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Properties

Label 154.3.h.a
Level $154$
Weight $3$
Character orbit 154.h
Analytic conductor $4.196$
Analytic rank $0$
Dimension $24$
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] = [154,3,Mod(45,154)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(154, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("154.45");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 154.h (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: \(4.19619607115\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 12 q^{3} - 24 q^{4} - 12 q^{7} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 12 q^{3} - 24 q^{4} - 12 q^{7} + 40 q^{9} - 24 q^{12} + 48 q^{14} - 56 q^{15} - 48 q^{16} + 108 q^{17} + 32 q^{18} + 60 q^{19} - 116 q^{21} - 40 q^{23} - 48 q^{24} - 4 q^{25} - 24 q^{28} + 112 q^{29} + 72 q^{30} - 36 q^{31} + 228 q^{35} - 160 q^{36} + 80 q^{37} - 96 q^{38} - 44 q^{39} - 96 q^{42} + 56 q^{43} - 276 q^{45} + 56 q^{46} - 204 q^{47} + 288 q^{49} - 152 q^{51} + 144 q^{52} + 84 q^{53} + 72 q^{54} - 48 q^{56} + 80 q^{57} - 72 q^{58} - 24 q^{59} + 56 q^{60} - 24 q^{61} - 404 q^{63} + 192 q^{64} - 108 q^{65} + 112 q^{67} - 216 q^{68} - 152 q^{70} - 472 q^{71} + 64 q^{72} - 84 q^{73} - 272 q^{74} + 564 q^{75} + 44 q^{77} + 96 q^{78} - 224 q^{79} + 28 q^{81} + 192 q^{82} + 80 q^{84} - 160 q^{85} + 120 q^{86} + 828 q^{87} - 180 q^{89} - 212 q^{91} + 160 q^{92} + 560 q^{93} + 480 q^{94} - 264 q^{95} + 96 q^{96} + 304 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
45.1 −0.707107 − 1.22474i −3.99481 − 2.30640i −1.00000 + 1.73205i −3.19736 + 1.84600i 6.52349i 2.83592 + 6.39981i 2.82843 6.13900 + 10.6331i 4.52175 + 2.61063i
45.2 −0.707107 − 1.22474i −3.16870 − 1.82945i −1.00000 + 1.73205i 1.07055 − 0.618084i 5.17446i −6.99994 − 0.0280653i 2.82843 2.19377 + 3.79972i −1.51399 − 0.874103i
45.3 −0.707107 − 1.22474i −2.31400 − 1.33599i −1.00000 + 1.73205i 6.08861 − 3.51526i 3.77875i 6.92355 + 1.03171i 2.82843 −0.930268 − 1.61127i −8.61060 − 4.97133i
45.4 −0.707107 − 1.22474i 0.400604 + 0.231289i −1.00000 + 1.73205i −0.161197 + 0.0930672i − 0.654184i −5.86928 − 3.81465i 2.82843 −4.39301 − 7.60892i 0.227967 + 0.131617i
45.5 −0.707107 − 1.22474i 2.97288 + 1.71640i −1.00000 + 1.73205i 3.35856 − 1.93906i − 4.85470i 2.44414 + 6.55943i 2.82843 1.39203 + 2.41106i −4.74972 − 2.74225i
45.6 −0.707107 − 1.22474i 4.86138 + 2.80672i −1.00000 + 1.73205i −7.15917 + 4.13335i − 7.93860i −6.57703 + 2.39638i 2.82843 11.2553 + 19.4948i 10.1246 + 5.84544i
45.7 0.707107 + 1.22474i −2.70880 − 1.56393i −1.00000 + 1.73205i 0.980364 − 0.566013i − 4.42345i 3.18865 − 6.23157i −2.82843 0.391731 + 0.678499i 1.38644 + 0.800464i
45.8 0.707107 + 1.22474i −1.06696 − 0.616008i −1.00000 + 1.73205i −4.19379 + 2.42129i − 1.74233i −5.82442 − 3.88279i −2.82843 −3.74107 − 6.47972i −5.93091 − 3.42421i
45.9 0.707107 + 1.22474i 0.870475 + 0.502569i −1.00000 + 1.73205i 6.27701 − 3.62403i 1.42148i 6.41182 + 2.80867i −2.82843 −3.99485 − 6.91928i 8.87703 + 5.12516i
45.10 0.707107 + 1.22474i 1.90606 + 1.10046i −1.00000 + 1.73205i −5.40088 + 3.11820i 3.11258i −2.04411 + 6.69489i −2.82843 −2.07796 − 3.59914i −7.63799 − 4.40980i
45.11 0.707107 + 1.22474i 3.81780 + 2.20421i −1.00000 + 1.73205i −2.08322 + 1.20275i 6.23444i 6.38266 − 2.87432i −2.82843 5.21707 + 9.03624i −2.94612 − 1.70094i
45.12 0.707107 + 1.22474i 4.42406 + 2.55423i −1.00000 + 1.73205i 4.42051 − 2.55218i 7.22446i −6.87195 + 1.33280i −2.82843 8.54822 + 14.8060i 6.25155 + 3.60933i
89.1 −0.707107 + 1.22474i −3.99481 + 2.30640i −1.00000 − 1.73205i −3.19736 − 1.84600i − 6.52349i 2.83592 − 6.39981i 2.82843 6.13900 − 10.6331i 4.52175 − 2.61063i
89.2 −0.707107 + 1.22474i −3.16870 + 1.82945i −1.00000 − 1.73205i 1.07055 + 0.618084i − 5.17446i −6.99994 + 0.0280653i 2.82843 2.19377 − 3.79972i −1.51399 + 0.874103i
89.3 −0.707107 + 1.22474i −2.31400 + 1.33599i −1.00000 − 1.73205i 6.08861 + 3.51526i − 3.77875i 6.92355 − 1.03171i 2.82843 −0.930268 + 1.61127i −8.61060 + 4.97133i
89.4 −0.707107 + 1.22474i 0.400604 − 0.231289i −1.00000 − 1.73205i −0.161197 − 0.0930672i 0.654184i −5.86928 + 3.81465i 2.82843 −4.39301 + 7.60892i 0.227967 − 0.131617i
89.5 −0.707107 + 1.22474i 2.97288 − 1.71640i −1.00000 − 1.73205i 3.35856 + 1.93906i 4.85470i 2.44414 − 6.55943i 2.82843 1.39203 − 2.41106i −4.74972 + 2.74225i
89.6 −0.707107 + 1.22474i 4.86138 − 2.80672i −1.00000 − 1.73205i −7.15917 − 4.13335i 7.93860i −6.57703 − 2.39638i 2.82843 11.2553 − 19.4948i 10.1246 − 5.84544i
89.7 0.707107 − 1.22474i −2.70880 + 1.56393i −1.00000 − 1.73205i 0.980364 + 0.566013i 4.42345i 3.18865 + 6.23157i −2.82843 0.391731 − 0.678499i 1.38644 − 0.800464i
89.8 0.707107 − 1.22474i −1.06696 + 0.616008i −1.00000 − 1.73205i −4.19379 − 2.42129i 1.74233i −5.82442 + 3.88279i −2.82843 −3.74107 + 6.47972i −5.93091 + 3.42421i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 45.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.d odd 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 154.3.h.a ✓ 24
7.c even 3 1 1078.3.b.c 24
7.d odd 6 1 inner 154.3.h.a ✓ 24
7.d odd 6 1 1078.3.b.c 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.3.h.a ✓ 24 1.a even 1 1 trivial
154.3.h.a ✓ 24 7.d odd 6 1 inner
1078.3.b.c 24 7.c even 3 1
1078.3.b.c 24 7.d odd 6 1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(154, [\chi])\).