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Properties

Label 105.3.v.a
Level $105$
Weight $3$
Character orbit 105.v
Analytic conductor $2.861$
Analytic rank $0$
Dimension $64$
Inner twists $4$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [105,3,Mod(37,105)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("105.37"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(105, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 3, 4])) N = Newforms(chi, 3, names="a")
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.v (of order \(12\), degree \(4\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 64 q + 4 q^{5} - 4 q^{7} + 24 q^{8} - 16 q^{10} + 16 q^{11} - 48 q^{15} + 80 q^{16} + 56 q^{17} + 24 q^{21} - 96 q^{22} + 72 q^{23} - 4 q^{25} - 288 q^{26} - 380 q^{28} - 48 q^{30} - 136 q^{31} - 48 q^{32}+ \cdots + 272 q^{98}+O(q^{100}) \) 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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
37.1 −3.56483 + 0.955194i −1.67303 − 0.448288i 8.33154 − 4.81021i −1.05941 + 4.88648i 6.39228 −6.28878 + 3.07429i −14.6673 + 14.6673i 2.59808 + 1.50000i −0.890898 − 18.4314i
37.2 −3.18498 + 0.853412i 1.67303 + 0.448288i 5.95167 − 3.43620i −4.91224 + 0.932701i −5.71115 5.00478 + 4.89410i −6.69718 + 6.69718i 2.59808 + 1.50000i 14.8494 − 7.16279i
37.3 −2.87375 + 0.770020i 1.67303 + 0.448288i 4.20143 − 2.42570i 3.78688 + 3.26489i −5.15308 −1.65502 − 6.80154i −1.79111 + 1.79111i 2.59808 + 1.50000i −13.3966 − 6.46653i
37.4 −2.38023 + 0.637781i −1.67303 − 0.448288i 1.79464 − 1.03614i 2.91424 − 4.06291i 4.26812 −4.25379 + 5.55925i 3.35897 − 3.35897i 2.59808 + 1.50000i −4.34532 + 11.5293i
37.5 −1.91023 + 0.511845i −1.67303 − 0.448288i −0.0771041 + 0.0445161i −4.99333 − 0.258093i 3.42533 6.99587 + 0.240410i 5.71805 − 5.71805i 2.59808 + 1.50000i 9.67053 − 2.06280i
37.6 −1.84280 + 0.493776i 1.67303 + 0.448288i −0.312015 + 0.180142i −1.82066 − 4.65674i −3.30441 −6.63712 − 2.22456i 5.88211 − 5.88211i 2.59808 + 1.50000i 5.65448 + 7.68243i
37.7 −0.445275 + 0.119311i −1.67303 − 0.448288i −3.28007 + 1.89375i 4.59550 − 1.97013i 0.798445 −0.171680 − 6.99789i 2.53844 − 2.53844i 2.59808 + 1.50000i −1.81120 + 1.42554i
37.8 −0.435396 + 0.116664i 1.67303 + 0.448288i −3.28814 + 1.89841i 3.62365 − 3.44517i −0.780730 6.87993 + 1.29096i 2.48509 − 2.48509i 2.59808 + 1.50000i −1.17579 + 1.92276i
37.9 0.232416 − 0.0622758i 1.67303 + 0.448288i −3.41396 + 1.97105i −2.65242 + 4.23847i 0.416757 −4.06422 + 5.69931i −1.35127 + 1.35127i 2.59808 + 1.50000i −0.352512 + 1.15027i
37.10 0.901161 − 0.241465i −1.67303 − 0.448288i −2.71032 + 1.56480i 2.44472 + 4.36158i −1.61592 5.41162 + 4.44009i −4.70337 + 4.70337i 2.59808 + 1.50000i 3.25625 + 3.34017i
37.11 0.984292 − 0.263740i −1.67303 − 0.448288i −2.56483 + 1.48081i −4.04958 − 2.93273i −1.76498 −5.81621 + 3.89508i −5.01620 + 5.01620i 2.59808 + 1.50000i −4.75945 − 1.81862i
37.12 2.13226 − 0.571337i 1.67303 + 0.448288i 0.756006 − 0.436480i 2.78563 + 4.15214i 3.82346 2.73668 − 6.44287i −4.88107 + 4.88107i 2.59808 + 1.50000i 8.31195 + 7.26192i
37.13 2.56059 − 0.686107i 1.67303 + 0.448288i 2.62176 − 1.51367i 1.32982 − 4.81992i 4.59152 0.158915 + 6.99820i −1.82323 + 1.82323i 2.59808 + 1.50000i 0.0981374 − 13.2542i
37.14 2.88660 − 0.773463i −1.67303 − 0.448288i 4.27013 − 2.46536i 0.160937 − 4.99741i −5.17611 5.19830 − 4.68804i 1.96674 − 1.96674i 2.59808 + 1.50000i −3.40075 − 14.5500i
37.15 3.41166 − 0.914152i 1.67303 + 0.448288i 7.33966 − 4.23756i −4.98672 + 0.364163i 6.11763 −6.35750 − 2.92953i 11.1766 − 11.1766i 2.59808 + 1.50000i −16.6801 + 5.80102i
37.16 3.52852 − 0.945463i −1.67303 − 0.448288i 8.09242 − 4.67216i 3.83301 + 3.21062i −6.32716 −6.80203 + 1.65300i 13.8047 − 13.8047i 2.59808 + 1.50000i 16.5603 + 7.70474i
58.1 −0.945463 − 3.52852i 0.448288 − 1.67303i −8.09242 + 4.67216i −4.69698 − 1.71417i −6.32716 1.65300 + 6.80203i 13.8047 + 13.8047i −2.59808 − 1.50000i −1.60767 + 18.1940i
58.2 −0.914152 − 3.41166i −0.448288 + 1.67303i −7.33966 + 4.23756i 2.17799 + 4.50071i 6.11763 −2.92953 + 6.35750i 11.1766 + 11.1766i −2.59808 − 1.50000i 13.3639 − 11.5449i
58.3 −0.773463 − 2.88660i 0.448288 − 1.67303i −4.27013 + 2.46536i 4.24741 − 2.63808i −5.17611 −4.68804 − 5.19830i 1.96674 + 1.96674i −2.59808 − 1.50000i −10.9003 − 10.2201i
58.4 −0.686107 − 2.56059i −0.448288 + 1.67303i −2.62176 + 1.51367i 3.50926 − 3.56161i 4.59152 6.99820 − 0.158915i −1.82323 − 1.82323i −2.59808 − 1.50000i −11.5275 − 6.54211i
See all 64 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 37.16
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner
7.c even 3 1 inner
35.l odd 12 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 105.3.v.a ✓ 64
3.b odd 2 1 315.3.ca.b 64
5.c odd 4 1 inner 105.3.v.a ✓ 64
7.c even 3 1 inner 105.3.v.a ✓ 64
15.e even 4 1 315.3.ca.b 64
21.h odd 6 1 315.3.ca.b 64
35.l odd 12 1 inner 105.3.v.a ✓ 64
105.x even 12 1 315.3.ca.b 64
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
105.3.v.a ✓ 64 1.a even 1 1 trivial
105.3.v.a ✓ 64 5.c odd 4 1 inner
105.3.v.a ✓ 64 7.c even 3 1 inner
105.3.v.a ✓ 64 35.l odd 12 1 inner
315.3.ca.b 64 3.b odd 2 1
315.3.ca.b 64 15.e even 4 1
315.3.ca.b 64 21.h odd 6 1
315.3.ca.b 64 105.x even 12 1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(105, [\chi])\).