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Properties

Label 9065.2.a.bc
Level $9065$
Weight $2$
Character orbit 9065.a
Self dual yes
Analytic conductor $72.384$
Analytic rank $0$
Dimension $34$
CM no
Inner twists $1$

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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] = [9065,2,Mod(1,9065)] 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("9065.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9065, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 9065 = 5 \cdot 7^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9065.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [34,-2,10,30,-34,8,0,-6,28,2,-30] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(72.3843894323\)
Analytic rank: \(0\)
Dimension: \(34\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 34 q - 2 q^{2} + 10 q^{3} + 30 q^{4} - 34 q^{5} + 8 q^{6} - 6 q^{8} + 28 q^{9} + 2 q^{10} - 30 q^{11} + 20 q^{12} + 18 q^{13} - 10 q^{15} + 18 q^{16} + 10 q^{17} + 40 q^{19} - 30 q^{20} - 4 q^{22} - 16 q^{23}+ \cdots - 100 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.66222 −1.56275 5.08743 −1.00000 4.16040 0 −8.21942 −0.557797 2.66222
1.2 −2.56888 1.26981 4.59913 −1.00000 −3.26199 0 −6.67686 −1.38758 2.56888
1.3 −2.48256 −0.775934 4.16310 −1.00000 1.92630 0 −5.37002 −2.39793 2.48256
1.4 −2.38943 2.87301 3.70935 −1.00000 −6.86485 0 −4.08437 5.25421 2.38943
1.5 −2.13953 −1.85560 2.57757 −1.00000 3.97010 0 −1.23573 0.443251 2.13953
1.6 −2.01251 −3.11640 2.05020 −1.00000 6.27179 0 −0.101025 6.71196 2.01251
1.7 −2.01175 2.93465 2.04715 −1.00000 −5.90379 0 −0.0948516 5.61216 2.01175
1.8 −1.87679 0.533259 1.52234 −1.00000 −1.00082 0 0.896460 −2.71564 1.87679
1.9 −1.84557 1.65469 1.40612 −1.00000 −3.05385 0 1.09605 −0.261986 1.84557
1.10 −1.44430 0.961877 0.0859993 −1.00000 −1.38924 0 2.76439 −2.07479 1.44430
1.11 −1.32533 −0.629353 −0.243496 −1.00000 0.834101 0 2.97338 −2.60392 1.32533
1.12 −1.08141 2.38078 −0.830562 −1.00000 −2.57459 0 3.06099 2.66813 1.08141
1.13 −0.909782 0.118964 −1.17230 −1.00000 −0.108231 0 2.88610 −2.98585 0.909782
1.14 −0.676237 −1.98168 −1.54270 −1.00000 1.34009 0 2.39571 0.927064 0.676237
1.15 −0.408377 2.69131 −1.83323 −1.00000 −1.09907 0 1.56540 4.24314 0.408377
1.16 −0.328879 −2.26637 −1.89184 −1.00000 0.745362 0 1.27995 2.13643 0.328879
1.17 −0.320371 −1.94969 −1.89736 −1.00000 0.624625 0 1.24860 0.801298 0.320371
1.18 0.0566779 1.88944 −1.99679 −1.00000 0.107089 0 −0.226529 0.569966 −0.0566779
1.19 0.557321 −2.46465 −1.68939 −1.00000 −1.37360 0 −2.05618 3.07450 −0.557321
1.20 0.559083 0.530934 −1.68743 −1.00000 0.296836 0 −2.06158 −2.71811 −0.559083
See all 34 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.34
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \( +1 \)
\(7\) \( +1 \)
\(37\) \( -1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 9065.2.a.bc yes 34
7.b odd 2 1 9065.2.a.bb ✓ 34
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
9065.2.a.bb ✓ 34 7.b odd 2 1
9065.2.a.bc yes 34 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(9065))\):

\( T_{2}^{34} + 2 T_{2}^{33} - 47 T_{2}^{32} - 92 T_{2}^{31} + 995 T_{2}^{30} + 1898 T_{2}^{29} + \cdots - 322 \) Copy content Toggle raw display
\( T_{3}^{34} - 10 T_{3}^{33} - 15 T_{3}^{32} + 452 T_{3}^{31} - 621 T_{3}^{30} - 8702 T_{3}^{29} + \cdots + 12175 \) Copy content Toggle raw display
\( T_{11}^{34} + 30 T_{11}^{33} + 243 T_{11}^{32} - 1392 T_{11}^{31} - 30811 T_{11}^{30} + \cdots - 1048867859392 \) Copy content Toggle raw display