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Properties

Label 230.4.g.d
Level $230$
Weight $4$
Character orbit 230.g
Analytic conductor $13.570$
Analytic rank $0$
Dimension $70$
Inner twists $2$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [230,4,Mod(31,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.31"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 230.g (of order \(11\), degree \(10\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [70,-14,3] 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: no
Analytic conductor: \(13.5704393013\)
Analytic rank: \(0\)
Dimension: \(70\)
Relative dimension: \(7\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 70 q - 14 q^{2} + 3 q^{3} - 28 q^{4} - 35 q^{5} + 6 q^{6} - 78 q^{7} - 56 q^{8} - 24 q^{9} - 70 q^{10} - 15 q^{11} - 120 q^{12} - 270 q^{13} + 64 q^{14} + 15 q^{15} - 112 q^{16} + 114 q^{17} - 48 q^{18}+ \cdots + 11285 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
31.1 −0.284630 + 1.97964i −4.10508 − 8.98887i −3.83797 − 1.12693i −3.27430 − 3.77875i 18.9632 − 5.56809i −23.3667 − 15.0169i 3.32332 − 7.27706i −46.2669 + 53.3948i 8.41254 − 5.40641i
31.2 −0.284630 + 1.97964i −2.58225 − 5.65433i −3.83797 − 1.12693i −3.27430 − 3.77875i 11.9285 − 3.50254i 8.08665 + 5.19698i 3.32332 − 7.27706i −7.62224 + 8.79653i 8.41254 − 5.40641i
31.3 −0.284630 + 1.97964i −0.557048 − 1.21977i −3.83797 − 1.12693i −3.27430 − 3.77875i 2.57325 − 0.755575i 4.15187 + 2.66824i 3.32332 − 7.27706i 16.5037 − 19.0463i 8.41254 − 5.40641i
31.4 −0.284630 + 1.97964i 0.779667 + 1.70723i −3.83797 − 1.12693i −3.27430 − 3.77875i −3.60163 + 1.05753i −17.1073 − 10.9942i 3.32332 − 7.27706i 15.3745 − 17.7431i 8.41254 − 5.40641i
31.5 −0.284630 + 1.97964i 0.934566 + 2.04642i −3.83797 − 1.12693i −3.27430 − 3.77875i −4.31718 + 1.26764i 13.5404 + 8.70192i 3.32332 − 7.27706i 14.3668 − 16.5802i 8.41254 − 5.40641i
31.6 −0.284630 + 1.97964i 3.50164 + 7.66752i −3.83797 − 1.12693i −3.27430 − 3.77875i −16.1756 + 4.74959i −21.3660 − 13.7311i 3.32332 − 7.27706i −28.8481 + 33.2925i 8.41254 − 5.40641i
31.7 −0.284630 + 1.97964i 3.62947 + 7.94742i −3.83797 − 1.12693i −3.27430 − 3.77875i −16.7661 + 4.92297i 25.2655 + 16.2371i 3.32332 − 7.27706i −32.3073 + 37.2846i 8.41254 − 5.40641i
41.1 −1.91899 − 0.563465i −5.62703 + 6.49394i 3.36501 + 2.16256i −0.711574 + 4.94911i 14.4573 − 9.29114i −0.0746076 − 0.163368i −5.23889 − 6.04600i −6.66528 − 46.3580i 4.15415 − 9.09632i
41.2 −1.91899 − 0.563465i −5.54798 + 6.40271i 3.36501 + 2.16256i −0.711574 + 4.94911i 14.2542 − 9.16062i −0.812937 − 1.78008i −5.23889 − 6.04600i −6.37211 − 44.3190i 4.15415 − 9.09632i
41.3 −1.91899 − 0.563465i −2.31675 + 2.67368i 3.36501 + 2.16256i −0.711574 + 4.94911i 5.95234 − 3.82534i 13.3612 + 29.2569i −5.23889 − 6.04600i 2.06130 + 14.3367i 4.15415 − 9.09632i
41.4 −1.91899 − 0.563465i −1.37651 + 1.58858i 3.36501 + 2.16256i −0.711574 + 4.94911i 3.53661 − 2.27284i −11.8356 − 25.9163i −5.23889 − 6.04600i 3.21370 + 22.3518i 4.15415 − 9.09632i
41.5 −1.91899 − 0.563465i 1.16443 − 1.34382i 3.36501 + 2.16256i −0.711574 + 4.94911i −2.99172 + 1.92266i −6.00332 − 13.1454i −5.23889 − 6.04600i 3.39254 + 23.5956i 4.15415 − 9.09632i
41.6 −1.91899 − 0.563465i 3.35821 − 3.87558i 3.36501 + 2.16256i −0.711574 + 4.94911i −8.62810 + 5.54495i 3.71145 + 8.12693i −5.23889 − 6.04600i 0.0999547 + 0.695200i 4.15415 − 9.09632i
41.7 −1.91899 − 0.563465i 4.61105 − 5.32144i 3.36501 + 2.16256i −0.711574 + 4.94911i −11.8470 + 7.61360i 4.61346 + 10.1021i −5.23889 − 6.04600i −3.21340 − 22.3497i 4.15415 − 9.09632i
71.1 1.68251 + 1.08128i −1.32808 − 9.23701i 1.66166 + 3.63853i −4.79746 − 1.40866i 7.75331 − 16.9774i −7.67166 + 8.85357i −1.13852 + 7.91857i −57.6523 + 16.9282i −6.54861 − 7.55750i
71.2 1.68251 + 1.08128i −0.573704 − 3.99020i 1.66166 + 3.63853i −4.79746 − 1.40866i 3.34927 − 7.33387i 8.19371 − 9.45604i −1.13852 + 7.91857i 10.3138 − 3.02840i −6.54861 − 7.55750i
71.3 1.68251 + 1.08128i −0.533706 − 3.71201i 1.66166 + 3.63853i −4.79746 − 1.40866i 3.11576 − 6.82257i −11.4866 + 13.2562i −1.13852 + 7.91857i 12.4121 − 3.64453i −6.54861 − 7.55750i
71.4 1.68251 + 1.08128i 0.0867437 + 0.603316i 1.66166 + 3.63853i −4.79746 − 1.40866i −0.506407 + 1.10888i −3.02881 + 3.49544i −1.13852 + 7.91857i 25.5498 − 7.50211i −6.54861 − 7.55750i
71.5 1.68251 + 1.08128i 0.442628 + 3.07854i 1.66166 + 3.63853i −4.79746 − 1.40866i −2.58405 + 5.65828i 21.5377 − 24.8559i −1.13852 + 7.91857i 16.6248 − 4.88148i −6.54861 − 7.55750i
71.6 1.68251 + 1.08128i 0.811575 + 5.64463i 1.66166 + 3.63853i −4.79746 − 1.40866i −4.73795 + 10.3747i −22.1574 + 25.5710i −1.13852 + 7.91857i −5.29690 + 1.55531i −6.54861 − 7.55750i
See all 70 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 31.7
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.c even 11 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 230.4.g.d ✓ 70
23.c even 11 1 inner 230.4.g.d ✓ 70
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
230.4.g.d ✓ 70 1.a even 1 1 trivial
230.4.g.d ✓ 70 23.c even 11 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{70} - 3 T_{3}^{69} + 111 T_{3}^{68} - 581 T_{3}^{67} + 10870 T_{3}^{66} - 41622 T_{3}^{65} + \cdots + 20\!\cdots\!96 \) acting on \(S_{4}^{\mathrm{new}}(230, [\chi])\). Copy content Toggle raw display