gp: [N,k,chi] = [102,5,Mod(53,102)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
sage: from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(102, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 7]))
N = Newforms(chi, 5, names="a")
magma: //Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("102.53");
S:= CuspForms(chi, 5);
N := Newforms(S);
Newform invariants
sage: traces = [44,88]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
gp: f = lf[1] \\ Warning: the index may be different
The algebraic q q q -expansion of this newform has not been computed, but we have computed the trace expansion .
For each embedding ι m \iota_m ι m of the coefficient field, the values ι m ( a n ) \iota_m(a_n) ι m ( a n ) are shown below.
For more information on an embedded modular form you can click on its label.
gp: mfembed(f)
Refresh table
This newform subspace can be constructed as the kernel of the linear operator
T 5 44 − 72 T 5 43 + 1648 T 5 42 + 38112 T 5 41 − 3210880 T 5 40 + ⋯ + 24 ⋯ 12 T_{5}^{44} - 72 T_{5}^{43} + 1648 T_{5}^{42} + 38112 T_{5}^{41} - 3210880 T_{5}^{40} + \cdots + 24\!\cdots\!12 T 5 4 4 − 7 2 T 5 4 3 + 1 6 4 8 T 5 4 2 + 3 8 1 1 2 T 5 4 1 − 3 2 1 0 8 8 0 T 5 4 0 + ⋯ + 2 4 ⋯ 1 2
T5^44 - 72*T5^43 + 1648*T5^42 + 38112*T5^41 - 3210880*T5^40 + 39982656*T5^39 + 6535303016*T5^38 - 249614273216*T5^37 + 16839461314449*T5^36 - 720083895411080*T5^35 + 18136951308062200*T5^34 - 17995269524848800*T5^33 - 11003176881843006432*T5^32 + 279977084070992204800*T5^31 + 34169809088051391342016*T5^30 - 961168283801215693143872*T5^29 + 71498388879213710113166096*T5^28 - 2176788453119257716009972736*T5^27 + 69630326163437491242856451424*T5^26 - 1045733544332335153690559430784*T5^25 + 1096199304776885701681320548608*T5^24 + 320061867903368289534291464758272*T5^23 - 699840942589376937586277733196160*T5^22 + 88302777975770961128688324032964352*T5^21 + 2576164267617696972284277335323949920*T5^20 + 33395538030815640716269961722560509696*T5^19 + 1507891376407639819279735403063009391488*T5^18 - 12320725020922361053624428645584610412032*T5^17 - 138335596277679366281950881567234841040384*T5^16 + 5890723837354181269297049377424815490420736*T5^15 - 26790781622108702142771780346812058958199808*T5^14 - 841395282176423723605452694032824658956528640*T5^13 + 19228934676437266492262780939516934017338433536*T5^12 + 71337600655409669774850463640515961074447177728*T5^11 - 1237636608708808502930255146658103257227415070208*T5^10 + 14177731369576649516742345129353721789646365190144*T5^9 + 100952299775460488574415671440958243467607353483264*T5^8 - 1360947915437588293715192843600934134580776541700096*T5^7 + 2590776845264719577140615114419000530436870580948992*T5^6 + 33075201707787517242849003940329840906777469016592384*T5^5 + 18748590289510142163793495926032416910781565608263936*T5^4 + 1130140624210290204291319751133657540287971962118428672*T5^3 + 13679409352581444106919402061978967960506182805554171904*T5^2 + 64904608291371660707019255694888167782149603759089778688*T5 + 241975286842697605807879160461338120001454490779471347712
acting on S 5 n e w ( 102 , [ χ ] ) S_{5}^{\mathrm{new}}(102, [\chi]) S 5 n e w ( 1 0 2 , [ χ ] ) .