Properties

 Label 95.11.j.a Level $95$ Weight $11$ Character orbit 95.j Analytic conductor $60.359$ Analytic rank $0$ Dimension $136$ CM no Inner twists $2$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,11,Mod(31,95)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 11, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("95.31");

S:= CuspForms(chi, 11);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$95 = 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$11$$ Character orbit: $$[\chi]$$ $$=$$ 95.j (of order $$6$$, degree $$2$$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$60.3589390040$$ Analytic rank: $$0$$ Dimension: $$136$$ Relative dimension: $$68$$ over $$\Q(\zeta_{6})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic $$q$$-expansion, but we have computed the trace expansion.

 $$\operatorname{Tr}(f)(q) =$$ $$136 q - 132 q^{3} + 37474 q^{4} - 1022 q^{6} - 76620 q^{7} + 1448988 q^{9}+O(q^{10})$$ 136 * q - 132 * q^3 + 37474 * q^4 - 1022 * q^6 - 76620 * q^7 + 1448988 * q^9 $$\operatorname{Tr}(f)(q) =$$ $$136 q - 132 q^{3} + 37474 q^{4} - 1022 q^{6} - 76620 q^{7} + 1448988 q^{9} + 93750 q^{10} + 418144 q^{11} - 1256574 q^{13} + 612480 q^{14} - 20575630 q^{16} + 3635834 q^{17} + 10572814 q^{19} + 8494308 q^{21} - 31311360 q^{22} - 11728554 q^{23} - 1627348 q^{24} - 132812500 q^{25} - 5280948 q^{26} - 81401852 q^{28} - 36928518 q^{29} + 79750000 q^{30} + 196574250 q^{32} + 359004150 q^{33} + 205341462 q^{34} + 19937500 q^{35} - 1128154804 q^{36} + 1584974 q^{38} + 224945180 q^{39} + 96000000 q^{40} + 1170402744 q^{41} + 173440898 q^{42} - 390292220 q^{43} - 49120052 q^{44} - 148625000 q^{45} - 445097680 q^{47} + 362033562 q^{48} + 3958185060 q^{49} + 995976516 q^{51} + 7766334 q^{52} + 815693040 q^{53} + 2049344062 q^{54} + 3831676392 q^{57} + 3983452220 q^{58} + 2842939668 q^{59} - 1389656250 q^{60} + 1929307508 q^{61} - 2885441744 q^{62} - 5022307122 q^{63} - 29425336368 q^{64} + 2939512012 q^{66} + 1891858296 q^{67} + 18554561860 q^{68} - 810562500 q^{70} - 8973340848 q^{71} + 7541812308 q^{72} + 4947578188 q^{73} - 23389998076 q^{74} + 15724739728 q^{76} - 5682818404 q^{77} - 10507817400 q^{78} + 16066927146 q^{79} + 3604750000 q^{80} - 43776877608 q^{81} - 13564413998 q^{82} + 2628386824 q^{83} - 2399750000 q^{85} + 38885030448 q^{86} + 12840668220 q^{87} - 35640122064 q^{89} + 3198281250 q^{90} + 4174912572 q^{91} - 23134882520 q^{92} - 36221884016 q^{93} - 1613500000 q^{95} + 13864395128 q^{96} - 23558943450 q^{97} + 31730410686 q^{98} - 8878413234 q^{99}+O(q^{100})$$ 136 * q - 132 * q^3 + 37474 * q^4 - 1022 * q^6 - 76620 * q^7 + 1448988 * q^9 + 93750 * q^10 + 418144 * q^11 - 1256574 * q^13 + 612480 * q^14 - 20575630 * q^16 + 3635834 * q^17 + 10572814 * q^19 + 8494308 * q^21 - 31311360 * q^22 - 11728554 * q^23 - 1627348 * q^24 - 132812500 * q^25 - 5280948 * q^26 - 81401852 * q^28 - 36928518 * q^29 + 79750000 * q^30 + 196574250 * q^32 + 359004150 * q^33 + 205341462 * q^34 + 19937500 * q^35 - 1128154804 * q^36 + 1584974 * q^38 + 224945180 * q^39 + 96000000 * q^40 + 1170402744 * q^41 + 173440898 * q^42 - 390292220 * q^43 - 49120052 * q^44 - 148625000 * q^45 - 445097680 * q^47 + 362033562 * q^48 + 3958185060 * q^49 + 995976516 * q^51 + 7766334 * q^52 + 815693040 * q^53 + 2049344062 * q^54 + 3831676392 * q^57 + 3983452220 * q^58 + 2842939668 * q^59 - 1389656250 * q^60 + 1929307508 * q^61 - 2885441744 * q^62 - 5022307122 * q^63 - 29425336368 * q^64 + 2939512012 * q^66 + 1891858296 * q^67 + 18554561860 * q^68 - 810562500 * q^70 - 8973340848 * q^71 + 7541812308 * q^72 + 4947578188 * q^73 - 23389998076 * q^74 + 15724739728 * q^76 - 5682818404 * q^77 - 10507817400 * q^78 + 16066927146 * q^79 + 3604750000 * q^80 - 43776877608 * q^81 - 13564413998 * q^82 + 2628386824 * q^83 - 2399750000 * q^85 + 38885030448 * q^86 + 12840668220 * q^87 - 35640122064 * q^89 + 3198281250 * q^90 + 4174912572 * q^91 - 23134882520 * q^92 - 36221884016 * q^93 - 1613500000 * q^95 + 13864395128 * q^96 - 23558943450 * q^97 + 31730410686 * q^98 - 8878413234 * q^99

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.

comment: embeddings in the coefficient field

gp: mfembed(f)

Label $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
31.1 −55.1125 + 31.8192i −163.702 + 94.5131i 1512.93 2620.47i −698.771 1210.31i 6014.67 10417.7i −7297.48 127395.i −11659.0 + 20194.1i 77022.1 + 44468.7i
31.2 −54.7601 + 31.6158i 384.837 222.186i 1487.11 2575.75i −698.771 1210.31i −14049.1 + 24333.8i −21417.1 123316.i 69208.4 119872.i 76529.5 + 44184.4i
31.3 −54.0957 + 31.2322i −104.277 + 60.2044i 1438.90 2492.25i 698.771 + 1210.31i 3760.63 6513.60i 25452.5 115796.i −22275.4 + 38582.1i −75601.1 43648.3i
31.4 −49.4043 + 28.5236i −389.179 + 224.692i 1115.19 1931.56i 698.771 + 1210.31i 12818.1 22201.5i −22520.4 68820.2i 71448.8 123753.i −69044.5 39862.9i
31.5 −49.4010 + 28.5217i 283.434 163.641i 1114.97 1931.19i 698.771 + 1210.31i −9334.62 + 16168.0i 14256.8 68791.2i 24032.1 41624.8i −69040.0 39860.3i
31.6 −46.9206 + 27.0896i −55.2676 + 31.9088i 955.692 1655.31i 698.771 + 1210.31i 1728.79 2994.35i −16956.0 48077.8i −27488.2 + 47610.9i −65573.5 37858.9i
31.7 −46.8725 + 27.0619i −321.755 + 185.765i 952.688 1650.10i −698.771 1210.31i 10054.3 17414.6i 6325.06 47703.3i 39493.1 68404.0i 65506.3 + 37820.1i
31.8 −45.4180 + 26.2221i 256.648 148.176i 863.197 1495.10i 698.771 + 1210.31i −7770.95 + 13459.7i −12801.3 36836.5i 14387.5 24919.8i −63473.6 36646.5i
31.9 −45.3886 + 26.2051i 21.9013 12.6447i 861.416 1492.02i −698.771 1210.31i −662.712 + 1147.85i −8328.10 36625.9i −29204.7 + 50584.1i 63432.5 + 36622.8i
31.10 −44.7004 + 25.8078i 159.805 92.2637i 820.085 1420.43i −698.771 1210.31i −4762.24 + 8248.45i 20604.6 31804.0i −12499.3 + 21649.5i 62470.7 + 36067.5i
31.11 −43.8877 + 25.3386i −295.608 + 170.669i 772.088 1337.30i 698.771 + 1210.31i 8649.03 14980.6i 7938.17 26361.1i 28731.4 49764.2i −61335.0 35411.8i
31.12 −39.2612 + 22.6675i −120.396 + 69.5106i 515.630 893.097i −698.771 1210.31i 3151.26 5458.15i 5360.19 329.105i −19861.0 + 34400.3i 54869.2 + 31678.8i
31.13 −36.2096 + 20.9056i 226.838 130.965i 362.088 627.155i −698.771 1210.31i −5475.81 + 9484.39i −22249.6 12536.0i 4779.29 8277.98i 50604.4 + 29216.5i
31.14 −36.0213 + 20.7969i −273.691 + 158.015i 353.024 611.455i −698.771 1210.31i 6572.46 11383.8i −23836.7 13224.9i 20413.2 35356.7i 50341.3 + 29064.6i
31.15 −35.1665 + 20.3034i 343.273 198.189i 312.457 541.192i 698.771 + 1210.31i −8047.81 + 13939.2i −10159.9 16205.6i 49032.9 84927.5i −49146.7 28374.9i
31.16 −34.3476 + 19.8306i −103.917 + 59.9967i 274.503 475.453i 698.771 + 1210.31i 2379.54 4121.48i 10548.9 18838.8i −22325.3 + 38668.5i −48002.2 27714.1i
31.17 −33.8581 + 19.5480i 406.250 234.548i 252.249 436.908i −698.771 1210.31i −9169.90 + 15882.7i 18342.0 20310.4i 80501.3 139432.i 47318.2 + 27319.2i
31.18 −32.4277 + 18.7221i 7.34597 4.24120i 189.037 327.422i 698.771 + 1210.31i −158.809 + 275.065i 3275.68 24186.2i −29488.5 + 51075.6i −45319.1 26165.0i
31.19 −28.0175 + 16.1759i −84.0928 + 48.5510i 11.3205 19.6077i −698.771 1210.31i 1570.71 2720.56i 29146.1 32395.8i −24810.1 + 42972.3i 39155.7 + 22606.5i
31.20 −27.4928 + 15.8730i 225.371 130.118i −8.09708 + 14.0246i −698.771 1210.31i −4130.72 + 7154.62i −22928.7 33022.0i 4336.90 7511.74i 38422.4 + 22183.2i
See next 80 embeddings (of 136 total)
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 31.68 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
19.d odd 6 1 inner

Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 95.11.j.a 136
19.d odd 6 1 inner 95.11.j.a 136

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.11.j.a 136 1.a even 1 1 trivial
95.11.j.a 136 19.d odd 6 1 inner

Hecke kernels

This newform subspace is the entire newspace $$S_{11}^{\mathrm{new}}(95, [\chi])$$.