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Properties

Label 1011.4.a.c
Level $1011$
Weight $4$
Character orbit 1011.a
Self dual yes
Analytic conductor $59.651$
Analytic rank $0$
Dimension $46$
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] = [1011,4,Mod(1,1011)] 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("1011.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1011, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 1011 = 3 \cdot 337 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1011.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [46] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(59.6509310158\)
Analytic rank: \(0\)
Dimension: \(46\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 46 q + 7 q^{2} - 138 q^{3} + 207 q^{4} + 42 q^{5} - 21 q^{6} - 72 q^{7} + 105 q^{8} + 414 q^{9} - 32 q^{10} + 126 q^{11} - 621 q^{12} + 114 q^{13} + 111 q^{14} - 126 q^{15} + 915 q^{16} + 154 q^{17} + 63 q^{18}+ \cdots + 1134 q^{99}+O(q^{100}) \) 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 −5.47715 −3.00000 21.9991 −9.67745 16.4314 −29.0367 −76.6753 9.00000 53.0048
1.2 −5.29881 −3.00000 20.0773 3.54817 15.8964 −11.2614 −63.9955 9.00000 −18.8010
1.3 −5.01360 −3.00000 17.1362 9.67835 15.0408 20.3764 −45.8054 9.00000 −48.5234
1.4 −4.62472 −3.00000 13.3880 2.45381 13.8742 10.6939 −24.9180 9.00000 −11.3482
1.5 −4.59531 −3.00000 13.1169 −0.882500 13.7859 −25.5503 −23.5136 9.00000 4.05536
1.6 −4.55149 −3.00000 12.7160 19.0551 13.6545 28.2151 −21.4649 9.00000 −86.7291
1.7 −4.52216 −3.00000 12.4499 −15.6658 13.5665 −2.98830 −20.1234 9.00000 70.8434
1.8 −4.46964 −3.00000 11.9777 8.02662 13.4089 6.30799 −17.7789 9.00000 −35.8761
1.9 −3.93610 −3.00000 7.49290 16.9852 11.8083 −32.2376 1.99598 9.00000 −66.8554
1.10 −3.92365 −3.00000 7.39501 −14.7876 11.7709 −6.54928 2.37377 9.00000 58.0213
1.11 −3.38284 −3.00000 3.44360 20.5381 10.1485 0.835972 15.4136 9.00000 −69.4769
1.12 −3.07541 −3.00000 1.45812 −6.39601 9.22622 0.626874 20.1189 9.00000 19.6703
1.13 −2.66818 −3.00000 −0.880817 −10.8109 8.00454 −4.15190 23.6956 9.00000 28.8455
1.14 −2.43025 −3.00000 −2.09386 −20.7968 7.29076 10.8989 24.5307 9.00000 50.5415
1.15 −1.86378 −3.00000 −4.52631 12.8402 5.59135 16.8655 23.3463 9.00000 −23.9313
1.16 −1.77378 −3.00000 −4.85371 7.19793 5.32134 −25.0716 22.7996 9.00000 −12.7675
1.17 −1.67739 −3.00000 −5.18636 −10.3096 5.03218 −14.8478 22.1187 9.00000 17.2932
1.18 −1.34241 −3.00000 −6.19794 12.1140 4.02723 −29.9968 19.0594 9.00000 −16.2620
1.19 −1.33926 −3.00000 −6.20638 −9.21699 4.01779 27.5315 19.0261 9.00000 12.3440
1.20 −1.10445 −3.00000 −6.78020 −4.09679 3.31334 −16.3434 16.3239 9.00000 4.52468
See all 46 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.46
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(337\) \( +1 \)

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 1011.4.a.c ✓ 46
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1011.4.a.c ✓ 46 1.a even 1 1 trivial