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Properties

Label 105.3.o.b
Level $105$
Weight $3$
Character orbit 105.o
Analytic conductor $2.861$
Analytic rank $0$
Dimension $40$
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,3,Mod(44,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.44");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.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: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 44 q^{4} + 80 q^{6} + 12 q^{9} + 62 q^{10} + 84 q^{15} - 116 q^{16} - 56 q^{19} + 36 q^{21} - 12 q^{24} - 6 q^{25} - 20 q^{30} - 444 q^{31} + 256 q^{34} - 688 q^{36} + 168 q^{39} + 54 q^{40} - 40 q^{45}+ \cdots - 336 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
44.1 −1.85988 + 3.22141i −2.47330 + 1.69788i −4.91833 − 8.51879i 4.36624 − 2.43637i −0.869509 − 11.1254i −4.87678 − 5.02166i 21.7110 3.23443 − 8.39872i −0.272141 + 18.5968i
44.2 −1.85988 + 3.22141i 2.70705 − 1.29300i −4.91833 − 8.51879i −0.0731607 − 4.99946i −0.869509 + 11.1254i 4.87678 + 5.02166i 21.7110 5.65629 − 7.00046i 16.2414 + 9.06274i
44.3 −1.60486 + 2.77971i −2.69226 − 1.32352i −3.15118 − 5.45800i −4.78223 + 1.45954i 7.99972 − 5.35963i 6.02754 − 3.55932i 7.38994 5.49658 + 7.12655i 3.61773 − 15.6356i
44.4 −1.60486 + 2.77971i 0.199928 − 2.99333i −3.15118 − 5.45800i 1.12712 + 4.87130i 7.99972 + 5.35963i −6.02754 + 3.55932i 7.38994 −8.92006 − 1.19690i −15.3497 − 4.68473i
44.5 −0.949639 + 1.64482i −2.65035 − 1.40558i 0.196373 + 0.340128i 4.51617 − 2.14574i 4.82880 − 3.02455i 4.60961 + 5.26797i −8.34304 5.04868 + 7.45056i −0.759373 + 9.46598i
44.6 −0.949639 + 1.64482i 0.107903 − 2.99806i 0.196373 + 0.340128i −0.399822 − 4.98399i 4.82880 + 3.02455i −4.60961 − 5.26797i −8.34304 −8.97671 − 0.647002i 8.57746 + 4.07535i
44.7 −0.897800 + 1.55504i −2.08367 + 2.15832i 0.387909 + 0.671879i −3.31295 − 3.74491i −1.48554 − 5.17791i −1.39571 + 6.85945i −8.57546 −0.316668 − 8.99443i 8.79784 − 1.78957i
44.8 −0.897800 + 1.55504i 2.91099 − 0.725349i 0.387909 + 0.671879i 4.89966 + 0.996641i −1.48554 + 5.17791i 1.39571 − 6.85945i −8.57546 7.94774 − 4.22297i −5.94873 + 6.72437i
44.9 −0.0859580 + 0.148884i 0.346935 + 2.97987i 1.98522 + 3.43851i 4.85467 − 1.19675i −0.473476 − 0.204491i −6.99566 + 0.246384i −1.37025 −8.75927 + 2.06764i −0.239121 + 0.825650i
44.10 −0.0859580 + 0.148884i 2.40718 + 1.79039i 1.98522 + 3.43851i −1.39092 − 4.80264i −0.473476 + 0.204491i 6.99566 − 0.246384i −1.37025 2.58900 + 8.61957i 0.834595 + 0.205740i
44.11 0.0859580 − 0.148884i −2.40718 − 1.79039i 1.98522 + 3.43851i −4.85467 + 1.19675i −0.473476 + 0.204491i −6.99566 + 0.246384i 1.37025 2.58900 + 8.61957i −0.239121 + 0.825650i
44.12 0.0859580 − 0.148884i −0.346935 − 2.97987i 1.98522 + 3.43851i 1.39092 + 4.80264i −0.473476 − 0.204491i 6.99566 − 0.246384i 1.37025 −8.75927 + 2.06764i 0.834595 + 0.205740i
44.13 0.897800 − 1.55504i −2.91099 + 0.725349i 0.387909 + 0.671879i 3.31295 + 3.74491i −1.48554 + 5.17791i −1.39571 + 6.85945i 8.57546 7.94774 − 4.22297i 8.79784 − 1.78957i
44.14 0.897800 − 1.55504i 2.08367 − 2.15832i 0.387909 + 0.671879i −4.89966 − 0.996641i −1.48554 − 5.17791i 1.39571 − 6.85945i 8.57546 −0.316668 − 8.99443i −5.94873 + 6.72437i
44.15 0.949639 − 1.64482i −0.107903 + 2.99806i 0.196373 + 0.340128i −4.51617 + 2.14574i 4.82880 + 3.02455i 4.60961 + 5.26797i 8.34304 −8.97671 − 0.647002i −0.759373 + 9.46598i
44.16 0.949639 − 1.64482i 2.65035 + 1.40558i 0.196373 + 0.340128i 0.399822 + 4.98399i 4.82880 − 3.02455i −4.60961 − 5.26797i 8.34304 5.04868 + 7.45056i 8.57746 + 4.07535i
44.17 1.60486 − 2.77971i −0.199928 + 2.99333i −3.15118 − 5.45800i 4.78223 − 1.45954i 7.99972 + 5.35963i 6.02754 − 3.55932i −7.38994 −8.92006 − 1.19690i 3.61773 − 15.6356i
44.18 1.60486 − 2.77971i 2.69226 + 1.32352i −3.15118 − 5.45800i −1.12712 − 4.87130i 7.99972 − 5.35963i −6.02754 + 3.55932i −7.38994 5.49658 + 7.12655i −15.3497 − 4.68473i
44.19 1.85988 − 3.22141i −2.70705 + 1.29300i −4.91833 − 8.51879i −4.36624 + 2.43637i −0.869509 + 11.1254i −4.87678 − 5.02166i −21.7110 5.65629 − 7.00046i −0.272141 + 18.5968i
44.20 1.85988 − 3.22141i 2.47330 − 1.69788i −4.91833 − 8.51879i 0.0731607 + 4.99946i −0.869509 − 11.1254i 4.87678 + 5.02166i −21.7110 3.23443 − 8.39872i 16.2414 + 9.06274i
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 44.20
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
5.b even 2 1 inner
7.c even 3 1 inner
15.d odd 2 1 inner
21.h odd 6 1 inner
35.j even 6 1 inner
105.o odd 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 105.3.o.b ✓ 40
3.b odd 2 1 inner 105.3.o.b ✓ 40
5.b even 2 1 inner 105.3.o.b ✓ 40
7.c even 3 1 inner 105.3.o.b ✓ 40
15.d odd 2 1 inner 105.3.o.b ✓ 40
21.h odd 6 1 inner 105.3.o.b ✓ 40
35.j even 6 1 inner 105.3.o.b ✓ 40
105.o odd 6 1 inner 105.3.o.b ✓ 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
105.3.o.b ✓ 40 1.a even 1 1 trivial
105.3.o.b ✓ 40 3.b odd 2 1 inner
105.3.o.b ✓ 40 5.b even 2 1 inner
105.3.o.b ✓ 40 7.c even 3 1 inner
105.3.o.b ✓ 40 15.d odd 2 1 inner
105.3.o.b ✓ 40 21.h odd 6 1 inner
105.3.o.b ✓ 40 35.j even 6 1 inner
105.3.o.b ✓ 40 105.o odd 6 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{20} + 31 T_{2}^{18} + 641 T_{2}^{16} + 7392 T_{2}^{14} + 61521 T_{2}^{12} + 299439 T_{2}^{10} + \cdots + 2401 \) acting on \(S_{3}^{\mathrm{new}}(105, [\chi])\). Copy content Toggle raw display