↑

Properties

Label 290.2.l.a
Level $290$
Weight $2$
Character orbit 290.l
Analytic conductor $2.316$
Analytic rank $0$
Dimension $48$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [290,2,Mod(9,290)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("290.9"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(290, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 5])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 290 = 2 \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 290.l (of order \(14\), degree \(6\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [48,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.31566165862\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(8\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 8 q^{2} + 4 q^{3} - 8 q^{4} - 6 q^{5} - 3 q^{6} - 7 q^{7} - 8 q^{8} - 8 q^{9} + q^{10} - 10 q^{12} - 4 q^{15} - 8 q^{16} + 30 q^{17} - 8 q^{18} + 8 q^{20} + 7 q^{21} - 7 q^{23} - 3 q^{24} - 12 q^{25}+ \cdots + 27 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
9.1 −0.900969 + 0.433884i −2.08821 − 2.61854i 0.623490 − 0.781831i 0.920038 + 2.03802i 3.01756 + 1.45318i −1.86353 + 1.48611i −0.222521 + 0.974928i −1.82854 + 8.01136i −1.71319 − 1.43700i
9.2 −0.900969 + 0.433884i −1.44121 − 1.80722i 0.623490 − 0.781831i −2.22349 − 0.236866i 2.08261 + 1.00293i 3.02357 − 2.41121i −0.222521 + 0.974928i −0.521398 + 2.28440i 2.10606 − 0.751326i
9.3 −0.900969 + 0.433884i −1.02784 − 1.28888i 0.623490 − 0.781831i 1.26113 − 1.84650i 1.48528 + 0.715272i 0.318876 − 0.254295i −0.222521 + 0.974928i 0.0628256 − 0.275257i −0.335077 + 2.21082i
9.4 −0.900969 + 0.433884i −0.183457 − 0.230048i 0.623490 − 0.781831i 1.90027 + 1.17855i 0.265103 + 0.127667i 1.32570 − 1.05721i −0.222521 + 0.974928i 0.648297 − 2.84038i −2.22344 − 0.237341i
9.5 −0.900969 + 0.433884i 0.251521 + 0.315397i 0.623490 − 0.781831i −0.980510 + 2.00963i −0.363458 − 0.175032i −2.61384 + 2.08447i −0.222521 + 0.974928i 0.631350 − 2.76613i 0.0114644 − 2.23604i
9.6 −0.900969 + 0.433884i 0.581531 + 0.729217i 0.623490 − 0.781831i −1.45176 − 1.70070i −0.840337 − 0.404685i −0.608556 + 0.485308i −0.222521 + 0.974928i 0.473984 − 2.07666i 2.04590 + 0.902385i
9.7 −0.900969 + 0.433884i 1.80982 + 2.26945i 0.623490 − 0.781831i −0.159291 + 2.23039i −2.61527 − 1.25945i 2.48331 − 1.98037i −0.222521 + 0.974928i −1.20737 + 5.28982i −0.824213 − 2.07862i
9.8 −0.900969 + 0.433884i 1.97436 + 2.47577i 0.623490 − 0.781831i 1.42563 − 1.72267i −2.85304 − 1.37395i −3.28805 + 2.62213i −0.222521 + 0.974928i −1.56378 + 6.85135i −0.537013 + 2.17063i
109.1 −0.222521 − 0.974928i −2.65998 − 1.28098i −0.900969 + 0.433884i −2.23379 − 0.100857i −0.656961 + 2.87833i 0.0648222 − 0.134605i 0.623490 + 0.781831i 3.56412 + 4.46926i 0.398737 + 2.20023i
109.2 −0.222521 − 0.974928i −2.12638 − 1.02401i −0.900969 + 0.433884i 1.63101 + 1.52964i −0.525173 + 2.30094i −0.814227 + 1.69076i 0.623490 + 0.781831i 1.60244 + 2.00939i 1.12836 − 1.93050i
109.3 −0.222521 − 0.974928i −0.577693 − 0.278202i −0.900969 + 0.433884i −1.06440 + 1.96648i −0.142678 + 0.625115i 1.73730 − 3.60754i 0.623490 + 0.781831i −1.61414 − 2.02406i 2.15403 + 0.600127i
109.4 −0.222521 − 0.974928i −0.0258055 − 0.0124273i −0.900969 + 0.433884i −0.925159 − 2.03570i −0.00637343 + 0.0279238i −1.83110 + 3.80231i 0.623490 + 0.781831i −1.86996 − 2.34485i −1.77879 + 1.35495i
109.5 −0.222521 − 0.974928i 0.668503 + 0.321934i −0.900969 + 0.433884i 1.77748 − 1.35668i 0.165107 − 0.723379i 0.462566 − 0.960527i 0.623490 + 0.781831i −1.52721 − 1.91507i −1.71819 − 1.43102i
109.6 −0.222521 − 0.974928i 0.893741 + 0.430403i −0.900969 + 0.433884i −1.90047 + 1.17823i 0.220736 − 0.967106i −1.53438 + 3.18618i 0.623490 + 0.781831i −1.25694 − 1.57616i 1.57158 + 1.59064i
109.7 −0.222521 − 0.974928i 2.53367 + 1.22015i −0.900969 + 0.433884i −1.25293 − 1.85207i 0.625765 − 2.74166i 1.72264 − 3.57710i 0.623490 + 0.781831i 3.06025 + 3.83743i −1.52683 + 1.63364i
109.8 −0.222521 − 0.974928i 2.69492 + 1.29780i −0.900969 + 0.433884i −0.0806615 + 2.23461i 0.665589 − 2.91614i −0.184132 + 0.382354i 0.623490 + 0.781831i 3.70781 + 4.64945i 2.19654 − 0.418609i
129.1 −0.900969 − 0.433884i −2.08821 + 2.61854i 0.623490 + 0.781831i 0.920038 − 2.03802i 3.01756 − 1.45318i −1.86353 − 1.48611i −0.222521 − 0.974928i −1.82854 − 8.01136i −1.71319 + 1.43700i
129.2 −0.900969 − 0.433884i −1.44121 + 1.80722i 0.623490 + 0.781831i −2.22349 + 0.236866i 2.08261 − 1.00293i 3.02357 + 2.41121i −0.222521 − 0.974928i −0.521398 − 2.28440i 2.10606 + 0.751326i
129.3 −0.900969 − 0.433884i −1.02784 + 1.28888i 0.623490 + 0.781831i 1.26113 + 1.84650i 1.48528 − 0.715272i 0.318876 + 0.254295i −0.222521 − 0.974928i 0.0628256 + 0.275257i −0.335077 − 2.21082i
129.4 −0.900969 − 0.433884i −0.183457 + 0.230048i 0.623490 + 0.781831i 1.90027 − 1.17855i 0.265103 − 0.127667i 1.32570 + 1.05721i −0.222521 − 0.974928i 0.648297 + 2.84038i −2.22344 + 0.237341i
See all 48 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 9.8
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
145.l even 14 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 290.2.l.a ✓ 48
5.b even 2 1 290.2.l.b yes 48
29.e even 14 1 290.2.l.b yes 48
145.l even 14 1 inner 290.2.l.a ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
290.2.l.a ✓ 48 1.a even 1 1 trivial
290.2.l.a ✓ 48 145.l even 14 1 inner
290.2.l.b yes 48 5.b even 2 1
290.2.l.b yes 48 29.e even 14 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{48} - 4 T_{3}^{47} + 24 T_{3}^{46} - 65 T_{3}^{45} + 346 T_{3}^{44} - 981 T_{3}^{43} + \cdots + 4096 \) acting on \(S_{2}^{\mathrm{new}}(290, [\chi])\). Copy content Toggle raw display