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Properties

Label 184.2.i.a
Level $184$
Weight $2$
Character orbit 184.i
Analytic conductor $1.469$
Analytic rank $0$
Dimension $30$
Inner twists $2$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [184,2,Mod(9,184)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("184.9"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(184, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 0, 10])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 184 = 2^{3} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 184.i (of order \(11\), degree \(10\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [30,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.46924739719\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 30 q - 2 q^{3} + 2 q^{5} + 13 q^{7} - 23 q^{9} - 4 q^{11} - 2 q^{15} + 26 q^{17} - 5 q^{19} + 2 q^{21} - q^{23} - 11 q^{25} + 19 q^{27} - 19 q^{29} - 6 q^{31} + 20 q^{33} - 63 q^{35} + 36 q^{37} - 22 q^{39}+ \cdots + 201 q^{99}+O(q^{100}) \) 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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
9.1 0 −0.366836 − 0.423352i 0 0.533687 + 3.71187i 0 −1.40226 + 3.07052i 0 0.382287 − 2.65886i 0
9.2 0 −0.211214 − 0.243754i 0 −0.354040 − 2.46240i 0 0.114164 − 0.249984i 0 0.412140 − 2.86650i 0
9.3 0 1.83472 + 2.11738i 0 0.104983 + 0.730173i 0 1.59958 − 3.50260i 0 −0.690154 + 4.80013i 0
25.1 0 −0.459912 − 3.19876i 0 2.70555 + 0.794422i 0 1.70484 − 1.96749i 0 −7.14204 + 2.09709i 0
25.2 0 −0.0579878 − 0.403314i 0 −2.25586 − 0.662379i 0 2.18085 − 2.51684i 0 2.71918 − 0.798423i 0
25.3 0 0.278454 + 1.93669i 0 1.46929 + 0.431422i 0 −0.616482 + 0.711458i 0 −0.794747 + 0.233359i 0
41.1 0 −0.366836 + 0.423352i 0 0.533687 − 3.71187i 0 −1.40226 − 3.07052i 0 0.382287 + 2.65886i 0
41.2 0 −0.211214 + 0.243754i 0 −0.354040 + 2.46240i 0 0.114164 + 0.249984i 0 0.412140 + 2.86650i 0
41.3 0 1.83472 − 2.11738i 0 0.104983 − 0.730173i 0 1.59958 + 3.50260i 0 −0.690154 − 4.80013i 0
49.1 0 −1.35007 + 2.95624i 0 −0.836673 + 0.965572i 0 0.644005 − 0.413877i 0 −4.95209 − 5.71501i 0
49.2 0 0.0870522 − 0.190618i 0 0.0866818 − 0.100036i 0 2.06143 − 1.32480i 0 1.93583 + 2.23406i 0
49.3 0 1.14478 − 2.50671i 0 2.05971 − 2.37704i 0 −2.73308 + 1.75644i 0 −3.00852 − 3.47201i 0
73.1 0 −1.91205 + 0.561427i 0 1.04139 + 0.669262i 0 0.154214 + 1.07258i 0 0.816957 − 0.525026i 0
73.2 0 −0.262516 + 0.0770816i 0 −3.42011 − 2.19797i 0 −0.433778 − 3.01699i 0 −2.46079 + 1.58145i 0
73.3 0 1.37739 − 0.404437i 0 0.696214 + 0.447429i 0 0.722941 + 5.02816i 0 −0.790138 + 0.507791i 0
81.1 0 −0.459912 + 3.19876i 0 2.70555 − 0.794422i 0 1.70484 + 1.96749i 0 −7.14204 − 2.09709i 0
81.2 0 −0.0579878 + 0.403314i 0 −2.25586 + 0.662379i 0 2.18085 + 2.51684i 0 2.71918 + 0.798423i 0
81.3 0 0.278454 − 1.93669i 0 1.46929 − 0.431422i 0 −0.616482 − 0.711458i 0 −0.794747 − 0.233359i 0
105.1 0 −2.33471 − 1.50043i 0 −1.43825 + 3.14933i 0 3.52121 + 1.03392i 0 1.95334 + 4.27722i 0
105.2 0 −0.741585 − 0.476588i 0 1.02542 − 2.24535i 0 −1.34070 − 0.393666i 0 −0.923433 − 2.02204i 0
See all 30 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 9.3
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 184.2.i.a ✓ 30
4.b odd 2 1 368.2.m.f 30
23.c even 11 1 inner 184.2.i.a ✓ 30
23.c even 11 1 4232.2.a.y 15
23.d odd 22 1 4232.2.a.z 15
92.g odd 22 1 368.2.m.f 30
92.g odd 22 1 8464.2.a.ci 15
92.h even 22 1 8464.2.a.cj 15
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
184.2.i.a ✓ 30 1.a even 1 1 trivial
184.2.i.a ✓ 30 23.c even 11 1 inner
368.2.m.f 30 4.b odd 2 1
368.2.m.f 30 92.g odd 22 1
4232.2.a.y 15 23.c even 11 1
4232.2.a.z 15 23.d odd 22 1
8464.2.a.ci 15 92.g odd 22 1
8464.2.a.cj 15 92.h even 22 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{30} + 2 T_{3}^{29} + 18 T_{3}^{28} + 31 T_{3}^{27} + 171 T_{3}^{26} + 413 T_{3}^{25} + 1383 T_{3}^{24} + \cdots + 121 \) acting on \(S_{2}^{\mathrm{new}}(184, [\chi])\). Copy content Toggle raw display