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Properties

Label 5243.2.a.p
Level $5243$
Weight $2$
Character orbit 5243.a
Self dual yes
Analytic conductor $41.866$
Analytic rank $0$
Dimension $35$
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] = [5243,2,Mod(1,5243)] 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("5243.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5243, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 5243 = 7^{2} \cdot 107 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5243.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [35,0,11] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(41.8655657798\)
Analytic rank: \(0\)
Dimension: \(35\)
Twist minimal: no (minimal twist has level 749)
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.

\(\operatorname{Tr}(f)(q) = \) \( 35 q + 11 q^{3} + 34 q^{4} + 13 q^{5} + 8 q^{6} + 36 q^{9} + 20 q^{10} - q^{11} + 27 q^{12} + 42 q^{13} + 6 q^{15} + 32 q^{16} + 20 q^{17} - q^{18} + 15 q^{19} + 24 q^{20} - 8 q^{22} - 3 q^{23} + 28 q^{24}+ \cdots - 16 q^{99}+O(q^{100}) \) 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 −2.73748 2.60526 5.49379 −1.71309 −7.13183 0 −9.56416 3.78736 4.68954
1.2 −2.70627 −1.40898 5.32389 −1.92044 3.81309 0 −8.99534 −1.01476 5.19722
1.3 −2.40830 −3.01316 3.79990 −0.973086 7.25660 0 −4.33471 6.07915 2.34348
1.4 −2.18014 1.36730 2.75301 1.78245 −2.98090 0 −1.64167 −1.13050 −3.88599
1.5 −2.16010 3.31919 2.66603 3.34297 −7.16978 0 −1.43870 8.01701 −7.22115
1.6 −2.09420 0.944780 2.38567 3.15476 −1.97856 0 −0.807680 −2.10739 −6.60670
1.7 −2.00863 1.17921 2.03460 −2.21400 −2.36860 0 −0.0694964 −1.60947 4.44710
1.8 −1.89220 −0.639071 1.58043 0.473842 1.20925 0 0.793908 −2.59159 −0.896606
1.9 −1.60578 −2.61496 0.578537 1.09246 4.19905 0 2.28256 3.83800 −1.75425
1.10 −1.48422 −1.25591 0.202914 −3.66325 1.86405 0 2.66727 −1.42269 5.43707
1.11 −1.48278 −0.486385 0.198635 −0.0423250 0.721202 0 2.67103 −2.76343 0.0627586
1.12 −1.27164 1.39488 −0.382928 3.46565 −1.77379 0 3.03023 −1.05431 −4.40706
1.13 −0.878369 −0.426716 −1.22847 3.53828 0.374814 0 2.83579 −2.81791 −3.10792
1.14 −0.819036 3.12177 −1.32918 −2.97582 −2.55684 0 2.72672 6.74543 2.43731
1.15 −0.296520 0.294428 −1.91208 −0.136294 −0.0873038 0 1.16001 −2.91331 0.0404138
1.16 −0.197340 1.51950 −1.96106 −3.92300 −0.299858 0 0.781676 −0.691132 0.774166
1.17 −0.153437 −2.77896 −1.97646 3.45814 0.426396 0 0.610135 4.72264 −0.530606
1.18 −0.0457903 −1.99485 −1.99790 −2.70163 0.0913447 0 0.183065 0.979418 0.123708
1.19 0.0926697 2.97201 −1.99141 −1.02525 0.275416 0 −0.369883 5.83287 −0.0950096
1.20 0.537946 −1.06988 −1.71061 3.35919 −0.575535 0 −1.99611 −1.85537 1.80706
See all 35 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.35
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(7\) \( +1 \)
\(107\) \( -1 \)

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 5243.2.a.p 35
7.b odd 2 1 5243.2.a.m 35
7.c even 3 2 749.2.e.a ✓ 70
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
749.2.e.a ✓ 70 7.c even 3 2
5243.2.a.m 35 7.b odd 2 1
5243.2.a.p 35 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5243))\):

\( T_{2}^{35} - 52 T_{2}^{33} + 1223 T_{2}^{31} - 3 T_{2}^{30} - 17219 T_{2}^{29} + 145 T_{2}^{28} + \cdots - 37 \) Copy content Toggle raw display
\( T_{3}^{35} - 11 T_{3}^{34} - 10 T_{3}^{33} + 518 T_{3}^{32} - 1033 T_{3}^{31} - 10085 T_{3}^{30} + \cdots - 62225 \) Copy content Toggle raw display