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Properties

Label 152.2.o.c
Level $152$
Weight $2$
Character orbit 152.o
Analytic conductor $1.214$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [152,2,Mod(27,152)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(152, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("152.27");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 152.o (of order \(6\), degree \(2\), 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: \(1.21372611072\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32} + 36 q^{33} - 12 q^{34} - 28 q^{35} - 8 q^{36} + 38 q^{38} - 48 q^{40} + 6 q^{41} + 14 q^{42} + 30 q^{43} + 5 q^{44} - 15 q^{48} - 68 q^{49} - 42 q^{51} + 36 q^{52} + 23 q^{54} - 26 q^{57} + 20 q^{58} - 18 q^{59} - 42 q^{60} + 22 q^{62} + 70 q^{64} - 27 q^{66} + 78 q^{67} + 4 q^{68} + 18 q^{70} - 24 q^{72} + 14 q^{73} + 4 q^{74} + 47 q^{76} - 30 q^{78} - 20 q^{80} + 6 q^{81} + 23 q^{82} - 32 q^{83} + 42 q^{86} - 18 q^{89} - 96 q^{90} - 12 q^{91} + 46 q^{92} + 50 q^{96} + 30 q^{97} + 15 q^{98} - 28 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
27.1 −1.40620 − 0.150327i −2.03079 − 1.17247i 1.95480 + 0.422781i 1.50560 + 0.869259i 2.67944 + 1.95402i − 2.63359i −2.68529 − 0.888375i 1.24939 + 2.16401i −1.98650 − 1.44869i
27.2 −1.40330 − 0.175316i 0.179130 + 0.103421i 1.93853 + 0.492043i 0.520463 + 0.300489i −0.233242 − 0.176535i 4.27429i −2.63408 − 1.03034i −1.47861 − 2.56102i −0.677687 − 0.512924i
27.3 −1.34230 + 0.445227i 0.705625 + 0.407393i 1.60355 − 1.19526i −3.59735 − 2.07693i −1.12854 − 0.232681i − 3.24695i −1.62028 + 2.31834i −1.16806 − 2.02314i 5.75343 + 1.18623i
27.4 −0.861662 + 1.12140i 2.07624 + 1.19872i −0.515076 − 1.93254i 0.418341 + 0.241529i −3.13326 + 1.29541i 1.56686i 2.61097 + 1.08759i 1.37385 + 2.37958i −0.631319 + 0.261011i
27.5 −0.853480 − 1.12764i 0.179130 + 0.103421i −0.543142 + 1.92484i −0.520463 − 0.300489i −0.0362625 − 0.290261i − 4.27429i 2.63408 − 1.03034i −1.47861 − 2.56102i 0.105361 + 0.843356i
27.6 −0.833288 − 1.14264i −2.03079 − 1.17247i −0.611263 + 1.90430i −1.50560 − 0.869259i 0.352510 + 3.29747i 2.63359i 2.68529 − 0.888375i 1.24939 + 2.16401i 0.261346 + 2.44470i
27.7 −0.285573 − 1.38508i 0.705625 + 0.407393i −1.83690 + 0.791084i 3.59735 + 2.07693i 0.362764 − 1.09369i 3.24695i 1.62028 + 2.31834i −1.16806 − 2.02314i 1.84941 − 5.57573i
27.8 −0.151949 + 1.40603i −1.05104 − 0.606818i −1.95382 − 0.427288i −2.45005 − 1.41453i 1.01291 − 1.38558i 0.450769i 0.897660 − 2.68220i −0.763544 − 1.32250i 2.36116 − 3.22989i
27.9 0.397742 + 1.35713i 1.27630 + 0.736872i −1.68360 + 1.07957i 2.34524 + 1.35403i −0.492393 + 2.02519i − 3.01597i −2.13476 − 1.85548i −0.414040 − 0.717138i −0.904789 + 3.72135i
27.10 0.540330 − 1.30692i 2.07624 + 1.19872i −1.41609 − 1.41234i −0.418341 − 0.241529i 2.68848 − 2.06578i − 1.56686i −2.61097 + 1.08759i 1.37385 + 2.37958i −0.541701 + 0.416233i
27.11 0.771641 + 1.18515i −2.65547 − 1.53314i −0.809140 + 1.82901i 2.25688 + 1.30301i −0.232080 − 4.33015i 4.30088i −2.79201 + 0.452395i 3.20101 + 5.54431i 0.197245 + 3.68018i
27.12 1.14168 − 0.834605i −1.05104 − 0.606818i 0.606869 − 1.90570i 2.45005 + 1.41453i −1.70640 + 0.184411i − 0.450769i −0.897660 − 2.68220i −0.763544 − 1.32250i 3.97775 − 0.429874i
27.13 1.37418 − 0.334110i 1.27630 + 0.736872i 1.77674 − 0.918256i −2.34524 − 1.35403i 2.00006 + 0.586169i 3.01597i 2.13476 − 1.85548i −0.414040 − 0.717138i −3.67518 − 1.07711i
27.14 1.41219 + 0.0756882i −2.65547 − 1.53314i 1.98854 + 0.213772i −2.25688 − 1.30301i −3.63398 − 2.36606i − 4.30088i 2.79201 + 0.452395i 3.20101 + 5.54431i −3.08851 − 2.01091i
107.1 −1.40620 + 0.150327i −2.03079 + 1.17247i 1.95480 − 0.422781i 1.50560 − 0.869259i 2.67944 − 1.95402i 2.63359i −2.68529 + 0.888375i 1.24939 − 2.16401i −1.98650 + 1.44869i
107.2 −1.40330 + 0.175316i 0.179130 − 0.103421i 1.93853 − 0.492043i 0.520463 − 0.300489i −0.233242 + 0.176535i − 4.27429i −2.63408 + 1.03034i −1.47861 + 2.56102i −0.677687 + 0.512924i
107.3 −1.34230 − 0.445227i 0.705625 − 0.407393i 1.60355 + 1.19526i −3.59735 + 2.07693i −1.12854 + 0.232681i 3.24695i −1.62028 − 2.31834i −1.16806 + 2.02314i 5.75343 − 1.18623i
107.4 −0.861662 − 1.12140i 2.07624 − 1.19872i −0.515076 + 1.93254i 0.418341 − 0.241529i −3.13326 − 1.29541i − 1.56686i 2.61097 − 1.08759i 1.37385 − 2.37958i −0.631319 − 0.261011i
107.5 −0.853480 + 1.12764i 0.179130 − 0.103421i −0.543142 − 1.92484i −0.520463 + 0.300489i −0.0362625 + 0.290261i 4.27429i 2.63408 + 1.03034i −1.47861 + 2.56102i 0.105361 − 0.843356i
107.6 −0.833288 + 1.14264i −2.03079 + 1.17247i −0.611263 − 1.90430i −1.50560 + 0.869259i 0.352510 − 3.29747i − 2.63359i 2.68529 + 0.888375i 1.24939 − 2.16401i 0.261346 − 2.44470i
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 27.14
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.d odd 2 1 inner
19.d odd 6 1 inner
152.o even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 152.2.o.c ✓ 28
4.b odd 2 1 608.2.s.c 28
8.b even 2 1 608.2.s.c 28
8.d odd 2 1 inner 152.2.o.c ✓ 28
19.d odd 6 1 inner 152.2.o.c ✓ 28
76.f even 6 1 608.2.s.c 28
152.l odd 6 1 608.2.s.c 28
152.o even 6 1 inner 152.2.o.c ✓ 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
152.2.o.c ✓ 28 1.a even 1 1 trivial
152.2.o.c ✓ 28 8.d odd 2 1 inner
152.2.o.c ✓ 28 19.d odd 6 1 inner
152.2.o.c ✓ 28 152.o even 6 1 inner
608.2.s.c 28 4.b odd 2 1
608.2.s.c 28 8.b even 2 1
608.2.s.c 28 76.f even 6 1
608.2.s.c 28 152.l odd 6 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{14} + 3 T_{3}^{13} - 8 T_{3}^{12} - 33 T_{3}^{11} + 65 T_{3}^{10} + 210 T_{3}^{9} - 201 T_{3}^{8} + \cdots + 27 \) acting on \(S_{2}^{\mathrm{new}}(152, [\chi])\). Copy content Toggle raw display