Properties

Label 1155.3.b.a
Level $1155$
Weight $3$
Character orbit 1155.b
Analytic conductor $31.471$
Analytic rank $0$
Dimension $96$
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] = [1155,3,Mod(736,1155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1155.736");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1155.b (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: \(31.4714705336\)
Analytic rank: \(0\)
Dimension: \(96\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 96 q - 216 q^{4} + 288 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 96 q - 216 q^{4} + 288 q^{9} + 40 q^{11} - 56 q^{14} + 488 q^{16} + 56 q^{22} + 16 q^{23} + 480 q^{25} - 64 q^{26} + 192 q^{31} + 24 q^{33} + 176 q^{34} - 648 q^{36} - 112 q^{37} - 272 q^{38} - 520 q^{44} + 416 q^{47} - 192 q^{48} - 672 q^{49} + 112 q^{53} - 80 q^{55} + 280 q^{56} - 352 q^{58} + 512 q^{59} - 1112 q^{64} + 288 q^{66} - 304 q^{67} - 480 q^{71} + 224 q^{77} + 240 q^{78} + 864 q^{81} - 720 q^{82} - 432 q^{86} - 376 q^{88} - 32 q^{89} - 384 q^{92} + 384 q^{93} + 272 q^{97} + 120 q^{99}+O(q^{100}) \) 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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
736.1 3.97461i −1.73205 −11.7975 −2.23607 6.88422i 2.64575i 30.9920i 3.00000 8.88749i
736.2 3.80731i −1.73205 −10.4956 −2.23607 6.59446i 2.64575i 24.7309i 3.00000 8.51341i
736.3 3.79404i 1.73205 −10.3948 2.23607 6.57148i 2.64575i 24.2621i 3.00000 8.48374i
736.4 3.73924i 1.73205 −9.98188 −2.23607 6.47655i 2.64575i 22.3677i 3.00000 8.36118i
736.5 3.73084i −1.73205 −9.91918 2.23607 6.46201i 2.64575i 22.0835i 3.00000 8.34242i
736.6 3.67613i 1.73205 −9.51395 −2.23607 6.36725i 2.64575i 20.2700i 3.00000 8.22008i
736.7 3.66479i −1.73205 −9.43072 2.23607 6.34761i 2.64575i 19.9025i 3.00000 8.19473i
736.8 3.64908i 1.73205 −9.31580 2.23607 6.32039i 2.64575i 19.3978i 3.00000 8.15959i
736.9 3.57619i −1.73205 −8.78910 2.23607 6.19413i 2.64575i 17.1267i 3.00000 7.99659i
736.10 3.57202i 1.73205 −8.75932 −2.23607 6.18692i 2.64575i 17.0004i 3.00000 7.98728i
736.11 3.29262i 1.73205 −6.84133 2.23607 5.70298i 2.64575i 9.35542i 3.00000 7.36252i
736.12 3.27785i −1.73205 −6.74433 −2.23607 5.67741i 2.64575i 8.99550i 3.00000 7.32950i
736.13 3.25995i 1.73205 −6.62729 2.23607 5.64640i 2.64575i 8.56486i 3.00000 7.28948i
736.14 2.97479i 1.73205 −4.84935 2.23607 5.15248i 2.64575i 2.52665i 3.00000 6.65182i
736.15 2.94196i 1.73205 −4.65512 −2.23607 5.09562i 2.64575i 1.92733i 3.00000 6.57842i
736.16 2.91962i −1.73205 −4.52416 2.23607 5.05692i 2.64575i 1.53034i 3.00000 6.52846i
736.17 2.91387i −1.73205 −4.49063 2.23607 5.04697i 2.64575i 1.42964i 3.00000 6.51561i
736.18 2.89693i −1.73205 −4.39221 2.23607 5.01763i 2.64575i 1.13621i 3.00000 6.47774i
736.19 2.81721i −1.73205 −3.93666 −2.23607 4.87955i 2.64575i 0.178435i 3.00000 6.29947i
736.20 2.77171i −1.73205 −3.68240 −2.23607 4.80075i 2.64575i 0.880291i 3.00000 6.19774i
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 736.96
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1155.3.b.a 96
11.b odd 2 1 inner 1155.3.b.a 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1155.3.b.a 96 1.a even 1 1 trivial
1155.3.b.a 96 11.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(1155, [\chi])\).