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Properties

Label 983.2.c.a
Level $983$
Weight $2$
Character orbit 983.c
Analytic conductor $7.849$
Analytic rank $0$
Dimension $39690$
Inner twists $2$

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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] = [983,2,Mod(2,983)] 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("983.2"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(983, base_ring=CyclotomicField(982)) chi = DirichletCharacter(H, H._module([674])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 983 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 983.c (of order \(491\), degree \(490\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.84929451869\)
Analytic rank: \(0\)
Dimension: \(39690\)
Relative dimension: \(81\) over \(\Q(\zeta_{491})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{491}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 39690 q - 489 q^{2} - 487 q^{3} - 565 q^{4} - 485 q^{5} - 477 q^{6} - 489 q^{7} - 485 q^{8} - 558 q^{9} - 471 q^{10} - 477 q^{11} - 463 q^{12} - 483 q^{13} - 473 q^{14} - 461 q^{15} - 543 q^{16} - 481 q^{17}+ \cdots - 299 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2.1 −0.882111 + 2.63433i 2.23553 + 1.25595i −4.56485 − 3.44317i −1.70964 + 2.57870i −5.28058 + 4.78124i 0.512184 − 1.13021i 8.51597 − 5.84418i 1.85965 + 3.05328i −5.28506 − 6.77846i
2.2 −0.882011 + 2.63403i −2.15731 − 1.21201i −4.56345 − 3.44211i −0.627390 + 0.946311i 5.09524 − 4.61342i 1.88896 − 4.16828i 8.51098 − 5.84075i 1.62450 + 2.66720i −1.93925 − 2.48722i
2.3 −0.873868 + 2.60971i −2.35753 − 1.32449i −4.45024 − 3.35672i 0.433776 − 0.654278i 5.51671 − 4.99503i −1.45490 + 3.21047i 8.11063 − 5.56601i 2.24312 + 3.68287i 1.32841 + 1.70378i
2.4 −0.862858 + 2.57683i 1.07786 + 0.605560i −4.29883 − 3.24251i 1.73663 − 2.61941i −2.49047 + 2.25496i −1.58443 + 3.49630i 7.58350 − 5.20426i −0.765444 − 1.25675i 5.25132 + 6.73519i
2.5 −0.815103 + 2.43422i 1.99272 + 1.11954i −3.66431 − 2.76391i 0.269938 − 0.407156i −4.34946 + 3.93817i 0.302286 − 0.667041i 5.48157 − 3.76178i 1.15702 + 1.89966i 0.771079 + 0.988963i
2.6 −0.805572 + 2.40575i −0.153383 − 0.0861729i −3.54199 − 2.67165i −0.680394 + 1.02626i 0.330872 − 0.299584i 1.03475 − 2.28334i 5.09698 − 3.49786i −1.54443 − 2.53574i −1.92082 − 2.46358i
2.7 −0.782295 + 2.33624i −0.0510472 − 0.0286790i −3.24932 − 2.45089i −1.37935 + 2.08052i 0.106935 − 0.0968230i −1.52243 + 3.35948i 4.20501 − 2.88573i −1.55875 − 2.55925i −3.78153 − 4.85008i
2.8 −0.752960 + 2.24863i −1.39225 − 0.782183i −2.89269 − 2.18189i 0.987618 − 1.48965i 2.80715 − 2.54170i −0.299880 + 0.661733i 3.17392 − 2.17814i −0.233998 − 0.384191i 2.60605 + 3.34244i
2.9 −0.752267 + 2.24656i −0.810068 − 0.455108i −2.88443 − 2.17566i 2.05128 − 3.09401i 1.63182 − 1.47751i 0.245279 − 0.541247i 3.15078 − 2.16226i −1.11145 − 1.82484i 5.40777 + 6.93585i
2.10 −0.696245 + 2.07926i −2.48076 − 1.39373i −2.24185 − 1.69098i 1.99175 − 3.00421i 4.62514 − 4.18777i 1.53695 − 3.39151i 1.46097 − 1.00260i 2.65117 + 4.35284i 4.85979 + 6.23303i
2.11 −0.695622 + 2.07740i 1.13868 + 0.639727i −2.23498 − 1.68580i 0.512099 − 0.772414i −2.12106 + 1.92049i 1.35903 − 2.99891i 1.44412 − 0.991043i −0.673191 − 1.10528i 1.24839 + 1.60114i
2.12 −0.691522 + 2.06516i −1.31722 − 0.740034i −2.18995 − 1.65183i −2.30250 + 3.47293i 2.43917 − 2.20852i 0.363807 − 0.802796i 1.33432 − 0.915691i −0.373111 − 0.612595i −5.57991 − 7.15662i
2.13 −0.682299 + 2.03761i −2.29977 − 1.29204i −2.08961 − 1.57615i −0.572361 + 0.863308i 4.20182 − 3.80448i −1.13382 + 2.50196i 1.09385 − 0.750669i 2.05904 + 3.38064i −1.36857 − 1.75528i
2.14 −0.668269 + 1.99571i 2.16322 + 1.21533i −1.93958 − 1.46298i −1.46604 + 2.21127i −3.87105 + 3.50500i −1.51734 + 3.34825i 0.745241 − 0.511430i 1.64195 + 2.69585i −3.43336 − 4.40352i
2.15 −0.649824 + 1.94063i 2.50384 + 1.40669i −1.74706 − 1.31777i 2.25729 − 3.40473i −4.35692 + 3.94491i 1.07843 − 2.37972i 0.317759 − 0.218066i 2.72988 + 4.48207i 5.14048 + 6.59303i
2.16 −0.612989 + 1.83062i 1.04506 + 0.587130i −1.37872 − 1.03994i 1.11482 − 1.68151i −1.71543 + 1.55321i −1.16764 + 2.57657i −0.434644 + 0.298279i −0.813104 − 1.33500i 2.39485 + 3.07156i
2.17 −0.585179 + 1.74757i −2.62769 − 1.47627i −1.11487 − 0.840921i −1.01017 + 1.52367i 4.11756 − 3.72820i 0.654151 − 1.44349i −0.917117 + 0.629381i 3.16483 + 5.19619i −2.07160 − 2.65697i
2.18 −0.578509 + 1.72765i 2.91461 + 1.63747i −1.05340 − 0.794559i −0.586439 + 0.884543i −4.51512 + 4.08815i −0.437511 + 0.965436i −1.02232 + 0.701577i 4.25313 + 6.98303i −1.18893 − 1.52488i
2.19 −0.555704 + 1.65955i 0.352885 + 0.198256i −0.848581 − 0.640067i −0.636799 + 0.960502i −0.525115 + 0.475459i −1.20682 + 2.66304i −1.35223 + 0.927979i −1.47531 − 2.42225i −1.24013 − 1.59055i
2.20 −0.529551 + 1.58145i 0.208046 + 0.116883i −0.623831 − 0.470542i −1.17513 + 1.77249i −0.295015 + 0.267117i 1.73067 − 3.81900i −1.67570 + 1.14996i −1.53091 − 2.51354i −2.18080 − 2.79703i
See next 80 embeddings (of 39690 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2.81
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
983.c even 491 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 983.2.c.a ✓ 39690
983.c even 491 1 inner 983.2.c.a ✓ 39690
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
983.2.c.a ✓ 39690 1.a even 1 1 trivial
983.2.c.a ✓ 39690 983.c even 491 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(983, [\chi])\).

Additional information

This newform has the largest dimension among those with $Nk^2$ $\le 4000$.