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Properties

Label 151.3.i.a
Level $151$
Weight $3$
Character orbit 151.i
Analytic conductor $4.114$
Analytic rank $0$
Dimension $192$
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] = [151,3,Mod(23,151)] 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("151.23"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(151, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([23])) N = Newforms(chi, 3, names="a")
 
Level: \( N \) \(=\) \( 151 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 151.i (of order \(30\), degree \(8\), 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: \(4.11445199184\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(24\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 192 q - 5 q^{2} - 10 q^{3} - 181 q^{4} - 9 q^{5} + 13 q^{6} - 31 q^{7} + 80 q^{8} + 124 q^{9} + 41 q^{10} + 25 q^{11} + 55 q^{12} - 28 q^{13} + 7 q^{14} - 34 q^{15} - 321 q^{16} - 82 q^{17} - 194 q^{18}+ \cdots - 1441 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
23.1 −1.93517 + 3.35182i −3.05782 − 0.993547i −5.48979 − 9.50859i 2.16257 − 0.962838i 9.24760 − 8.32658i 0.898574 + 2.01823i 27.0134 1.08199 + 0.786114i −0.957688 + 9.11179i
23.2 −1.88170 + 3.25920i 4.08248 + 1.32648i −5.08158 − 8.80156i −7.74565 + 3.44858i −12.0053 + 10.8096i −3.03905 − 6.82581i 23.1945 7.62595 + 5.54058i 3.33536 − 31.7338i
23.3 −1.68811 + 2.92388i 3.36424 + 1.09311i −3.69940 − 6.40755i 6.84085 − 3.04574i −8.87531 + 7.99136i 0.328068 + 0.736852i 11.4751 2.84206 + 2.06488i −2.64268 + 25.1434i
23.4 −1.52844 + 2.64734i −1.17971 − 0.383311i −2.67228 − 4.62852i −6.31759 + 2.81277i 2.81787 − 2.53722i 1.77668 + 3.99049i 4.11014 −6.03637 − 4.38568i 2.20971 − 21.0240i
23.5 −1.36107 + 2.35744i −0.235072 − 0.0763796i −1.70502 − 2.95319i 2.62499 − 1.16872i 0.500010 − 0.450211i −3.59421 − 8.07273i −1.60594 −7.23173 − 5.25416i −0.817602 + 7.77897i
23.6 −1.25591 + 2.17530i −5.63733 − 1.83168i −1.15461 − 1.99984i −6.31006 + 2.80942i 11.0644 − 9.96245i −3.02001 − 6.78306i −4.24693 21.1433 + 15.3615i 1.81353 − 17.2546i
23.7 −1.07636 + 1.86432i −3.53417 − 1.14832i −0.317116 − 0.549260i 3.75572 − 1.67215i 5.94489 − 5.35281i 5.17823 + 11.6305i −7.24558 3.89059 + 2.82668i −0.925096 + 8.80170i
23.8 −1.02244 + 1.77092i 2.55024 + 0.828622i −0.0907679 − 0.157215i −2.84007 + 1.26448i −4.07489 + 3.66905i 2.27369 + 5.10679i −7.80830 −1.46406 − 1.06370i 0.664509 − 6.32238i
23.9 −0.818005 + 1.41683i 5.55490 + 1.80490i 0.661735 + 1.14616i 0.459602 − 0.204628i −7.10116 + 6.39392i −0.285442 − 0.641112i −8.70925 20.3181 + 14.7620i −0.0860344 + 0.818563i
23.10 −0.500098 + 0.866195i −3.18165 − 1.03378i 1.49980 + 2.59774i 4.64072 − 2.06618i 2.48659 − 2.23893i −0.986535 − 2.21579i −7.00098 1.77302 + 1.28817i −0.531098 + 5.05306i
23.11 −0.241615 + 0.418490i −2.30057 − 0.747499i 1.88324 + 3.26187i −2.85296 + 1.27022i 0.868672 − 0.782156i −2.60718 − 5.85582i −3.75300 −2.54730 − 1.85072i 0.157745 − 1.50084i
23.12 −0.156548 + 0.271149i 2.13180 + 0.692663i 1.95099 + 3.37921i 6.07118 − 2.70306i −0.521543 + 0.469600i 1.43118 + 3.21449i −2.47407 −3.21638 − 2.33683i −0.217498 + 2.06935i
23.13 −0.0834964 + 0.144620i 0.00330483 + 0.00107380i 1.98606 + 3.43995i −6.46654 + 2.87909i −0.000431235 0 0.000388285i 1.28282 + 2.88125i −1.33129 −7.28114 − 5.29006i 0.123559 − 1.17558i
23.14 0.398212 − 0.689723i 3.42774 + 1.11374i 1.68285 + 2.91479i 3.71720 − 1.65500i 2.13314 − 1.92069i −4.77453 − 10.7238i 5.86623 3.22783 + 2.34516i 0.338739 − 3.22288i
23.15 0.521036 − 0.902461i 3.94895 + 1.28309i 1.45704 + 2.52367i −6.71173 + 2.98825i 3.21549 − 2.89524i −0.363712 − 0.816911i 7.20498 6.66673 + 4.84366i −0.800270 + 7.61406i
23.16 0.539756 − 0.934884i −5.04057 − 1.63778i 1.41733 + 2.45488i 6.91575 − 3.07909i −4.25181 + 3.82835i −1.76615 − 3.96684i 7.37809 15.4439 + 11.2206i 0.854222 − 8.12738i
23.17 0.791290 − 1.37055i 0.0462745 + 0.0150355i 0.747722 + 1.29509i 1.52635 − 0.679573i 0.0572235 − 0.0515242i 5.29112 + 11.8841i 8.69697 −7.27924 − 5.28868i 0.276390 − 2.62968i
23.18 0.801333 − 1.38795i −4.43411 − 1.44073i 0.715731 + 1.23968i −3.68271 + 1.63965i −5.55285 + 4.99981i 1.87491 + 4.21111i 8.70482 10.3044 + 7.48662i −0.675328 + 6.42532i
23.19 1.06322 − 1.84155i −0.635805 − 0.206586i −0.260862 − 0.451825i 2.60051 − 1.15782i −1.05644 + 0.951219i −3.21190 − 7.21404i 7.39633 −6.91958 − 5.02737i 0.632726 − 6.01998i
23.20 1.36444 − 2.36329i −1.08231 − 0.351664i −1.72341 − 2.98504i −5.93894 + 2.64419i −2.30784 + 2.07798i −4.06171 − 9.12275i 1.50954 −6.23342 − 4.52885i −1.85438 + 17.6433i
See next 80 embeddings (of 192 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 23.24
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
151.i odd 30 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 151.3.i.a ✓ 192
151.i odd 30 1 inner 151.3.i.a ✓ 192
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
151.3.i.a ✓ 192 1.a even 1 1 trivial
151.3.i.a ✓ 192 151.i odd 30 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(151, [\chi])\).