LMFDB - Newform orbit 435.2.u.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,2,Mod(16,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("435.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$435 = 3 \cdot 5 \cdot 29$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	435.u (of order $7$ , degree $6$ , 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:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

$q$ -expansion

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

\operatorname{Tr}(f)(q) =

30 q + q^{2} - 5 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} - 5 q^{9} + 6 q^{10} - 18 q^{11} + 32 q^{12} - 5 q^{13} + 18 q^{14} + 5 q^{15} - 13 q^{16} + 44 q^{17} + q^{18} - 8 q^{19} + 10 q^{20} + 7 q^{21} - 19 q^{22}+ \cdots + 10 q^{99}+O(q^{100})

30 * q + q^2 - 5 * q^3 - 3 * q^4 + 5 * q^5 + q^6 - 5 * q^9 + 6 * q^10 - 18 * q^11 + 32 * q^12 - 5 * q^13 + 18 * q^14 + 5 * q^15 - 13 * q^16 + 44 * q^17 + q^18 - 8 * q^19 + 10 * q^20 + 7 * q^21 - 19 * q^22 + 8 * q^23 + 14 * q^24 - 5 * q^25 - 34 * q^26 - 5 * q^27 - 102 * q^28 - 27 * q^29 - 8 * q^30 + 5 * q^31 - 2 * q^32 + 10 * q^33 - 5 * q^34 - 3 * q^36 + 9 * q^37 + 7 * q^38 + 2 * q^39 + 6 * q^41 - 17 * q^42 + 33 * q^43 + 5 * q^45 + 98 * q^46 - 30 * q^47 + q^48 - 9 * q^49 + q^50 - 26 * q^51 - 45 * q^52 + 38 * q^53 - 6 * q^54 - 10 * q^55 - 70 * q^56 - 8 * q^57 - 27 * q^58 + 102 * q^59 + 3 * q^60 + 8 * q^61 - 22 * q^62 + 30 * q^64 - 2 * q^65 - 40 * q^66 - 2 * q^67 + 23 * q^68 - 13 * q^69 + 24 * q^70 - 12 * q^71 + 14 * q^72 - 28 * q^73 - 65 * q^74 + 30 * q^75 - 41 * q^76 + 24 * q^77 + 71 * q^78 + 31 * q^79 - q^80 - 5 * q^81 - 39 * q^82 - 17 * q^83 - 11 * q^84 - 2 * q^85 + 38 * q^86 - 27 * q^87 + 22 * q^88 + 25 * q^89 + 6 * q^90 + 90 * q^91 + 39 * q^92 + 5 * q^93 + 11 * q^94 + 8 * q^95 - 16 * q^96 - 27 * q^97 - 47 * q^98 + 10 * 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	$a_{2}$			$a_{3}$			$a_{4}$			$a_{5}$			$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$			$a_{10}$
16.1	−1.70259	−	0.819922i	0.623490	−	0.781831i	0.979547	+	1.22831i	0.900969	+	0.433884i	−1.70259	+	0.819922i	−0.471718	+	0.591515i	0.180366	+	0.790235i	−0.222521	−	0.974928i	−1.17823	−	1.47745i
16.2	−1.57475	−	0.758361i	0.623490	−	0.781831i	0.657755	+	0.824799i	0.900969	+	0.433884i	−1.57475	+	0.758361i	−2.68227	+	3.36346i	0.367557	+	1.61037i	−0.222521	−	0.974928i	−1.08976	−	1.36652i
16.3	−0.212418	−	0.102295i	0.623490	−	0.781831i	−1.21232	−	1.52020i	0.900969	+	0.433884i	−0.212418	+	0.102295i	2.04210	−	2.56071i	0.206936	+	0.906644i	−0.222521	−	0.974928i	−0.146998	−	0.184330i
16.4	1.52210	+	0.733005i	0.623490	−	0.781831i	0.532514	+	0.667752i	0.900969	+	0.433884i	1.52210	−	0.733005i	1.30031	−	1.63054i	−0.430781	−	1.88737i	−0.222521	−	0.974928i	1.05333	+	1.32083i
16.5	2.19018	+	1.05473i	0.623490	−	0.781831i	2.43743	+	3.05645i	0.900969	+	0.433884i	2.19018	−	1.05473i	−1.71288	+	2.14789i	1.03282	+	4.52507i	−0.222521	−	0.974928i	1.51565	+	1.90056i
136.1	−1.70259	+	0.819922i	0.623490	+	0.781831i	0.979547	−	1.22831i	0.900969	−	0.433884i	−1.70259	−	0.819922i	−0.471718	−	0.591515i	0.180366	−	0.790235i	−0.222521	+	0.974928i	−1.17823	+	1.47745i
136.2	−1.57475	+	0.758361i	0.623490	+	0.781831i	0.657755	−	0.824799i	0.900969	−	0.433884i	−1.57475	−	0.758361i	−2.68227	−	3.36346i	0.367557	−	1.61037i	−0.222521	+	0.974928i	−1.08976	+	1.36652i
136.3	−0.212418	+	0.102295i	0.623490	+	0.781831i	−1.21232	+	1.52020i	0.900969	−	0.433884i	−0.212418	−	0.102295i	2.04210	+	2.56071i	0.206936	−	0.906644i	−0.222521	+	0.974928i	−0.146998	+	0.184330i
136.4	1.52210	−	0.733005i	0.623490	+	0.781831i	0.532514	−	0.667752i	0.900969	−	0.433884i	1.52210	+	0.733005i	1.30031	+	1.63054i	−0.430781	+	1.88737i	−0.222521	+	0.974928i	1.05333	−	1.32083i
136.5	2.19018	−	1.05473i	0.623490	+	0.781831i	2.43743	−	3.05645i	0.900969	−	0.433884i	2.19018	+	1.05473i	−1.71288	−	2.14789i	1.03282	−	4.52507i	−0.222521	+	0.974928i	1.51565	−	1.90056i
181.1	−0.525740	−	2.30342i	−0.900969	−	0.433884i	−3.22739	+	1.55423i	0.222521	+	0.974928i	−0.525740	+	2.30342i	3.87321	+	1.86524i	2.33062	+	2.92251i	0.623490	+	0.781831i	2.12868	−	1.02512i
181.2	−0.410184	−	1.79714i	−0.900969	−	0.433884i	−1.25951	+	0.606547i	0.222521	+	0.974928i	−0.410184	+	1.79714i	−3.46070	−	1.66659i	−0.691946	−	0.867673i	0.623490	+	0.781831i	1.66080	−	0.799801i
181.3	−0.224650	−	0.984254i	−0.900969	−	0.433884i	0.883648	−	0.425543i	0.222521	+	0.974928i	−0.224650	+	0.984254i	2.01432	+	0.970046i	−1.87626	−	2.35276i	0.623490	+	0.781831i	0.909588	−	0.438034i
181.4	0.124254	+	0.544394i	−0.900969	−	0.433884i	1.52101	−	0.732481i	0.222521	+	0.974928i	0.124254	−	0.544394i	1.04157	+	0.501593i	1.28406	+	1.61016i	0.623490	+	0.781831i	−0.503096	+	0.242278i
181.5	0.412830	+	1.80872i	−0.900969	−	0.433884i	−1.29912	+	0.625623i	0.222521	+	0.974928i	0.412830	−	1.80872i	−2.78995	−	1.34357i	0.645551	+	0.809496i	0.623490	+	0.781831i	−1.67151	+	0.804958i
226.1	−1.44601	+	1.81324i	−0.222521	+	0.974928i	−0.751852	−	3.29408i	−0.623490	+	0.781831i	−1.44601	−	1.81324i	0.715709	−	3.13572i	2.88105	+	1.38744i	−0.900969	−	0.433884i	−0.516076	−	2.26107i
226.2	−0.703739	+	0.882461i	−0.222521	+	0.974928i	0.161554	+	0.707812i	−0.623490	+	0.781831i	−0.703739	−	0.882461i	0.123775	−	0.542294i	−2.77217	−	1.33501i	−0.900969	−	0.433884i	−0.251161	−	1.10041i
226.3	0.320185	−	0.401499i	−0.222521	+	0.974928i	0.386359	+	1.69275i	−0.623490	+	0.781831i	0.320185	+	0.401499i	−0.169813	+	0.744000i	1.72870	+	0.832500i	−0.900969	−	0.433884i	0.114273	+	0.500661i
226.4	1.12553	−	1.41136i	−0.222521	+	0.974928i	−0.280099	−	1.22719i	−0.623490	+	0.781831i	1.12553	+	1.41136i	−0.863563	+	3.78351i	1.20558	+	0.580579i	−0.900969	−	0.433884i	0.401695	+	1.75994i
226.5	1.60501	−	2.01262i	−0.222521	+	0.974928i	−1.02953	−	4.51069i	−0.623490	+	0.781831i	1.60501	+	2.01262i	1.03990	−	4.55611i	−6.09209	−	2.93379i	−0.900969	−	0.433884i	0.572821	+	2.50969i

See all 30 embeddings

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
29.d	even	7	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	435.2.u.a	✓	30
29.d	even	7	1	inner	435.2.u.a	✓	30

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
435.2.u.a	✓	30	1.a	even	1	1	trivial
435.2.u.a	✓	30	29.d	even	7	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{2}^{30} - T_{2}^{29} + 7 T_{2}^{28} - 8 T_{2}^{27} + 54 T_{2}^{26} - 13 T_{2}^{25} + 227 T_{2}^{24} + \cdots + 8281$ T2^30 - T2^29 + 7*T2^28 - 8*T2^27 + 54*T2^26 - 13*T2^25 + 227*T2^24 - 120*T2^23 + 1049*T2^22 + 1104*T2^21 + 6283*T2^20 + 4422*T2^19 + 27447*T2^18 + 11386*T2^17 + 76225*T2^16 + 52840*T2^15 + 182021*T2^14 + 161462*T2^13 + 499523*T2^12 + 118795*T2^11 + 1606457*T2^10 + 1411073*T2^9 + 3330969*T2^8 + 1462441*T2^7 + 2253707*T2^6 + 155617*T2^5 + 826679*T2^4 + 101759*T2^3 + 82026*T2^2 + 47138*T2 + 8281 acting on $S_{2}^{\mathrm{new}}(435, [\chi])$ .

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$n$ :		e.g. 2-40 or 990-1000
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