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Properties

Label 151.4.g.a
Level $151$
Weight $4$
Character orbit 151.g
Analytic conductor $8.909$
Analytic rank $0$
Dimension $296$
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] = [151,4,Mod(2,151)] 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("151.2"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(151, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([14])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 151 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 151.g (of order \(15\), 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: \(8.90928841087\)
Analytic rank: \(0\)
Dimension: \(296\)
Relative dimension: \(37\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 296 q - 5 q^{2} - 18 q^{3} - 581 q^{4} - 9 q^{5} + 117 q^{6} - 9 q^{7} + 144 q^{8} - 604 q^{9} + 117 q^{10} - 41 q^{11} + 171 q^{12} - 57 q^{13} + 221 q^{14} + 294 q^{15} - 2229 q^{16} - 7 q^{17} + 980 q^{18}+ \cdots - 7624 q^{99}+O(q^{100}) \) 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 −2.80477 + 4.85800i −1.60499 + 1.16609i −11.7335 − 20.3229i 6.99573 + 7.76955i −1.16326 − 11.0677i 22.4805 + 24.9672i 86.7622 −7.12724 + 21.9354i −57.3659 + 12.1935i
2.2 −2.68690 + 4.65384i −3.72791 + 2.70849i −10.4388 − 18.0806i −6.63268 − 7.36634i −2.58836 − 24.6266i −13.6872 − 15.2012i 69.2020 −1.78202 + 5.48451i 52.1031 − 11.0749i
2.3 −2.37694 + 4.11699i 3.03178 − 2.20272i −7.29973 − 12.6435i 3.77979 + 4.19788i 1.86219 + 17.7175i −10.4318 − 11.5857i 31.3730 −4.00373 + 12.3222i −26.2670 + 5.58322i
2.4 −2.30731 + 3.99638i 7.27030 − 5.28218i −6.64735 − 11.5136i 6.39073 + 7.09762i 4.33476 + 41.2425i 4.12998 + 4.58680i 24.4331 16.6123 − 51.1275i −43.1101 + 9.16334i
2.5 −2.29518 + 3.97537i 4.19879 − 3.05060i −6.53571 − 11.3202i −13.1492 − 14.6037i 2.49028 + 23.6934i 22.8028 + 25.3250i 23.2797 −0.0197866 + 0.0608970i 88.2349 − 18.7549i
2.6 −2.11867 + 3.66965i −8.13114 + 5.90762i −4.97756 − 8.62138i 2.04590 + 2.27221i −4.45167 − 42.3548i 1.77447 + 1.97075i 8.28451 22.8720 − 70.3929i −12.6728 + 2.69369i
2.7 −2.11076 + 3.65595i −4.23752 + 3.07874i −4.91062 − 8.50545i 13.3721 + 14.8512i −2.31131 − 21.9906i −6.66147 − 7.39831i 7.68843 0.134486 − 0.413904i −82.5206 + 17.5403i
2.8 −2.07565 + 3.59513i 2.06657 − 1.50145i −4.61665 − 7.99627i −5.30470 − 5.89146i 1.10844 + 10.5461i −7.56592 − 8.40280i 5.11980 −6.32711 + 19.4728i 32.1913 − 6.84247i
2.9 −2.03542 + 3.52545i −4.15012 + 3.01524i −4.28585 − 7.42331i −9.43023 − 10.4733i −2.18284 − 20.7683i −0.772609 − 0.858069i 2.32731 −0.211621 + 0.651302i 56.1176 − 11.9282i
2.10 −1.54027 + 2.66782i −3.47335 + 2.52354i −0.744842 − 1.29010i 2.46373 + 2.73625i −1.38246 − 13.1532i 17.5651 + 19.5080i −20.0552 −2.64754 + 8.14828i −11.0946 + 2.35824i
2.11 −1.28603 + 2.22747i 1.48437 − 1.07846i 0.692263 + 1.19904i 11.2382 + 12.4813i 0.493288 + 4.69332i −3.79312 − 4.21269i −24.1375 −7.30317 + 22.4768i −42.2543 + 8.98143i
2.12 −1.24451 + 2.15556i 7.51203 − 5.45781i 0.902372 + 1.56295i −8.34348 − 9.26638i 2.41582 + 22.9850i −10.8249 − 12.0222i −24.4043 18.2995 − 56.3200i 30.3578 − 6.45275i
2.13 −1.19362 + 2.06741i −2.26277 + 1.64400i 1.15055 + 1.99282i −4.55360 − 5.05729i −0.697933 − 6.64038i 7.77463 + 8.63460i −24.5912 −5.92605 + 18.2385i 15.8907 − 3.37768i
2.14 −0.941747 + 1.63115i 5.16795 − 3.75474i 2.22623 + 3.85594i 6.08738 + 6.76072i 1.25765 + 11.9657i 17.3126 + 19.2276i −23.4541 4.26623 − 13.1301i −16.7605 + 3.56256i
2.15 −0.837389 + 1.45040i 2.80355 − 2.03690i 2.59756 + 4.49910i −5.26116 − 5.84311i 0.606657 + 5.77196i −13.1569 − 14.6122i −22.0989 −4.63251 + 14.2574i 12.8805 − 2.73783i
2.16 −0.792113 + 1.37198i −4.91112 + 3.56814i 2.74511 + 4.75467i 1.67774 + 1.86332i −1.00525 − 9.56433i −22.6641 − 25.1711i −21.3716 3.04404 − 9.36859i −3.88539 + 0.825865i
2.17 −0.394841 + 0.683884i −7.84239 + 5.69783i 3.68820 + 6.38815i −13.9275 − 15.4681i −0.800160 − 7.61301i 4.73971 + 5.26398i −12.1425 20.6943 − 63.6906i 16.0775 − 3.41738i
2.18 −0.123752 + 0.214345i 2.05807 − 1.49527i 3.96937 + 6.87515i −9.64239 − 10.7090i 0.0658143 + 0.626181i 12.1795 + 13.5267i −3.94491 −6.34366 + 19.5238i 3.48868 − 0.741543i
2.19 0.0447844 − 0.0775689i −6.10271 + 4.43388i 3.99599 + 6.92126i 10.7846 + 11.9775i 0.0706247 + 0.671949i 13.3806 + 14.8606i 1.43238 9.24033 − 28.4388i 1.41207 − 0.300144i
2.20 0.268707 − 0.465414i −3.91188 + 2.84215i 3.85559 + 6.67808i −2.87834 − 3.19672i 0.271626 + 2.58435i 5.36860 + 5.96243i 8.44340 −1.11844 + 3.44221i −2.26123 + 0.480639i
See next 80 embeddings (of 296 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2.37
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
151.g even 15 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 151.4.g.a ✓ 296
151.g even 15 1 inner 151.4.g.a ✓ 296
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
151.4.g.a ✓ 296 1.a even 1 1 trivial
151.4.g.a ✓ 296 151.g even 15 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(151, [\chi])\).