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Properties

Label 35.3.l.a
Level $35$
Weight $3$
Character orbit 35.l
Analytic conductor $0.954$
Analytic rank $0$
Dimension $24$
Inner twists $4$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [35,3,Mod(2,35)] 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("35.2"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 4])) N = Newforms(chi, 3, names="a")
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 35.l (of order \(12\), degree \(4\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.953680925261\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 6 q^{7} - 36 q^{8} + 14 q^{10} - 24 q^{11} - 46 q^{12} - 8 q^{13} + 52 q^{15} + 20 q^{16} - 48 q^{17} - 4 q^{18} - 72 q^{20} + 56 q^{21} + 104 q^{22} - 86 q^{23} - 16 q^{25}+ \cdots + 482 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2.1 −3.54535 + 0.949975i −1.41502 − 0.379154i 8.20298 − 4.73599i 0.551807 − 4.96946i 5.37694 3.87123 − 5.83212i −14.2019 + 14.2019i −5.93570 − 3.42698i 2.76451 + 18.1427i
2.2 −1.89206 + 0.506976i 2.62470 + 0.703286i −0.141229 + 0.0815388i 4.09808 + 2.86456i −5.32264 2.16120 + 6.65802i 5.76622 − 5.76622i −1.39979 − 0.808169i −9.20609 − 3.34229i
2.3 −1.23172 + 0.330037i −4.01589 − 1.07605i −2.05590 + 1.18698i −1.75247 + 4.68282i 5.30157 −3.92739 − 5.79445i 5.74725 − 5.74725i 7.17525 + 4.14263i 0.613038 − 6.34629i
2.4 0.585559 − 0.156900i 4.00038 + 1.07190i −3.14584 + 1.81625i −4.51288 − 2.15265i 2.51064 3.65026 − 5.97291i −3.27174 + 3.27174i 7.05981 + 4.07598i −2.98031 − 0.552433i
2.5 1.75904 − 0.471334i −0.195743 − 0.0524492i −0.592022 + 0.341804i 4.78371 − 1.45469i −0.369042 −6.97731 − 0.563209i −6.03113 + 6.03113i −7.75866 − 4.47947i 7.72911 − 4.81359i
2.6 2.95850 − 0.792728i −2.36445 − 0.633552i 4.66022 − 2.69058i −4.16825 + 2.76146i −7.49746 5.78419 + 3.94249i 2.99127 − 2.99127i −2.60501 − 1.50400i −10.1427 + 11.4741i
18.1 −3.54535 − 0.949975i −1.41502 + 0.379154i 8.20298 + 4.73599i 0.551807 + 4.96946i 5.37694 3.87123 + 5.83212i −14.2019 − 14.2019i −5.93570 + 3.42698i 2.76451 − 18.1427i
18.2 −1.89206 − 0.506976i 2.62470 − 0.703286i −0.141229 − 0.0815388i 4.09808 − 2.86456i −5.32264 2.16120 − 6.65802i 5.76622 + 5.76622i −1.39979 + 0.808169i −9.20609 + 3.34229i
18.3 −1.23172 − 0.330037i −4.01589 + 1.07605i −2.05590 − 1.18698i −1.75247 − 4.68282i 5.30157 −3.92739 + 5.79445i 5.74725 + 5.74725i 7.17525 − 4.14263i 0.613038 + 6.34629i
18.4 0.585559 + 0.156900i 4.00038 − 1.07190i −3.14584 − 1.81625i −4.51288 + 2.15265i 2.51064 3.65026 + 5.97291i −3.27174 − 3.27174i 7.05981 − 4.07598i −2.98031 + 0.552433i
18.5 1.75904 + 0.471334i −0.195743 + 0.0524492i −0.592022 − 0.341804i 4.78371 + 1.45469i −0.369042 −6.97731 + 0.563209i −6.03113 − 6.03113i −7.75866 + 4.47947i 7.72911 + 4.81359i
18.6 2.95850 + 0.792728i −2.36445 + 0.633552i 4.66022 + 2.69058i −4.16825 − 2.76146i −7.49746 5.78419 − 3.94249i 2.99127 + 2.99127i −2.60501 + 1.50400i −10.1427 − 11.4741i
23.1 −0.792728 − 2.95850i 0.633552 − 2.36445i −4.66022 + 2.69058i −0.307372 + 4.99054i −7.49746 3.94249 − 5.78419i 2.99127 + 2.99127i 2.60501 + 1.50400i 15.0082 − 3.04678i
23.2 −0.471334 − 1.75904i 0.0524492 − 0.195743i 0.592022 − 0.341804i −1.13206 − 4.87016i −0.369042 −0.563209 + 6.97731i −6.03113 − 6.03113i 7.75866 + 4.47947i −8.03325 + 4.28681i
23.3 −0.156900 − 0.585559i −1.07190 + 4.00038i 3.14584 − 1.81625i 4.12069 + 2.83194i 2.51064 −5.97291 − 3.65026i −3.27174 − 3.27174i −7.05981 − 4.07598i 1.01173 − 2.85724i
23.4 0.330037 + 1.23172i 1.07605 − 4.01589i 2.05590 − 1.18698i −3.17921 + 3.85910i 5.30157 −5.79445 + 3.92739i 5.74725 + 5.74725i −7.17525 − 4.14263i −5.80257 − 2.64224i
23.5 0.506976 + 1.89206i −0.703286 + 2.62470i 0.141229 − 0.0815388i −4.52982 − 2.11677i −5.32264 6.65802 − 2.16120i 5.76622 + 5.76622i 1.39979 + 0.808169i 1.70854 − 9.64386i
23.6 0.949975 + 3.54535i 0.379154 − 1.41502i −8.20298 + 4.73599i 4.02777 − 2.96261i 5.37694 −5.83212 − 3.87123i −14.2019 − 14.2019i 5.93570 + 3.42698i 14.3298 + 11.4655i
32.1 −0.792728 + 2.95850i 0.633552 + 2.36445i −4.66022 − 2.69058i −0.307372 − 4.99054i −7.49746 3.94249 + 5.78419i 2.99127 − 2.99127i 2.60501 − 1.50400i 15.0082 + 3.04678i
32.2 −0.471334 + 1.75904i 0.0524492 + 0.195743i 0.592022 + 0.341804i −1.13206 + 4.87016i −0.369042 −0.563209 − 6.97731i −6.03113 + 6.03113i 7.75866 − 4.47947i −8.03325 − 4.28681i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2.6
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner
7.c even 3 1 inner
35.l odd 12 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 35.3.l.a ✓ 24
3.b odd 2 1 315.3.ca.a 24
5.b even 2 1 175.3.p.c 24
5.c odd 4 1 inner 35.3.l.a ✓ 24
5.c odd 4 1 175.3.p.c 24
7.b odd 2 1 245.3.m.b 24
7.c even 3 1 inner 35.3.l.a ✓ 24
7.c even 3 1 245.3.g.c 12
7.d odd 6 1 245.3.g.b 12
7.d odd 6 1 245.3.m.b 24
15.e even 4 1 315.3.ca.a 24
21.h odd 6 1 315.3.ca.a 24
35.f even 4 1 245.3.m.b 24
35.j even 6 1 175.3.p.c 24
35.k even 12 1 245.3.g.b 12
35.k even 12 1 245.3.m.b 24
35.l odd 12 1 inner 35.3.l.a ✓ 24
35.l odd 12 1 175.3.p.c 24
35.l odd 12 1 245.3.g.c 12
105.x even 12 1 315.3.ca.a 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
35.3.l.a ✓ 24 1.a even 1 1 trivial
35.3.l.a ✓ 24 5.c odd 4 1 inner
35.3.l.a ✓ 24 7.c even 3 1 inner
35.3.l.a ✓ 24 35.l odd 12 1 inner
175.3.p.c 24 5.b even 2 1
175.3.p.c 24 5.c odd 4 1
175.3.p.c 24 35.j even 6 1
175.3.p.c 24 35.l odd 12 1
245.3.g.b 12 7.d odd 6 1
245.3.g.b 12 35.k even 12 1
245.3.g.c 12 7.c even 3 1
245.3.g.c 12 35.l odd 12 1
245.3.m.b 24 7.b odd 2 1
245.3.m.b 24 7.d odd 6 1
245.3.m.b 24 35.f even 4 1
245.3.m.b 24 35.k even 12 1
315.3.ca.a 24 3.b odd 2 1
315.3.ca.a 24 15.e even 4 1
315.3.ca.a 24 21.h odd 6 1
315.3.ca.a 24 105.x even 12 1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(35, [\chi])\).