↑

Properties

Label 7865.2.a.bn
Level $7865$
Weight $2$
Character orbit 7865.a
Self dual yes
Analytic conductor $62.802$
Analytic rank $0$
Dimension $26$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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 −2.69156 1.93322 5.24447 −1.00000 −5.20337 4.93110 −8.73268 0.737345 2.69156
1.2 −2.68902 −1.19366 5.23084 −1.00000 3.20977 3.18383 −8.68781 −1.57519 2.68902
1.3 −2.43769 −0.251242 3.94233 −1.00000 0.612451 −2.20056 −4.73480 −2.93688 2.43769
1.4 −2.09354 3.28162 2.38290 −1.00000 −6.87020 −1.40212 −0.801619 7.76905 2.09354
1.5 −2.05689 −2.38398 2.23080 −1.00000 4.90359 0.222650 −0.474739 2.68336 2.05689
1.6 −1.95186 −2.82450 1.80976 −1.00000 5.51303 0.464099 0.371316 4.97779 1.95186
1.7 −1.74838 1.70625 1.05684 −1.00000 −2.98318 −3.39882 1.64901 −0.0887010 1.74838
1.8 −1.65385 −0.802760 0.735212 −1.00000 1.32764 2.81488 2.09177 −2.35558 1.65385
1.9 −0.801571 2.53408 −1.35748 −1.00000 −2.03125 −2.85744 2.69126 3.42157 0.801571
1.10 −0.700503 0.188724 −1.50930 −1.00000 −0.132202 −3.15432 2.45827 −2.96438 0.700503
1.11 −0.515369 3.41257 −1.73439 −1.00000 −1.75873 3.94718 1.92459 8.64561 0.515369
1.12 −0.352577 2.29811 −1.87569 −1.00000 −0.810261 1.01025 1.36648 2.28133 0.352577
1.13 −0.192418 −2.62399 −1.96298 −1.00000 0.504903 −4.30754 0.762546 3.88535 0.192418
1.14 0.224075 −2.18156 −1.94979 −1.00000 −0.488831 1.71862 −0.885048 1.75918 −0.224075
1.15 0.262089 −1.51512 −1.93131 −1.00000 −0.397096 3.12207 −1.03035 −0.704421 −0.262089
1.16 0.758879 1.52594 −1.42410 −1.00000 1.15801 2.88466 −2.59848 −0.671500 −0.758879
1.17 1.07047 2.22529 −0.854099 −1.00000 2.38210 −4.74788 −3.05522 1.95192 −1.07047
1.18 1.16994 −0.319624 −0.631232 −1.00000 −0.373943 −2.05233 −3.07839 −2.89784 −1.16994
1.19 1.40174 1.46774 −0.0351301 −1.00000 2.05738 −2.98758 −2.85272 −0.845753 −1.40174
1.20 1.50038 −1.26501 0.251132 −1.00000 −1.89799 2.28136 −2.62396 −1.39975 −1.50038
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.bn 26
11.b odd 2 1 7865.2.a.bm 26
11.d odd 10 2 715.2.v.d ✓ 52
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
715.2.v.d ✓ 52 11.d odd 10 2
7865.2.a.bm 26 11.b odd 2 1
7865.2.a.bn 26 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(7865))\):

\( T_{2}^{26} - T_{2}^{25} - 41 T_{2}^{24} + 39 T_{2}^{23} + 733 T_{2}^{22} - 661 T_{2}^{21} - 7506 T_{2}^{20} + \cdots - 191 \) 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