Properties

 Label 95.11.q.a Level $95$ Weight $11$ Character orbit 95.q Analytic conductor $60.359$ Analytic rank $0$ Dimension $1176$ CM no Inner twists $4$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,11,Mod(17,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([9, 20]))

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

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

chi := DirichletCharacter("95.17");

S:= CuspForms(chi, 11);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$95 = 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$11$$ Character orbit: $$[\chi]$$ $$=$$ 95.q (of order $$36$$, degree $$12$$, 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: $$1176$$ Relative dimension: $$98$$ over $$\Q(\zeta_{36})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

$q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$1176 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 14604 q^{6} - 11688 q^{7} - 6 q^{8}+O(q^{10})$$ 1176 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 14604 * q^6 - 11688 * q^7 - 6 * q^8 $$\operatorname{Tr}(f)(q) =$$ $$1176 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 14604 q^{6} - 11688 q^{7} - 6 q^{8} - 12 q^{10} - 12 q^{11} - 6 q^{12} - 12 q^{13} + 3424146 q^{15} - 13618884 q^{16} - 3657378 q^{17} - 23774232 q^{18} + 38894436 q^{20} - 8689704 q^{21} - 22604556 q^{22} - 32885808 q^{23} + 42291732 q^{25} - 319452 q^{26} - 6 q^{27} + 144277488 q^{28} - 6 q^{30} - 12 q^{31} - 304326750 q^{32} + 265207902 q^{33} - 173435754 q^{35} - 288159144 q^{36} - 24 q^{37} + 1298228634 q^{38} - 1334600346 q^{40} + 659462736 q^{41} + 362797044 q^{42} - 961639656 q^{43} + 161157936 q^{45} - 12 q^{46} - 886017372 q^{47} + 1630739472 q^{48} + 2215521786 q^{50} + 1125126576 q^{51} + 6132 q^{52} - 657601770 q^{53} - 3332318022 q^{55} - 48 q^{56} - 967967226 q^{57} - 7596060648 q^{58} + 3688833012 q^{60} + 1851266016 q^{61} + 845228664 q^{62} + 3514567662 q^{63} - 1840657236 q^{65} + 19323290088 q^{66} + 20641904172 q^{67} - 5240868870 q^{68} - 8235161100 q^{70} - 24 q^{71} - 64729344936 q^{72} - 3449985870 q^{73} - 34306313016 q^{75} + 10512445536 q^{76} + 46076293368 q^{77} - 51672410862 q^{78} + 20602412592 q^{80} + 46901590776 q^{81} - 12506757996 q^{82} + 22786639188 q^{83} - 22949887236 q^{85} - 81567902124 q^{86} + 3763013226 q^{87} + 8846542842 q^{88} + 87014491266 q^{90} + 37012815456 q^{91} - 35376892980 q^{92} + 96817414890 q^{93} - 20594188944 q^{95} + 84921616752 q^{96} - 9492824088 q^{97} - 86078409906 q^{98}+O(q^{100})$$ 1176 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 14604 * q^6 - 11688 * q^7 - 6 * q^8 - 12 * q^10 - 12 * q^11 - 6 * q^12 - 12 * q^13 + 3424146 * q^15 - 13618884 * q^16 - 3657378 * q^17 - 23774232 * q^18 + 38894436 * q^20 - 8689704 * q^21 - 22604556 * q^22 - 32885808 * q^23 + 42291732 * q^25 - 319452 * q^26 - 6 * q^27 + 144277488 * q^28 - 6 * q^30 - 12 * q^31 - 304326750 * q^32 + 265207902 * q^33 - 173435754 * q^35 - 288159144 * q^36 - 24 * q^37 + 1298228634 * q^38 - 1334600346 * q^40 + 659462736 * q^41 + 362797044 * q^42 - 961639656 * q^43 + 161157936 * q^45 - 12 * q^46 - 886017372 * q^47 + 1630739472 * q^48 + 2215521786 * q^50 + 1125126576 * q^51 + 6132 * q^52 - 657601770 * q^53 - 3332318022 * q^55 - 48 * q^56 - 967967226 * q^57 - 7596060648 * q^58 + 3688833012 * q^60 + 1851266016 * q^61 + 845228664 * q^62 + 3514567662 * q^63 - 1840657236 * q^65 + 19323290088 * q^66 + 20641904172 * q^67 - 5240868870 * q^68 - 8235161100 * q^70 - 24 * q^71 - 64729344936 * q^72 - 3449985870 * q^73 - 34306313016 * q^75 + 10512445536 * q^76 + 46076293368 * q^77 - 51672410862 * q^78 + 20602412592 * q^80 + 46901590776 * q^81 - 12506757996 * q^82 + 22786639188 * q^83 - 22949887236 * q^85 - 81567902124 * q^86 + 3763013226 * q^87 + 8846542842 * q^88 + 87014491266 * q^90 + 37012815456 * q^91 - 35376892980 * q^92 + 96817414890 * q^93 - 20594188944 * q^95 + 84921616752 * q^96 - 9492824088 * q^97 - 86078409906 * q^98

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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
17.1 −50.7659 + 35.5466i −234.369 + 20.5046i 963.381 2646.87i −362.646 + 3103.89i 11169.1 9371.95i 7490.51 27955.0i 28755.4 + 107317.i −3643.75 + 642.492i −91922.7 170462.i
17.2 −50.3563 + 35.2599i 369.427 32.3207i 942.271 2588.87i −334.791 + 3107.01i −17463.4 + 14653.5i −2370.23 + 8845.80i 27541.4 + 102786.i 77279.7 13626.5i −92694.1 168262.i
17.3 −49.6554 + 34.7691i −103.426 + 9.04863i 906.541 2490.70i 1047.53 2944.20i 4821.06 4045.35i −2245.69 + 8381.04i 25519.1 + 95238.6i −47536.8 + 8382.02i 50351.4 + 182617.i
17.4 −49.2585 + 34.4912i 224.899 19.6761i 886.530 2435.72i −1840.89 2525.22i −10399.5 + 8726.24i 2289.79 8545.62i 24404.5 + 91078.8i −7959.53 + 1403.48i 177777. + 60893.9i
17.5 −48.1562 + 33.7193i −439.074 + 38.4140i 831.797 2285.34i −2756.69 1471.82i 19848.8 16655.2i −3225.89 + 12039.2i 21423.5 + 79953.5i 133159. 23479.5i 182381. 22076.4i
17.6 −47.6180 + 33.3425i −235.686 + 20.6198i 805.526 2213.16i 3022.82 + 792.567i 10535.4 8840.24i −6417.62 + 23950.9i 20028.4 + 74747.0i −3029.23 + 534.136i −170367. + 63048.0i
17.7 −46.8362 + 32.7951i −24.4621 + 2.14016i 767.885 2109.75i −2989.34 + 910.761i 1075.53 902.473i −697.602 + 2603.49i 18070.9 + 67441.7i −57558.1 + 10149.0i 110141. 140692.i
17.8 −46.3841 + 32.4785i 349.106 30.5428i 746.405 2050.73i 3016.75 815.370i −15201.0 + 12755.1i 3397.19 12678.5i 16976.1 + 63355.7i 62790.2 11071.6i −113447. + 135800.i
17.9 −45.2039 + 31.6521i 79.5717 6.96162i 691.310 1899.36i 1901.07 + 2480.24i −3376.60 + 2833.31i −3012.33 + 11242.2i 14243.4 + 53157.1i −51868.7 + 9145.86i −164440. 51943.7i
17.10 −44.8141 + 31.3791i 97.5372 8.53340i 673.420 1850.21i 3033.45 750.882i −4103.26 + 3443.05i 7277.21 27158.9i 13379.9 + 49934.6i −48711.2 + 8589.10i −112379. + 128837.i
17.11 −42.5372 + 29.7849i −412.736 + 36.1097i 572.048 1571.69i 2847.42 1287.57i 16481.1 13829.3i 4975.77 18569.8i 8716.62 + 32530.9i 110895. 19553.8i −82771.2 + 139580.i
17.12 −41.5866 + 29.1192i 438.355 38.3511i 531.286 1459.69i −2087.89 2325.16i −17112.9 + 14359.4i −4158.70 + 15520.5i 6955.82 + 25959.5i 132532. 23369.0i 154535. + 35897.6i
17.13 −40.3474 + 28.2516i 89.1647 7.80090i 479.534 1317.51i −2973.56 + 961.024i −3377.17 + 2833.79i −7850.04 + 29296.8i 4819.60 + 17987.0i −50262.4 + 8862.62i 92825.0 122782.i
17.14 −39.9850 + 27.9978i −353.522 + 30.9292i 464.693 1276.73i −328.374 + 3107.70i 13269.6 11134.5i −1527.16 + 5699.42i 4228.13 + 15779.6i 65869.3 11614.5i −73878.6 133455.i
17.15 −39.7286 + 27.8183i −187.378 + 16.3934i 454.278 1248.12i −3022.75 792.837i 6988.23 5863.82i 3119.23 11641.1i 3818.75 + 14251.8i −23310.2 + 4110.21i 142145. 52589.4i
17.16 −38.1123 + 26.6865i 359.654 31.4657i 390.150 1071.93i −2908.90 + 1141.90i −12867.6 + 10797.2i 6962.77 25985.4i 1405.56 + 5245.61i 70209.3 12379.8i 80391.6 121149.i
17.17 −37.8908 + 26.5314i 173.869 15.2116i 381.567 1048.35i 382.825 3101.46i −6184.44 + 5189.36i −3647.41 + 13612.3i 1096.94 + 4093.85i −28152.9 + 4964.12i 67780.6 + 127674.i
17.18 −36.3982 + 25.4863i 366.098 32.0294i 325.050 893.066i 2996.32 887.528i −12509.0 + 10496.3i −4989.15 + 18619.8i −846.641 3159.71i 74850.0 13198.1i −86440.8 + 108669.i
17.19 −36.0253 + 25.2252i −223.274 + 19.5340i 311.285 855.248i 917.445 2987.29i 7550.78 6335.86i −1342.59 + 5010.62i −1296.07 4837.00i −8682.06 + 1530.88i 42303.8 + 130761.i
17.20 −35.5850 + 24.9169i −159.445 + 13.9496i 295.212 811.088i −1338.88 2823.66i 5326.26 4469.26i 7073.63 26399.1i −1808.60 6749.79i −32923.8 + 5805.36i 118001. + 67119.1i
See next 80 embeddings (of 1176 total)
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 17.98 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

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 95.11.q.a 1176
5.c odd 4 1 inner 95.11.q.a 1176
19.e even 9 1 inner 95.11.q.a 1176
95.q odd 36 1 inner 95.11.q.a 1176

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.11.q.a 1176 1.a even 1 1 trivial
95.11.q.a 1176 5.c odd 4 1 inner
95.11.q.a 1176 19.e even 9 1 inner
95.11.q.a 1176 95.q odd 36 1 inner

Hecke kernels

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