $46$
Weight $4$
Character orbit 46.c
Analytic conductor $2.714$
Analytic rank $0$
Dimension $30$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [46,4,Mod(3,46)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(46, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("46.3");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 46 = 2 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 46.c (of order \(11\), degree \(10\), 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: \(2.71408786026\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(3\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 30 q + 6 q^{2} + 2 q^{3} - 12 q^{4} - 4 q^{6} - 115 q^{7} + 24 q^{8} - 83 q^{9} - 30 q^{11} + 52 q^{12} + 104 q^{13} - 56 q^{14} + 492 q^{15} - 48 q^{16} + 274 q^{17} + 166 q^{18} - 381 q^{19} - 176 q^{20}+ \cdots + 7587 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
3.1 0.284630 + 1.97964i −3.62606 + 7.93996i −3.83797 + 1.12693i 6.91905 − 7.98501i −16.7504 − 4.91835i −16.1046 + 10.3498i −3.32332 − 7.27706i −32.2134 − 37.1762i 17.7768 + 11.4245i
3.2 0.284630 + 1.97964i −0.493326 + 1.08023i −3.83797 + 1.12693i −10.8228 + 12.4902i −2.27889 − 0.669143i 0.379417 − 0.243837i −3.32332 − 7.27706i 16.7577 + 19.3394i −27.8066 − 17.8702i
3.3 0.284630 + 1.97964i 2.60327 − 5.70036i −3.83797 + 1.12693i 6.82565 − 7.87722i 12.0256 + 3.53105i 9.96901 − 6.40669i −3.32332 − 7.27706i −8.03584 − 9.27386i 17.5369 + 11.2703i
9.1 1.91899 − 0.563465i −3.58705 − 4.13968i 3.36501 − 2.16256i −1.27675 − 8.88002i −9.21607 − 5.92281i 1.52711 − 3.34391i 5.23889 − 6.04600i −0.427496 + 2.97330i −7.45366 − 16.3212i
9.2 1.91899 − 0.563465i 1.58551 + 1.82978i 3.36501 − 2.16256i 2.65345 + 18.4552i 4.07359 + 2.61794i 8.33333 − 18.2475i 5.23889 − 6.04600i 3.00826 − 20.9229i 15.4908 + 33.9201i
9.3 1.91899 − 0.563465i 4.34636 + 5.01597i 3.36501 − 2.16256i −1.02987 − 7.16288i 11.1669 + 7.17655i −7.28047 + 15.9420i 5.23889 − 6.04600i −2.42659 + 16.8773i −6.01233 − 13.1652i
13.1 1.30972 + 1.51150i −7.37753 − 4.74125i −0.569259 + 3.95929i −7.38096 + 16.1620i −2.49611 − 17.3608i −23.1426 − 6.79527i −6.73003 + 4.32513i 20.7323 + 45.3973i −34.0959 + 10.0115i
13.2 1.30972 + 1.51150i 2.26977 + 1.45869i −0.569259 + 3.95929i −3.30726 + 7.24189i 0.767954 + 5.34124i 19.2136 + 5.64162i −6.73003 + 4.32513i −8.19213 − 17.9383i −15.2777 + 4.48594i
13.3 1.30972 + 1.51150i 7.23466 + 4.64943i −0.569259 + 3.95929i 5.71615 − 12.5166i 2.44777 + 17.0246i −32.6087 − 9.57479i −6.73003 + 4.32513i 19.5068 + 42.7140i 26.4054 − 7.75334i
25.1 −1.68251 − 1.08128i −1.28869 − 8.96304i 1.66166 + 3.63853i −3.51873 − 1.03319i −7.52334 + 16.4738i −6.62723 + 7.64823i 1.13852 − 7.91857i −52.7690 + 15.4944i 4.80311 + 5.54308i
25.2 −1.68251 − 1.08128i 0.0510239 + 0.354879i 1.66166 + 3.63853i 8.79133 + 2.58137i 0.297876 − 0.652258i 10.6913 − 12.3384i 1.13852 − 7.91857i 25.7830 − 7.57056i −12.0003 − 13.8491i
25.3 −1.68251 − 1.08128i 0.625435 + 4.35000i 1.66166 + 3.63853i −12.8224 − 3.76500i 3.65127 − 7.99517i −19.0515 + 21.9866i 1.13852 − 7.91857i 7.37501 − 2.16550i 17.5028 + 20.1993i
27.1 −0.830830 − 1.81926i −4.95549 + 1.45506i −2.61944 + 3.02300i 5.53427 + 3.55666i 6.76431 + 7.80643i 4.17332 + 29.0261i 7.67594 + 2.25386i −0.274197 + 0.176216i 1.87247 − 13.0233i
27.2 −0.830830 − 1.81926i −0.430531 + 0.126415i −2.61944 + 3.02300i −13.5914 − 8.73463i 0.587680 + 0.678219i −2.74097 − 19.0638i 7.67594 + 2.25386i −22.5445 + 14.4885i −4.59850 + 31.9833i
27.3 −0.830830 − 1.81926i 4.04264 − 1.18703i −2.61944 + 3.02300i 17.3103 + 11.1246i −5.51826 − 6.36842i −4.23099 − 29.4272i 7.67594 + 2.25386i −7.77992 + 4.99985i 5.85675 − 40.7346i
29.1 −0.830830 + 1.81926i −4.95549 − 1.45506i −2.61944 − 3.02300i 5.53427 − 3.55666i 6.76431 − 7.80643i 4.17332 − 29.0261i 7.67594 − 2.25386i −0.274197 − 0.176216i 1.87247 + 13.0233i
29.2 −0.830830 + 1.81926i −0.430531 − 0.126415i −2.61944 − 3.02300i −13.5914 + 8.73463i 0.587680 − 0.678219i −2.74097 + 19.0638i 7.67594 − 2.25386i −22.5445 − 14.4885i −4.59850 − 31.9833i
29.3 −0.830830 + 1.81926i 4.04264 + 1.18703i −2.61944 − 3.02300i 17.3103 − 11.1246i −5.51826 + 6.36842i −4.23099 + 29.4272i 7.67594 − 2.25386i −7.77992 − 4.99985i 5.85675 + 40.7346i
31.1 0.284630 − 1.97964i −3.62606 − 7.93996i −3.83797 − 1.12693i 6.91905 + 7.98501i −16.7504 + 4.91835i −16.1046 − 10.3498i −3.32332 + 7.27706i −32.2134 + 37.1762i 17.7768 − 11.4245i
31.2 0.284630 − 1.97964i −0.493326 − 1.08023i −3.83797 − 1.12693i −10.8228 − 12.4902i −2.27889 + 0.669143i 0.379417 + 0.243837i −3.32332 + 7.27706i 16.7577 − 19.3394i −27.8066 + 17.8702i
See all 30 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 3.3
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.c even 11 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 46.4.c.b ✓ 30
23.c even 11 1 inner 46.4.c.b ✓ 30
23.c even 11 1 1058.4.a.u 15
23.d odd 22 1 1058.4.a.t 15
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
46.4.c.b ✓ 30 1.a even 1 1 trivial
46.4.c.b ✓ 30 23.c even 11 1 inner
1058.4.a.t 15 23.d odd 22 1
1058.4.a.u 15 23.c even 11 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{30} - 2 T_{3}^{29} + 84 T_{3}^{28} - 511 T_{3}^{27} + 6667 T_{3}^{26} - 11781 T_{3}^{25} + \cdots + 26\!\cdots\!29 \) acting on \(S_{4}^{\mathrm{new}}(46, [\chi])\). Copy content Toggle raw display