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Properties

Label 7865.2.a.bm
Level $7865$
Weight $2$
Character orbit 7865.a
Self dual yes
Analytic conductor $62.802$
Analytic rank $0$
Dimension $26$
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] = [7865,2,Mod(1,7865)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7865, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7865.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 7865 = 5 \cdot 11^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7865.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [26,-1,9,31,-26,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(62.8023411897\)
Analytic rank: \(0\)
Dimension: \(26\)
Twist minimal: no (minimal twist has level 715)
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.

\(\operatorname{Tr}(f)(q) = \) \( 26 q - q^{2} + 9 q^{3} + 31 q^{4} - 26 q^{5} - 9 q^{6} - 3 q^{7} - 3 q^{8} + 29 q^{9} + q^{10} + 16 q^{12} + 26 q^{13} - 7 q^{14} - 9 q^{15} + 45 q^{16} + 8 q^{17} + 11 q^{18} + 5 q^{19} - 31 q^{20} + 3 q^{21}+ \cdots - 6 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.75771 0.541601 5.60497 −1.00000 −1.49358 −1.75424 −9.94146 −2.70667 2.75771
1.2 −2.73985 2.95835 5.50680 −1.00000 −8.10545 0.428972 −9.60814 5.75184 2.73985
1.3 −2.31329 −1.58938 3.35130 −1.00000 3.67668 4.49627 −3.12594 −0.473883 2.31329
1.4 −2.30288 3.22162 3.30326 −1.00000 −7.41900 −2.76546 −3.00125 7.37881 2.30288
1.5 −2.24433 −1.78432 3.03702 −1.00000 4.00460 −4.60866 −2.32741 0.183786 2.24433
1.6 −2.13959 0.440008 2.57786 −1.00000 −0.941437 0.675228 −1.23638 −2.80639 2.13959
1.7 −1.50038 −1.26501 0.251132 −1.00000 1.89799 −2.28136 2.62396 −1.39975 1.50038
1.8 −1.40174 1.46774 −0.0351301 −1.00000 −2.05738 2.98758 2.85272 −0.845753 1.40174
1.9 −1.16994 −0.319624 −0.631232 −1.00000 0.373943 2.05233 3.07839 −2.89784 1.16994
1.10 −1.07047 2.22529 −0.854099 −1.00000 −2.38210 4.74788 3.05522 1.95192 1.07047
1.11 −0.758879 1.52594 −1.42410 −1.00000 −1.15801 −2.88466 2.59848 −0.671500 0.758879
1.12 −0.262089 −1.51512 −1.93131 −1.00000 0.397096 −3.12207 1.03035 −0.704421 0.262089
1.13 −0.224075 −2.18156 −1.94979 −1.00000 0.488831 −1.71862 0.885048 1.75918 0.224075
1.14 0.192418 −2.62399 −1.96298 −1.00000 −0.504903 4.30754 −0.762546 3.88535 −0.192418
1.15 0.352577 2.29811 −1.87569 −1.00000 0.810261 −1.01025 −1.36648 2.28133 −0.352577
1.16 0.515369 3.41257 −1.73439 −1.00000 1.75873 −3.94718 −1.92459 8.64561 −0.515369
1.17 0.700503 0.188724 −1.50930 −1.00000 0.132202 3.15432 −2.45827 −2.96438 −0.700503
1.18 0.801571 2.53408 −1.35748 −1.00000 2.03125 2.85744 −2.69126 3.42157 −0.801571
1.19 1.65385 −0.802760 0.735212 −1.00000 −1.32764 −2.81488 −2.09177 −2.35558 −1.65385
1.20 1.74838 1.70625 1.05684 −1.00000 2.98318 3.39882 −1.64901 −0.0887010 −1.74838
See all 26 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.26
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \( +1 \)
\(11\) \( +1 \)
\(13\) \( -1 \)

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 7865.2.a.bm 26
11.b odd 2 1 7865.2.a.bn 26
11.c even 5 2 715.2.v.d ✓ 52
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
715.2.v.d ✓ 52 11.c even 5 2
7865.2.a.bm 26 1.a even 1 1 trivial
7865.2.a.bn 26 11.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7865))\):

\( T_{2}^{26} + T_{2}^{25} - 41 T_{2}^{24} - 39 T_{2}^{23} + 733 T_{2}^{22} + 661 T_{2}^{21} - 7506 T_{2}^{20} + \cdots - 191 \) Copy content Toggle raw display
\( T_{3}^{26} - 9 T_{3}^{25} - 13 T_{3}^{24} + 323 T_{3}^{23} - 318 T_{3}^{22} - 4937 T_{3}^{21} + \cdots + 7409 \) Copy content Toggle raw display