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Properties

Label 151.5.j.a
Level $151$
Weight $5$
Character orbit 151.j
Analytic conductor $15.609$
Analytic rank $0$
Dimension $980$
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] = [151,5,Mod(3,151)] 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("151.3"); S:= CuspForms(chi, 5); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(151, base_ring=CyclotomicField(50)) chi = DirichletCharacter(H, H._module([27])) N = Newforms(chi, 5, names="a")
 
Level: \( N \) \(=\) \( 151 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 151.j (of order \(50\), degree \(20\), 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: \(15.6088644257\)
Analytic rank: \(0\)
Dimension: \(980\)
Relative dimension: \(49\) over \(\Q(\zeta_{50})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{50}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 980 q - 15 q^{2} - 20 q^{3} - 1855 q^{4} - 20 q^{5} - 30 q^{6} - 20 q^{7} + 145 q^{8} - 20 q^{9} + 700 q^{10} - 410 q^{11} + 465 q^{12} - 20 q^{13} + 1275 q^{14} + 1420 q^{15} - 12655 q^{16} - 740 q^{17}+ \cdots - 24980 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
3.1 −6.30140 + 4.57823i 10.5829 − 11.2696i 13.8031 − 42.4817i 1.38683 + 22.0430i −15.0920 + 119.466i 55.2178 + 35.0423i 69.0012 + 212.364i −9.92107 − 157.691i −109.657 − 132.552i
3.2 −6.17696 + 4.48782i −0.933276 + 0.993838i 13.0700 − 40.2252i −1.33351 − 21.1956i 1.30464 − 10.3273i 6.80933 + 4.32133i 62.0409 + 190.942i 4.96932 + 78.9851i 103.359 + 124.940i
3.3 −6.13052 + 4.45408i −6.17189 + 6.57240i 12.8001 − 39.3947i 2.89194 + 45.9660i 8.56290 − 67.7823i −5.79753 − 3.67923i 59.5296 + 183.213i −0.0181271 − 0.288122i −222.465 − 268.915i
3.4 −5.68130 + 4.12770i −11.7795 + 12.5438i 10.2949 − 31.6845i −1.44100 − 22.9040i 15.1453 − 119.887i 73.9507 + 46.9306i 37.5747 + 115.643i −13.5065 − 214.679i 102.728 + 124.176i
3.5 −5.42850 + 3.94404i 4.08132 − 4.34617i 8.96894 − 27.6036i −0.132735 − 2.10976i −5.01402 + 39.6901i −55.2462 − 35.0603i 27.0056 + 83.1146i 2.85406 + 45.3640i 9.04152 + 10.9293i
3.6 −5.38331 + 3.91120i 10.0737 − 10.7274i 8.73824 − 26.8935i −1.48839 − 23.6573i −12.2728 + 97.1488i −49.8065 − 31.6081i 25.2455 + 77.6978i −8.51157 − 135.288i 100.541 + 121.533i
3.7 −5.09610 + 3.70253i −8.53406 + 9.08785i 7.31720 − 22.5200i −0.567670 − 9.02286i 9.84235 − 77.9102i −63.0375 − 40.0048i 14.9474 + 46.0033i −4.67282 − 74.2724i 36.3003 + 43.8796i
3.8 −4.98566 + 3.62229i −3.92990 + 4.18492i 6.79151 − 20.9021i 1.01087 + 16.0674i 4.43414 − 35.0999i 19.0740 + 12.1047i 11.3838 + 35.0358i 3.01660 + 47.9475i −63.2406 − 76.4447i
3.9 −4.77204 + 3.46709i 6.36709 − 6.78026i 5.80739 − 17.8733i −2.78786 − 44.3117i −6.87623 + 54.4310i 51.0592 + 32.4032i 5.09116 + 15.6690i −0.346087 − 5.50089i 166.937 + 201.792i
3.10 −4.68738 + 3.40558i 4.67018 − 4.97324i 5.42930 − 16.7097i 1.04200 + 16.5622i −4.95415 + 39.2162i 40.0555 + 25.4200i 2.81019 + 8.64889i 2.16353 + 34.3883i −61.2882 − 74.0846i
3.11 −4.53748 + 3.29667i 5.01025 − 5.33538i 4.77638 − 14.7002i 2.42636 + 38.5658i −5.14493 + 40.7263i −35.2024 − 22.3401i −0.941616 − 2.89799i 1.72242 + 27.3770i −138.148 − 166.993i
3.12 −3.82094 + 2.77608i −2.56397 + 2.73035i 1.94873 − 5.99758i −0.636583 − 10.1182i 2.21712 − 17.5503i 43.1748 + 27.3996i −14.1478 − 43.5424i 4.20516 + 66.8391i 30.5212 + 36.8938i
3.13 −3.63189 + 2.63872i −5.34240 + 5.68908i 1.28350 − 3.95021i −2.84353 − 45.1966i 4.39111 − 34.7592i −21.9220 − 13.9121i −16.4342 − 50.5792i 1.26166 + 20.0535i 129.589 + 156.646i
3.14 −3.14192 + 2.28274i −9.43349 + 10.0456i −0.283514 + 0.872567i 2.36688 + 37.6204i 6.70768 − 53.0968i −10.6895 − 6.78374i −20.3028 − 62.4854i −6.83825 − 108.691i −93.3141 − 112.797i
3.15 −2.94711 + 2.14120i −9.36504 + 9.97275i −0.843543 + 2.59616i 0.795049 + 12.6369i 6.24614 − 49.4433i 32.8329 + 20.8364i −21.0840 − 64.8900i −6.66582 − 105.950i −29.4014 − 35.5401i
3.16 −2.89617 + 2.10419i 11.4949 − 12.2408i −0.984093 + 3.02873i 1.17063 + 18.6067i −7.53415 + 59.6389i −8.42783 − 5.34846i −21.2227 − 65.3168i −12.6190 − 200.574i −42.5424 − 51.4249i
3.17 −2.72509 + 1.97989i 7.71040 − 8.21074i −1.43815 + 4.42616i −1.83328 − 29.1391i −4.75513 + 37.6407i −25.0120 − 15.8731i −21.4985 − 66.1655i −2.87998 − 45.7760i 62.6881 + 75.7769i
3.18 −2.29386 + 1.66658i 1.93524 − 2.06082i −2.46000 + 7.57109i −0.729031 − 11.5876i −1.00463 + 7.95247i −41.4752 − 26.3209i −20.9938 − 64.6122i 4.58420 + 72.8638i 20.9840 + 25.3653i
3.19 −2.07674 + 1.50884i −1.62172 + 1.72696i −2.90801 + 8.94994i 1.71449 + 27.2511i 0.762193 − 6.03338i −79.7196 − 50.5916i −20.1568 − 62.0362i 4.73363 + 75.2389i −44.6782 − 54.0067i
3.20 −1.79674 + 1.30540i −2.41797 + 2.57488i −3.42010 + 10.5260i 0.853687 + 13.5690i 0.983197 − 7.78281i 22.4645 + 14.2564i −18.5763 − 57.1720i 4.30262 + 68.3882i −19.2468 − 23.2654i
See next 80 embeddings (of 980 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 3.49
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
151.j odd 50 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 151.5.j.a ✓ 980
151.j odd 50 1 inner 151.5.j.a ✓ 980
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
151.5.j.a ✓ 980 1.a even 1 1 trivial
151.5.j.a ✓ 980 151.j odd 50 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(151, [\chi])\).