↑

Properties

Label 184.4.i.a
Level $184$
Weight $4$
Character orbit 184.i
Analytic conductor $10.856$
Analytic rank $0$
Dimension $90$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [184,4,Mod(9,184)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
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, 4, names="a")
 
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, 4); N := Newforms(S);
 
Level: \( N \) \(=\) \( 184 = 2^{3} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 184.i (of order \(11\), degree \(10\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [90,0,-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: \(10.8563514411\)
Analytic rank: \(0\)
Dimension: \(90\)
Relative dimension: \(9\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 90 q - 2 q^{3} - 87 q^{7} - 113 q^{9} - 6 q^{11} - 8 q^{13} - 6 q^{15} + 306 q^{17} + 275 q^{19} + 350 q^{21} - 23 q^{23} - 289 q^{25} + 511 q^{27} + 309 q^{29} - 314 q^{31} - 1444 q^{33} - 1895 q^{35}+ \cdots + 5967 q^{99}+O(q^{100}) \) 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 −5.94247 − 6.85798i 0 1.22403 + 8.51331i 0 −0.883012 + 1.93353i 0 −7.87639 + 54.7815i 0
9.2 0 −4.18363 − 4.82817i 0 −1.83072 − 12.7329i 0 5.01523 − 10.9818i 0 −1.96594 + 13.6734i 0
9.3 0 −2.35591 − 2.71886i 0 −1.19678 − 8.32376i 0 0.353002 − 0.772967i 0 2.00059 − 13.9144i 0
9.4 0 −0.706025 − 0.814796i 0 2.59602 + 18.0557i 0 −10.5592 + 23.1213i 0 3.67708 − 25.5746i 0
9.5 0 −0.109976 − 0.126919i 0 0.998408 + 6.94408i 0 6.58373 − 14.4164i 0 3.83849 − 26.6973i 0
9.6 0 0.658159 + 0.759556i 0 −1.68723 − 11.7349i 0 −15.1088 + 33.0837i 0 3.69875 − 25.7254i 0
9.7 0 3.54956 + 4.09641i 0 −1.80389 − 12.5463i 0 6.26253 − 13.7130i 0 −0.338702 + 2.35572i 0
9.8 0 4.52690 + 5.22433i 0 1.93514 + 13.4592i 0 6.00851 − 13.1568i 0 −2.95822 + 20.5749i 0
9.9 0 5.82006 + 6.71670i 0 −0.234972 − 1.63426i 0 −8.08155 + 17.6961i 0 −7.39855 + 51.4580i 0
25.1 0 −1.44601 − 10.0572i 0 8.09489 + 2.37687i 0 −19.4919 + 22.4948i 0 −73.1500 + 21.4788i 0
25.2 0 −0.978797 − 6.80768i 0 −0.683572 − 0.200715i 0 16.8123 − 19.4024i 0 −19.4802 + 5.71990i 0
25.3 0 −0.477746 − 3.32280i 0 −17.5785 − 5.16150i 0 −4.65206 + 5.36877i 0 15.0936 − 4.43187i 0
25.4 0 −0.320892 − 2.23185i 0 −0.594725 − 0.174627i 0 −11.2697 + 13.0059i 0 21.0281 − 6.17441i 0
25.5 0 −0.259998 − 1.80833i 0 19.7692 + 5.80477i 0 7.16325 − 8.26683i 0 22.7039 − 6.66645i 0
25.6 0 0.400660 + 2.78665i 0 −5.04804 − 1.48224i 0 −8.61674 + 9.94424i 0 18.3014 − 5.37378i 0
25.7 0 0.678262 + 4.71742i 0 8.45978 + 2.48402i 0 6.03178 − 6.96105i 0 4.11232 − 1.20749i 0
25.8 0 0.961609 + 6.68814i 0 −17.3126 − 5.08343i 0 23.0068 − 26.5513i 0 −17.9002 + 5.25597i 0
25.9 0 1.20346 + 8.37027i 0 4.89348 + 1.43685i 0 −10.3520 + 11.9469i 0 −42.7068 + 12.5398i 0
41.1 0 −5.94247 + 6.85798i 0 1.22403 − 8.51331i 0 −0.883012 − 1.93353i 0 −7.87639 − 54.7815i 0
41.2 0 −4.18363 + 4.82817i 0 −1.83072 + 12.7329i 0 5.01523 + 10.9818i 0 −1.96594 − 13.6734i 0
See all 90 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 9.9
Significant digits:
Format:

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 184.4.i.a ✓ 90
23.c even 11 1 inner 184.4.i.a ✓ 90
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
184.4.i.a ✓ 90 1.a even 1 1 trivial
184.4.i.a ✓ 90 23.c even 11 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{90} + 2 T_{3}^{89} + 180 T_{3}^{88} + 223 T_{3}^{87} + 21633 T_{3}^{86} + 21233 T_{3}^{85} + \cdots + 11\!\cdots\!01 \) acting on \(S_{4}^{\mathrm{new}}(184, [\chi])\). Copy content Toggle raw display