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Properties

Label 187.4.d.a
Level $187$
Weight $4$
Character orbit 187.d
Analytic conductor $11.033$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [187,4,Mod(67,187)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(187, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("187.67");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 187 = 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 187.d (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: \(11.0333571711\)
Analytic rank: \(0\)
Dimension: \(44\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 44 q - 4 q^{2} + 192 q^{4} - 48 q^{8} - 360 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 44 q - 4 q^{2} + 192 q^{4} - 48 q^{8} - 360 q^{9} - 168 q^{13} - 48 q^{15} + 1120 q^{16} - 28 q^{17} + 40 q^{18} - 88 q^{19} + 48 q^{21} - 456 q^{25} + 924 q^{26} - 916 q^{30} - 1108 q^{32} - 132 q^{33} - 1004 q^{34} - 696 q^{35} - 1724 q^{36} - 852 q^{38} + 2880 q^{42} - 568 q^{43} - 1824 q^{47} - 2060 q^{49} + 3900 q^{50} - 2036 q^{51} - 1648 q^{52} + 180 q^{53} - 440 q^{55} + 2204 q^{59} - 2200 q^{60} + 2872 q^{64} + 528 q^{66} + 1028 q^{67} + 3740 q^{68} - 576 q^{69} + 3144 q^{70} + 6956 q^{72} - 5564 q^{76} + 528 q^{77} + 620 q^{81} + 1504 q^{83} - 1604 q^{84} - 2932 q^{85} + 4436 q^{86} + 3776 q^{87} - 1216 q^{89} + 3704 q^{93} + 5352 q^{94} + 1784 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
67.1 −5.58897 − 7.59978i 23.2366 − 19.6769i 42.4750i − 0.165042i −85.1571 −30.7566 109.974i
67.2 −5.58897 7.59978i 23.2366 19.6769i − 42.4750i 0.165042i −85.1571 −30.7566 − 109.974i
67.3 −4.95154 − 0.324089i 16.5177 1.41568i 1.60474i − 11.3936i −42.1758 26.8950 − 7.00977i
67.4 −4.95154 0.324089i 16.5177 − 1.41568i − 1.60474i 11.3936i −42.1758 26.8950 7.00977i
67.5 −4.89812 − 7.12234i 15.9916 11.7499i 34.8861i − 31.8696i −39.1437 −23.7277 − 57.5525i
67.6 −4.89812 7.12234i 15.9916 − 11.7499i − 34.8861i 31.8696i −39.1437 −23.7277 57.5525i
67.7 −4.59596 − 6.81259i 13.1228 17.7255i 31.3104i 29.1269i −23.5443 −19.4114 − 81.4657i
67.8 −4.59596 6.81259i 13.1228 − 17.7255i − 31.3104i − 29.1269i −23.5443 −19.4114 81.4657i
67.9 −3.64158 − 0.763359i 5.26110 − 12.3323i 2.77983i 6.63841i 9.97394 26.4173 44.9089i
67.10 −3.64158 0.763359i 5.26110 12.3323i − 2.77983i − 6.63841i 9.97394 26.4173 − 44.9089i
67.11 −3.60073 − 8.70374i 4.96525 − 0.316245i 31.3398i − 5.93203i 10.9273 −48.7551 1.13871i
67.12 −3.60073 8.70374i 4.96525 0.316245i − 31.3398i 5.93203i 10.9273 −48.7551 − 1.13871i
67.13 −2.67229 − 3.04731i −0.858879 − 14.5314i 8.14328i − 32.1496i 23.6735 17.7139 38.8320i
67.14 −2.67229 3.04731i −0.858879 14.5314i − 8.14328i 32.1496i 23.6735 17.7139 − 38.8320i
67.15 −1.55595 − 0.779521i −5.57902 11.0416i 1.21290i − 25.3132i 21.1283 26.3923 − 17.1801i
67.16 −1.55595 0.779521i −5.57902 − 11.0416i − 1.21290i 25.3132i 21.1283 26.3923 17.1801i
67.17 −1.45580 − 5.50148i −5.88065 7.22938i 8.00905i 6.72296i 20.2074 −3.26632 − 10.5245i
67.18 −1.45580 5.50148i −5.88065 − 7.22938i − 8.00905i − 6.72296i 20.2074 −3.26632 10.5245i
67.19 −1.40081 − 6.23790i −6.03773 16.8728i 8.73813i − 5.67139i 19.6642 −11.9114 − 23.6356i
67.20 −1.40081 6.23790i −6.03773 − 16.8728i − 8.73813i 5.67139i 19.6642 −11.9114 23.6356i
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 67.44
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
17.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 187.4.d.a ✓ 44
17.b even 2 1 inner 187.4.d.a ✓ 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
187.4.d.a ✓ 44 1.a even 1 1 trivial
187.4.d.a ✓ 44 17.b even 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(187, [\chi])\).