↑

Properties

Label 290.2.l.b
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 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")
 
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);
 
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 8 q^{2} - 4 q^{3} - 8 q^{4} + 8 q^{5} - 3 q^{6} + 7 q^{7} + 8 q^{8} - 8 q^{9} - q^{10} + 10 q^{12} - 10 q^{15} - 8 q^{16} - 30 q^{17} + 8 q^{18} - 13 q^{20} + 7 q^{21} + 7 q^{23} - 3 q^{24} - 12 q^{25}+ \cdots - 27 q^{98}+O(q^{100}) \) 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 −1.97436 − 2.47577i 0.623490 − 0.781831i 2.23570 − 0.0405388i −2.85304 − 1.37395i 3.28805 − 2.62213i 0.222521 − 0.974928i −1.56378 + 6.85135i 1.99671 − 1.00656i
9.2 0.900969 − 0.433884i −1.80982 − 2.26945i 0.623490 − 0.781831i −1.84310 − 1.26609i −2.61527 − 1.25945i −2.48331 + 1.98037i 0.222521 − 0.974928i −1.20737 + 5.28982i −2.20991 − 0.341011i
9.3 0.900969 − 0.433884i −0.581531 − 0.729217i 0.623490 − 0.781831i 0.424505 + 2.19540i −0.840337 − 0.404685i 0.608556 − 0.485308i 0.222521 − 0.974928i 0.473984 − 2.07666i 1.33502 + 1.79380i
9.4 0.900969 − 0.433884i −0.251521 − 0.315397i 0.623490 − 0.781831i −2.18253 − 0.486388i −0.363458 − 0.175032i 2.61384 − 2.08447i 0.222521 − 0.974928i 0.631350 − 2.76613i −2.17743 + 0.508742i
9.5 0.900969 − 0.433884i 0.183457 + 0.230048i 0.623490 − 0.781831i 0.263370 − 2.22050i 0.265103 + 0.127667i −1.32570 + 1.05721i 0.222521 − 0.974928i 0.648297 − 2.84038i −0.726152 − 2.11488i
9.6 0.900969 − 0.433884i 1.02784 + 1.28888i 0.623490 − 0.781831i 2.22995 + 0.165278i 1.48528 + 0.715272i −0.318876 + 0.254295i 0.222521 − 0.974928i 0.0628256 − 0.275257i 2.08083 − 0.818630i
9.7 0.900969 − 0.433884i 1.44121 + 1.80722i 0.623490 − 0.781831i −1.20113 + 1.88608i 2.08261 + 1.00293i −3.02357 + 2.41121i 0.222521 − 0.974928i −0.521398 + 2.28440i −0.263845 + 2.22045i
9.8 0.900969 − 0.433884i 2.08821 + 2.61854i 0.623490 − 0.781831i −1.01976 − 1.99000i 3.01756 + 1.45318i 1.86353 − 1.48611i 0.222521 − 0.974928i −1.82854 + 8.01136i −1.78220 − 1.35047i
109.1 0.222521 + 0.974928i −2.69492 − 1.29780i −0.900969 + 0.433884i 1.04224 + 1.97832i 0.665589 − 2.91614i 0.184132 − 0.382354i −0.623490 − 0.781831i 3.70781 + 4.64945i −1.69680 + 1.45632i
109.2 0.222521 + 0.974928i −2.53367 − 1.22015i −0.900969 + 0.433884i 0.325268 − 2.21228i 0.625765 − 2.74166i −1.72264 + 3.57710i −0.623490 − 0.781831i 3.06025 + 3.83743i 2.22920 − 0.175167i
109.3 0.222521 + 0.974928i −0.893741 − 0.430403i −0.900969 + 0.433884i 2.22348 + 0.236969i 0.220736 − 0.967106i 1.53438 − 3.18618i −0.623490 − 0.781831i −1.25694 − 1.57616i 0.263743 + 2.22046i
109.4 0.222521 + 0.974928i −0.668503 − 0.321934i −0.900969 + 0.433884i −2.19009 − 0.451105i 0.165107 − 0.723379i −0.462566 + 0.960527i −0.623490 − 0.781831i −1.52721 − 1.91507i −0.0475467 − 2.23556i
109.5 0.222521 + 0.974928i 0.0258055 + 0.0124273i −0.900969 + 0.433884i −0.0497182 − 2.23552i −0.00637343 + 0.0279238i 1.83110 − 3.80231i −0.623490 − 0.781831i −1.86996 − 2.34485i 2.16840 − 0.545921i
109.6 0.222521 + 0.974928i 0.577693 + 0.278202i −0.900969 + 0.433884i 1.81221 + 1.30992i −0.142678 + 0.625115i −1.73730 + 3.60754i −0.623490 − 0.781831i −1.61414 − 2.02406i −0.873818 + 2.05826i
109.7 0.222521 + 0.974928i 2.12638 + 1.02401i −0.900969 + 0.433884i −0.805804 + 2.08583i −0.525173 + 2.30094i 0.814227 − 1.69076i −0.623490 − 0.781831i 1.60244 + 2.00939i −2.21284 − 0.321460i
109.8 0.222521 + 0.974928i 2.65998 + 1.28098i −0.900969 + 0.433884i 1.96882 − 1.06008i −0.656961 + 2.87833i −0.0648222 + 0.134605i −0.623490 − 0.781831i 3.56412 + 4.46926i 1.47160 + 1.68357i
129.1 0.900969 + 0.433884i −1.97436 + 2.47577i 0.623490 + 0.781831i 2.23570 + 0.0405388i −2.85304 + 1.37395i 3.28805 + 2.62213i 0.222521 + 0.974928i −1.56378 − 6.85135i 1.99671 + 1.00656i
129.2 0.900969 + 0.433884i −1.80982 + 2.26945i 0.623490 + 0.781831i −1.84310 + 1.26609i −2.61527 + 1.25945i −2.48331 − 1.98037i 0.222521 + 0.974928i −1.20737 − 5.28982i −2.20991 + 0.341011i
129.3 0.900969 + 0.433884i −0.581531 + 0.729217i 0.623490 + 0.781831i 0.424505 − 2.19540i −0.840337 + 0.404685i 0.608556 + 0.485308i 0.222521 + 0.974928i 0.473984 + 2.07666i 1.33502 − 1.79380i
129.4 0.900969 + 0.433884i −0.251521 + 0.315397i 0.623490 + 0.781831i −2.18253 + 0.486388i −0.363458 + 0.175032i 2.61384 + 2.08447i 0.222521 + 0.974928i 0.631350 + 2.76613i −2.17743 − 0.508742i
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
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.b yes 48
5.b even 2 1 290.2.l.a ✓ 48
29.e even 14 1 290.2.l.a ✓ 48
145.l even 14 1 inner 290.2.l.b yes 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
290.2.l.a ✓ 48 5.b even 2 1
290.2.l.a ✓ 48 29.e even 14 1
290.2.l.b yes 48 1.a even 1 1 trivial
290.2.l.b yes 48 145.l even 14 1 inner

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