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Properties

Label 152.5.r.a
Level $152$
Weight $5$
Character orbit 152.r
Analytic conductor $15.712$
Analytic rank $0$
Dimension $120$
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] = [152,5,Mod(33,152)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(152, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 7]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("152.33");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 152.r (of order \(18\), degree \(6\), 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: \(15.7122343887\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 120 q - 12 q^{3} - 252 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 120 q - 12 q^{3} - 252 q^{9} - 264 q^{13} - 624 q^{15} - 432 q^{17} + 1248 q^{19} + 216 q^{21} + 720 q^{23} + 1632 q^{25} + 4140 q^{27} + 576 q^{29} - 2808 q^{31} - 4140 q^{33} - 4968 q^{35} + 5328 q^{39} + 3492 q^{41} + 11424 q^{43} + 3744 q^{45} + 1440 q^{47} - 23892 q^{49} - 3780 q^{51} + 3672 q^{53} + 13536 q^{55} + 5280 q^{57} - 12492 q^{59} - 21720 q^{61} - 34128 q^{63} + 16200 q^{65} + 44220 q^{67} + 27720 q^{71} + 12432 q^{73} - 10800 q^{77} - 42624 q^{79} - 55356 q^{81} + 11232 q^{83} + 8400 q^{85} - 7416 q^{87} + 10152 q^{89} + 30816 q^{91} + 25488 q^{93} + 28080 q^{95} + 66252 q^{97} + 7572 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
33.1 0 −16.8064 − 2.96342i 0 13.9895 + 11.7386i 0 −10.8181 − 18.7375i 0 197.557 + 71.9048i 0
33.2 0 −14.4459 − 2.54721i 0 −4.03276 − 3.38389i 0 28.4659 + 49.3045i 0 126.081 + 45.8899i 0
33.3 0 −11.0147 − 1.94220i 0 −6.47576 − 5.43381i 0 20.4949 + 35.4982i 0 41.4372 + 15.0819i 0
33.4 0 −10.7753 − 1.89998i 0 27.4114 + 23.0009i 0 −36.9146 − 63.9380i 0 36.3823 + 13.2421i 0
33.5 0 −10.4863 − 1.84902i 0 −15.0408 − 12.6207i 0 −24.2354 − 41.9769i 0 30.4290 + 11.0753i 0
33.6 0 −9.01715 − 1.58997i 0 −31.4170 − 26.3620i 0 −32.8907 − 56.9683i 0 2.66583 + 0.970281i 0
33.7 0 −4.94518 − 0.871969i 0 24.8851 + 20.8811i 0 8.88209 + 15.3842i 0 −52.4206 − 19.0795i 0
33.8 0 −4.31618 − 0.761059i 0 0.866351 + 0.726955i 0 9.86645 + 17.0892i 0 −58.0649 − 21.1339i 0
33.9 0 −4.20595 − 0.741622i 0 36.5930 + 30.7052i 0 38.0975 + 65.9868i 0 −58.9751 − 21.4652i 0
33.10 0 −2.16842 − 0.382352i 0 −36.0173 − 30.2221i 0 16.8198 + 29.1327i 0 −71.5592 − 26.0454i 0
33.11 0 2.31908 + 0.408916i 0 −2.11200 − 1.77218i 0 5.32096 + 9.21617i 0 −70.9042 − 25.8070i 0
33.12 0 2.85585 + 0.503563i 0 4.58119 + 3.84407i 0 −19.0959 − 33.0750i 0 −68.2128 − 24.8274i 0
33.13 0 3.06665 + 0.540734i 0 −23.5396 − 19.7521i 0 45.0993 + 78.1144i 0 −67.0031 − 24.3871i 0
33.14 0 3.12726 + 0.551420i 0 24.0952 + 20.2183i 0 −41.8268 − 72.4461i 0 −66.6394 − 24.2548i 0
33.15 0 7.29325 + 1.28600i 0 −9.58125 − 8.03962i 0 −23.6759 − 41.0078i 0 −24.5774 − 8.94544i 0
33.16 0 11.7256 + 2.06753i 0 2.61313 + 2.19268i 0 34.9526 + 60.5396i 0 57.0988 + 20.7823i 0
33.17 0 12.8736 + 2.26997i 0 24.9266 + 20.9159i 0 21.2664 + 36.8345i 0 84.4630 + 30.7420i 0
33.18 0 13.1565 + 2.31985i 0 −17.7491 − 14.8933i 0 −1.57548 − 2.72882i 0 91.5979 + 33.3389i 0
33.19 0 14.4883 + 2.55467i 0 21.5888 + 18.1152i 0 −23.5074 − 40.7159i 0 127.269 + 46.3220i 0
33.20 0 14.5808 + 2.57099i 0 −35.5846 − 29.8590i 0 −17.5042 − 30.3182i 0 129.875 + 47.2708i 0
See next 80 embeddings (of 120 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 33.20
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
19.f odd 18 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 152.5.r.a ✓ 120
19.f odd 18 1 inner 152.5.r.a ✓ 120
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
152.5.r.a ✓ 120 1.a even 1 1 trivial
152.5.r.a ✓ 120 19.f odd 18 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(152, [\chi])\).