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Properties

Label 253.3.g.a
Level $253$
Weight $3$
Character orbit 253.g
Analytic conductor $6.894$
Analytic rank $0$
Dimension $176$
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] = [253,3,Mod(24,253)] 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("253.24"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(253, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")
 
Level: \( N \) \(=\) \( 253 = 11 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 253.g (of order \(10\), degree \(4\), 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: \(6.89375068832\)
Analytic rank: \(0\)
Dimension: \(176\)
Relative dimension: \(44\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 176 q - 8 q^{3} + 88 q^{4} - 40 q^{6} - 120 q^{9} - 8 q^{14} - 12 q^{15} - 272 q^{16} - 80 q^{17} + 80 q^{18} - 60 q^{19} + 40 q^{20} + 136 q^{22} - 60 q^{24} - 268 q^{25} + 40 q^{26} + 148 q^{27} - 240 q^{28}+ \cdots - 414 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
24.1 −3.66609 − 1.19118i 2.03606 − 1.47929i 8.78522 + 6.38283i 1.27281 + 3.91730i −9.22649 + 2.99787i 3.33486 − 4.59004i −15.5412 − 21.3906i −0.823888 + 2.53567i − 15.8773i
24.2 −3.56389 − 1.15798i −4.16114 + 3.02325i 8.12432 + 5.90266i −0.312727 − 0.962476i 18.3307 − 5.95601i −2.38519 + 3.28293i −13.3086 − 18.3177i 5.39393 − 16.6008i 3.79229i
24.3 −3.35117 − 1.08886i 0.581295 − 0.422336i 6.80866 + 4.94678i −2.80322 − 8.62741i −2.40788 + 0.782369i −3.56198 + 4.90264i −9.14607 − 12.5885i −2.62162 + 8.06851i 31.9642i
24.4 −3.33336 − 1.08307i −0.631314 + 0.458676i 6.70215 + 4.86940i 0.676515 + 2.08210i 2.60117 − 0.845173i −2.94474 + 4.05308i −8.82624 − 12.1483i −2.59298 + 7.98037i − 7.67309i
24.5 −3.11475 − 1.01204i −1.48726 + 1.08056i 5.44137 + 3.95339i −1.25920 − 3.87543i 5.72602 − 1.86050i 6.37790 − 8.77843i −5.24743 − 7.22247i −1.73682 + 5.34537i 13.3454i
24.6 −3.11063 − 1.01070i 3.92768 − 2.85362i 5.41841 + 3.93671i 0.561936 + 1.72946i −15.1017 + 4.90684i −4.61408 + 6.35074i −5.18592 − 7.13780i 4.50232 − 13.8567i − 5.94766i
24.7 −2.81261 − 0.913872i −3.21219 + 2.33380i 3.83953 + 2.78958i 1.38144 + 4.25163i 11.1674 − 3.62852i 3.16567 − 4.35717i −1.29663 − 1.78466i 2.09044 − 6.43370i − 13.2206i
24.8 −2.74723 − 0.892629i 3.73742 − 2.71540i 3.51442 + 2.55337i −0.431955 − 1.32942i −12.6914 + 4.12369i −0.525097 + 0.722734i −0.584171 − 0.804043i 3.81380 − 11.7377i 4.03780i
24.9 −2.57568 − 0.836888i −1.71143 + 1.24343i 2.69766 + 1.95997i 2.68563 + 8.26552i 5.44870 − 1.77039i −6.08934 + 8.38126i 1.05939 + 1.45812i −1.39827 + 4.30344i − 23.5369i
24.10 −2.51750 − 0.817984i 1.62027 − 1.17720i 2.43262 + 1.76740i 2.85518 + 8.78734i −5.04196 + 1.63823i 3.48178 − 4.79226i 1.54518 + 2.12676i −1.54166 + 4.74475i − 24.4576i
24.11 −2.13012 − 0.692117i 3.32732 − 2.41744i 0.822309 + 0.597442i −1.58252 − 4.87050i −8.76074 + 2.84654i 7.61829 − 10.4857i 3.92783 + 5.40619i 2.44590 − 7.52771i 11.4700i
24.12 −2.07411 − 0.673919i 1.03114 − 0.749170i 0.611699 + 0.444425i −1.67954 − 5.16908i −2.64359 + 0.858953i −3.19360 + 4.39561i 4.15826 + 5.72335i −2.27915 + 7.01450i 11.8531i
24.13 −1.87192 − 0.608222i −1.22496 + 0.889986i −0.101932 − 0.0740581i −0.254234 − 0.782453i 2.83433 − 0.920931i −0.908239 + 1.25008i 4.77340 + 6.57002i −2.07270 + 6.37911i 1.61932i
24.14 −1.66340 − 0.540473i −3.78273 + 2.74831i −0.761265 − 0.553091i −2.93456 − 9.03165i 7.77759 − 2.52709i 3.11542 − 4.28800i 5.07952 + 6.99136i 3.97465 − 12.2327i 16.6093i
24.15 −1.61359 − 0.524288i −3.31109 + 2.40565i −0.907261 − 0.659164i −0.550058 − 1.69290i 6.60401 − 2.14577i −6.81304 + 9.37734i 5.10738 + 7.02971i 2.39502 − 7.37112i 3.02005i
24.16 −1.54107 − 0.500724i −4.35510 + 3.16417i −1.11189 − 0.807838i 1.31121 + 4.03550i 8.29590 − 2.69550i 4.37703 − 6.02447i 5.11874 + 7.04534i 6.17382 − 19.0011i − 6.87555i
24.17 −1.29246 − 0.419944i 1.60750 − 1.16792i −1.74198 − 1.26562i 0.782769 + 2.40912i −2.56809 + 0.834422i 0.433806 − 0.597082i 4.91507 + 6.76501i −1.56112 + 4.80464i − 3.44240i
24.18 −1.00173 − 0.325481i 4.44142 − 3.22688i −2.33855 − 1.69906i 2.73238 + 8.40940i −5.49938 + 1.78686i 1.12303 − 1.54572i 4.26598 + 5.87162i 6.53232 − 20.1044i − 9.31326i
24.19 −0.601292 − 0.195372i 2.06538 − 1.50059i −2.91269 − 2.11619i 0.860171 + 2.64733i −1.53507 + 0.498774i −5.31865 + 7.32049i 2.82441 + 3.88746i −0.767116 + 2.36094i − 1.75987i
24.20 −0.385327 − 0.125200i 4.25617 − 3.09229i −3.10327 − 2.25465i −2.72822 − 8.39661i −2.02717 + 0.658668i −7.32878 + 10.0872i 1.86607 + 2.56842i 5.77158 − 17.7631i 3.57701i
See next 80 embeddings (of 176 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 24.44
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.d odd 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 253.3.g.a ✓ 176
11.d odd 10 1 inner 253.3.g.a ✓ 176
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
253.3.g.a ✓ 176 1.a even 1 1 trivial
253.3.g.a ✓ 176 11.d odd 10 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(253, [\chi])\).