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Properties

Label 195.3.d.a
Level $195$
Weight $3$
Character orbit 195.d
Analytic conductor $5.313$
Analytic rank $0$
Dimension $32$
Inner twists $2$

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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] = [195,3,Mod(131,195)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 3, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("195.131"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: \( N \) \(=\) \( 195 = 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 195.d (of order \(2\), degree \(1\), 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: \(5.31336515503\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 8 q^{3} - 60 q^{4} - 8 q^{6} + 8 q^{9} - 20 q^{10} - 68 q^{12} + 172 q^{16} + 132 q^{18} - 16 q^{19} + 44 q^{21} - 64 q^{22} - 92 q^{24} - 160 q^{25} + 20 q^{27} + 224 q^{28} - 40 q^{30} - 56 q^{31}+ \cdots + 236 q^{99}+O(q^{100}) \) 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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
131.1 − 3.93415i 2.69917 − 1.30938i −11.4775 − 2.23607i −5.15128 − 10.6189i −7.95416 29.4176i 5.57106 − 7.06847i −8.79702
131.2 − 3.82682i 0.963256 + 2.84115i −10.6446 2.23607i 10.8726 − 3.68621i −0.765398 25.4276i −7.14428 + 5.47351i 8.55704
131.3 − 3.53170i −1.92847 − 2.29805i −8.47290 2.23607i −8.11601 + 6.81077i −3.35184 15.7969i −1.56203 + 8.86341i 7.89712
131.4 − 3.00673i −0.102540 + 2.99825i −5.04041 − 2.23607i 9.01491 + 0.308308i −3.51413 3.12822i −8.97897 − 0.614878i −6.72325
131.5 − 2.90487i 2.90740 + 0.739629i −4.43828 2.23607i 2.14853 − 8.44561i 2.78840 1.27314i 7.90590 + 4.30079i 6.49549
131.6 − 2.89144i −2.80506 − 1.06378i −4.36044 − 2.23607i −3.07587 + 8.11067i −8.81084 1.04219i 6.73672 + 5.96796i −6.46546
131.7 − 2.85994i 2.93220 + 0.634177i −4.17927 − 2.23607i 1.81371 − 8.38594i 12.7826 0.512712i 8.19564 + 3.71907i −6.39503
131.8 − 2.37720i 0.699727 − 2.91726i −1.65107 − 2.23607i −6.93489 − 1.66339i −2.88504 − 5.58388i −8.02077 − 4.08256i −5.31557
131.9 − 1.93202i −2.94929 − 0.549286i 0.267296 2.23607i −1.06123 + 5.69808i 10.3382 − 8.24450i 8.39657 + 3.24000i 4.32013
131.10 − 1.62827i −1.50101 − 2.59749i 1.34874 − 2.23607i −4.22942 + 2.44404i 9.21760 − 8.70919i −4.49395 + 7.79772i −3.64092
131.11 − 1.18601i −0.368414 + 2.97729i 2.59338 − 2.23607i 3.53110 + 0.436942i 8.17904 − 7.81981i −8.72854 − 2.19375i −2.65200
131.12 − 1.11947i 2.93515 − 0.620391i 2.74679 − 2.23607i −0.694509 − 3.28581i −5.59346 − 7.55282i 8.23023 − 3.64188i −2.50321
131.13 − 1.03396i −0.423726 − 2.96993i 2.93092 2.23607i −3.07080 + 0.438118i −13.7578 − 7.16632i −8.64091 + 2.51687i 2.31201
131.14 − 0.858859i 2.44162 − 1.74313i 3.26236 2.23607i −1.49710 − 2.09701i 2.16867 − 6.23734i 2.92302 − 8.51211i 1.92047
131.15 − 0.848705i 1.45000 + 2.62631i 3.27970 2.23607i 2.22896 − 1.23062i 5.71525 − 6.17832i −4.79500 + 7.61630i 1.89776
131.16 − 0.405877i −2.95003 + 0.545292i 3.83526 − 2.23607i 0.221321 + 1.19735i −4.55712 − 3.18015i 8.40531 − 3.21725i −0.907568
131.17 0.405877i −2.95003 − 0.545292i 3.83526 2.23607i 0.221321 − 1.19735i −4.55712 3.18015i 8.40531 + 3.21725i −0.907568
131.18 0.848705i 1.45000 − 2.62631i 3.27970 − 2.23607i 2.22896 + 1.23062i 5.71525 6.17832i −4.79500 − 7.61630i 1.89776
131.19 0.858859i 2.44162 + 1.74313i 3.26236 − 2.23607i −1.49710 + 2.09701i 2.16867 6.23734i 2.92302 + 8.51211i 1.92047
131.20 1.03396i −0.423726 + 2.96993i 2.93092 − 2.23607i −3.07080 − 0.438118i −13.7578 7.16632i −8.64091 − 2.51687i 2.31201
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 131.32
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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 195.3.d.a ✓ 32
3.b odd 2 1 inner 195.3.d.a ✓ 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
195.3.d.a ✓ 32 1.a even 1 1 trivial
195.3.d.a ✓ 32 3.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(195, [\chi])\).