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Properties

Label 95.5.q.a
Level $95$
Weight $5$
Character orbit 95.q
Analytic conductor $9.820$
Analytic rank $0$
Dimension $456$
Inner twists $4$

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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] = [95,5,Mod(17,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([9, 20])) N = Newforms(chi, 5, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("95.17"); S:= CuspForms(chi, 5); N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 95.q (of order \(36\), degree \(12\), 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: \(9.82014649297\)
Analytic rank: \(0\)
Dimension: \(456\)
Relative dimension: \(38\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 456 q - 12 q^{2} - 12 q^{3} - 12 q^{5} + 84 q^{6} - 96 q^{7} - 6 q^{8} - 12 q^{10} - 12 q^{11} - 6 q^{12} - 12 q^{13} - 534 q^{15} + 4092 q^{16} - 1362 q^{17} - 3864 q^{18} - 2364 q^{20} - 4776 q^{21} + 2004 q^{22}+ \cdots + 123726 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
17.1 −6.25850 + 4.38225i −16.5767 + 1.45028i 14.4924 − 39.8175i −18.2887 + 17.0448i 97.3900 − 81.7199i 5.37798 − 20.0709i 52.1506 + 194.629i 192.916 − 34.0163i 39.7650 − 186.820i
17.2 −6.07197 + 4.25164i −0.946507 + 0.0828086i 13.3201 − 36.5966i 2.51310 − 24.8734i 5.39509 − 4.52702i 19.4176 − 72.4674i 44.0206 + 164.287i −78.8804 + 13.9087i 90.4932 + 161.715i
17.3 −5.80689 + 4.06603i 6.77670 − 0.592885i 11.7151 − 32.1869i −24.5342 − 4.80323i −36.9409 + 30.9971i −12.2458 + 45.7020i 33.4888 + 124.982i −34.1972 + 6.02989i 161.998 − 71.8651i
17.4 −5.67420 + 3.97311i 15.2509 − 1.33428i 10.9385 − 30.0534i 24.9938 − 0.558702i −81.2353 + 68.1645i −4.02130 + 15.0077i 28.6531 + 106.935i 151.040 − 26.6324i −139.600 + 102.473i
17.5 −5.47669 + 3.83482i −6.25410 + 0.547163i 9.81595 − 26.9691i 24.9004 + 2.22916i 32.1535 − 26.9800i −14.6822 + 54.7948i 21.9761 + 82.0160i −40.9550 + 7.22147i −144.920 + 83.2802i
17.6 −5.03583 + 3.52613i 9.59883 − 0.839789i 7.45372 − 20.4789i −9.45130 + 23.1446i −45.3769 + 38.0757i 10.7783 − 40.2251i 9.21769 + 34.4009i 11.6629 − 2.05648i −34.0157 − 149.879i
17.7 −4.40466 + 3.08418i −4.44680 + 0.389045i 4.41656 − 12.1344i 9.38370 + 23.1721i 18.3868 − 15.4283i 12.2117 − 45.5748i −4.29593 − 16.0326i −60.1468 + 10.6055i −112.799 − 73.1242i
17.8 −4.22441 + 2.95796i −11.0210 + 0.964216i 3.62375 − 9.95617i −10.4339 − 22.7186i 43.7052 − 36.6731i −3.12456 + 11.6610i −7.21410 − 26.9234i 40.7643 − 7.18784i 111.278 + 65.1093i
17.9 −3.99118 + 2.79465i −5.71309 + 0.499831i 2.64709 − 7.27283i −22.6999 + 10.4746i 21.4051 − 17.9610i −18.0060 + 67.1995i −10.4168 − 38.8761i −47.3799 + 8.35435i 61.3264 − 105.244i
17.10 −3.52270 + 2.46662i 8.80247 − 0.770116i 0.852857 − 2.34320i −1.44605 − 24.9581i −29.1088 + 24.4252i −12.6105 + 47.0630i −15.0330 − 56.1041i −2.87906 + 0.507657i 66.6562 + 84.3531i
17.11 −2.89961 + 2.03033i 16.6091 − 1.45311i −1.18681 + 3.26073i −20.0321 − 14.9571i −45.2098 + 37.9355i 14.7254 − 54.9561i −17.8377 − 66.5710i 193.983 − 34.2044i 88.4532 + 2.69818i
17.12 −2.85823 + 2.00135i −17.1966 + 1.50451i −1.30827 + 3.59444i 24.7005 − 3.85796i 46.1409 − 38.7168i 8.19610 − 30.5883i −17.9038 − 66.8178i 213.692 − 37.6796i −62.8786 + 60.4614i
17.13 −2.63643 + 1.84605i 3.39029 − 0.296612i −1.92946 + 5.30115i 19.6316 − 15.4790i −8.39068 + 7.04062i 8.71165 − 32.5123i −18.0274 − 67.2790i −68.3634 + 12.0543i −23.1822 + 77.0502i
17.14 −2.23439 + 1.56454i −8.20490 + 0.717836i −2.92760 + 8.04351i −24.5311 − 4.81910i 17.2099 − 14.4408i 19.0367 − 71.0458i −17.3386 − 64.7086i −12.9644 + 2.28597i 62.3518 − 27.6121i
17.15 −2.17548 + 1.52329i 9.51502 − 0.832456i −3.06002 + 8.40734i 14.6395 + 20.2653i −19.4316 + 16.3051i −14.3821 + 53.6745i −17.1476 − 63.9956i 10.0731 − 1.77616i −62.7179 − 21.7866i
17.16 −1.23697 + 0.866132i 3.84076 − 0.336023i −4.69242 + 12.8923i −21.1770 + 13.2866i −4.45984 + 3.74225i 0.740717 − 2.76439i −11.6154 − 43.3493i −65.1309 + 11.4843i 14.6872 − 34.7772i
17.17 −0.940564 + 0.658590i −12.3455 + 1.08009i −5.02140 + 13.7962i 0.951781 + 24.9819i 10.9004 − 9.14651i −18.8968 + 70.5238i −9.11797 − 34.0287i 71.4748 − 12.6029i −17.3480 − 22.8702i
17.18 −0.222713 + 0.155945i −9.35354 + 0.818328i −5.44704 + 14.9656i 2.14303 − 24.9080i 1.95554 − 1.64089i −15.0955 + 56.3372i −2.24658 − 8.38436i 7.04956 − 1.24303i 3.40700 + 5.88152i
17.19 0.246108 − 0.172327i 13.9894 − 1.22391i −5.44145 + 14.9503i 21.4477 + 12.8450i 3.23199 − 2.71196i 22.6251 − 84.4380i 2.48131 + 9.26037i 114.436 − 20.1781i 7.49201 − 0.534746i
17.20 0.470940 − 0.329756i −3.66462 + 0.320613i −5.35928 + 14.7245i 24.1757 − 6.36689i −1.62009 + 1.35942i −0.0600223 + 0.224006i 4.71236 + 17.5867i −66.4428 + 11.7157i 9.28576 − 10.9705i
See next 80 embeddings (of 456 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 17.38
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner
19.e even 9 1 inner
95.q odd 36 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 95.5.q.a ✓ 456
5.c odd 4 1 inner 95.5.q.a ✓ 456
19.e even 9 1 inner 95.5.q.a ✓ 456
95.q odd 36 1 inner 95.5.q.a ✓ 456
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.5.q.a ✓ 456 1.a even 1 1 trivial
95.5.q.a ✓ 456 5.c odd 4 1 inner
95.5.q.a ✓ 456 19.e even 9 1 inner
95.5.q.a ✓ 456 95.q odd 36 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(95, [\chi])\).