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Properties

Label 841.2.d.m
Level $841$
Weight $2$
Character orbit 841.d
Analytic conductor $6.715$
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] = [841,2,Mod(190,841)] 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("841.190"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 841 = 29^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 841.d (of order \(7\), degree \(6\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,0,0,2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.71541880999\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{7})\)
Twist minimal: no (minimal twist has level 29)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 2 q^{4} + 2 q^{5} + 6 q^{6} - 22 q^{7} + 6 q^{9} - 18 q^{13} + 18 q^{16} - 22 q^{20} + 8 q^{22} - 10 q^{23} - 50 q^{24} + 26 q^{25} - 24 q^{28} + 4 q^{30} + 34 q^{33} + 26 q^{34} - 38 q^{35} - 80 q^{36}+ \cdots - 60 q^{96}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
190.1 −2.34472 − 1.12916i 0.273923 − 0.343489i 2.97573 + 3.73144i −2.32488 − 1.11960i −1.03013 + 0.496082i 0.0468435 − 0.0587399i −1.60566 − 7.03485i 0.624612 + 2.73660i 4.18698 + 5.25031i
190.2 −0.154074 − 0.0741982i −0.701005 + 0.879032i −1.22875 − 1.54080i 2.54740 + 1.22676i 0.173229 − 0.0834229i −1.82432 + 2.28763i 0.151100 + 0.662012i 0.386273 + 1.69237i −0.301465 − 0.378025i
190.3 0.154074 + 0.0741982i 0.701005 − 0.879032i −1.22875 − 1.54080i 2.54740 + 1.22676i 0.173229 − 0.0834229i −1.82432 + 2.28763i −0.151100 − 0.662012i 0.386273 + 1.69237i 0.301465 + 0.378025i
190.4 2.34472 + 1.12916i −0.273923 + 0.343489i 2.97573 + 3.73144i −2.32488 − 1.11960i −1.03013 + 0.496082i 0.0468435 − 0.0587399i 1.60566 + 7.03485i 0.624612 + 2.73660i −4.18698 − 5.25031i
571.1 −2.34472 + 1.12916i 0.273923 + 0.343489i 2.97573 − 3.73144i −2.32488 + 1.11960i −1.03013 − 0.496082i 0.0468435 + 0.0587399i −1.60566 + 7.03485i 0.624612 − 2.73660i 4.18698 − 5.25031i
571.2 −0.154074 + 0.0741982i −0.701005 − 0.879032i −1.22875 + 1.54080i 2.54740 − 1.22676i 0.173229 + 0.0834229i −1.82432 − 2.28763i 0.151100 − 0.662012i 0.386273 − 1.69237i −0.301465 + 0.378025i
571.3 0.154074 − 0.0741982i 0.701005 + 0.879032i −1.22875 + 1.54080i 2.54740 − 1.22676i 0.173229 + 0.0834229i −1.82432 − 2.28763i −0.151100 + 0.662012i 0.386273 − 1.69237i 0.301465 − 0.378025i
571.4 2.34472 − 1.12916i −0.273923 − 0.343489i 2.97573 − 3.73144i −2.32488 + 1.11960i −1.03013 − 0.496082i 0.0468435 + 0.0587399i 1.60566 − 7.03485i 0.624612 − 2.73660i −4.18698 + 5.25031i
574.1 −0.965958 + 1.21127i 0.653024 − 2.86109i −0.0890656 − 0.390222i −0.283269 + 0.355208i 2.83476 + 3.55468i −0.759522 + 3.32768i −2.23300 − 1.07536i −5.05647 − 2.43507i −0.156628 − 0.686232i
574.2 −0.725171 + 0.909335i 0.219141 − 0.960118i 0.144024 + 0.631009i 1.18424 − 1.48499i 0.714155 + 0.895521i −0.339509 + 1.48749i −2.77404 − 1.33591i 1.82910 + 0.880850i 0.491577 + 2.15374i
574.3 0.725171 − 0.909335i −0.219141 + 0.960118i 0.144024 + 0.631009i 1.18424 − 1.48499i 0.714155 + 0.895521i −0.339509 + 1.48749i 2.77404 + 1.33591i 1.82910 + 0.880850i −0.491577 − 2.15374i
574.4 0.965958 − 1.21127i −0.653024 + 2.86109i −0.0890656 − 0.390222i −0.283269 + 0.355208i 2.83476 + 3.55468i −0.759522 + 3.32768i 2.23300 + 1.07536i −5.05647 − 2.43507i 0.156628 + 0.686232i
605.1 −0.504621 + 2.21089i −2.55926 + 1.23248i −2.83146 − 1.36356i −0.0128801 + 0.0564316i −1.43341 − 6.28018i 1.40728 − 0.677709i 1.61565 − 2.02596i 3.16036 − 3.96297i −0.118264 − 0.0569531i
605.2 −0.122359 + 0.536089i 1.77743 − 0.855966i 1.52952 + 0.736577i −0.610610 + 2.67526i 0.241390 + 1.05760i −4.03077 + 1.94112i −1.26771 + 1.58965i 0.556117 − 0.697349i −1.35946 − 0.654683i
605.3 0.122359 − 0.536089i −1.77743 + 0.855966i 1.52952 + 0.736577i −0.610610 + 2.67526i 0.241390 + 1.05760i −4.03077 + 1.94112i 1.26771 − 1.58965i 0.556117 − 0.697349i 1.35946 + 0.654683i
605.4 0.504621 − 2.21089i 2.55926 − 1.23248i −2.83146 − 1.36356i −0.0128801 + 0.0564316i −1.43341 − 6.28018i 1.40728 − 0.677709i −1.61565 + 2.02596i 3.16036 − 3.96297i 0.118264 + 0.0569531i
645.1 −0.504621 − 2.21089i −2.55926 − 1.23248i −2.83146 + 1.36356i −0.0128801 − 0.0564316i −1.43341 + 6.28018i 1.40728 + 0.677709i 1.61565 + 2.02596i 3.16036 + 3.96297i −0.118264 + 0.0569531i
645.2 −0.122359 − 0.536089i 1.77743 + 0.855966i 1.52952 − 0.736577i −0.610610 − 2.67526i 0.241390 − 1.05760i −4.03077 − 1.94112i −1.26771 − 1.58965i 0.556117 + 0.697349i −1.35946 + 0.654683i
645.3 0.122359 + 0.536089i −1.77743 − 0.855966i 1.52952 − 0.736577i −0.610610 − 2.67526i 0.241390 − 1.05760i −4.03077 − 1.94112i 1.26771 + 1.58965i 0.556117 + 0.697349i 1.35946 − 0.654683i
645.4 0.504621 + 2.21089i 2.55926 + 1.23248i −2.83146 + 1.36356i −0.0128801 − 0.0564316i −1.43341 + 6.28018i 1.40728 + 0.677709i −1.61565 − 2.02596i 3.16036 + 3.96297i 0.118264 − 0.0569531i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 190.4
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
29.b even 2 1 inner
29.d even 7 1 inner
29.e even 14 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 841.2.d.m 24
29.b even 2 1 inner 841.2.d.m 24
29.c odd 4 1 29.2.e.a ✓ 12
29.c odd 4 1 841.2.e.i 12
29.d even 7 1 841.2.a.k 12
29.d even 7 2 841.2.d.k 24
29.d even 7 2 841.2.d.l 24
29.d even 7 1 inner 841.2.d.m 24
29.e even 14 1 841.2.a.k 12
29.e even 14 2 841.2.d.k 24
29.e even 14 2 841.2.d.l 24
29.e even 14 1 inner 841.2.d.m 24
29.f odd 28 1 29.2.e.a ✓ 12
29.f odd 28 2 841.2.b.e 12
29.f odd 28 2 841.2.e.a 12
29.f odd 28 2 841.2.e.e 12
29.f odd 28 2 841.2.e.f 12
29.f odd 28 2 841.2.e.h 12
29.f odd 28 1 841.2.e.i 12
87.f even 4 1 261.2.o.a 12
87.h odd 14 1 7569.2.a.bp 12
87.j odd 14 1 7569.2.a.bp 12
87.k even 28 1 261.2.o.a 12
116.e even 4 1 464.2.y.d 12
116.l even 28 1 464.2.y.d 12
145.e even 4 1 725.2.p.a 24
145.f odd 4 1 725.2.q.a 12
145.j even 4 1 725.2.p.a 24
145.o even 28 1 725.2.p.a 24
145.s odd 28 1 725.2.q.a 12
145.t even 28 1 725.2.p.a 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
29.2.e.a ✓ 12 29.c odd 4 1
29.2.e.a ✓ 12 29.f odd 28 1
261.2.o.a 12 87.f even 4 1
261.2.o.a 12 87.k even 28 1
464.2.y.d 12 116.e even 4 1
464.2.y.d 12 116.l even 28 1
725.2.p.a 24 145.e even 4 1
725.2.p.a 24 145.j even 4 1
725.2.p.a 24 145.o even 28 1
725.2.p.a 24 145.t even 28 1
725.2.q.a 12 145.f odd 4 1
725.2.q.a 12 145.s odd 28 1
841.2.a.k 12 29.d even 7 1
841.2.a.k 12 29.e even 14 1
841.2.b.e 12 29.f odd 28 2
841.2.d.k 24 29.d even 7 2
841.2.d.k 24 29.e even 14 2
841.2.d.l 24 29.d even 7 2
841.2.d.l 24 29.e even 14 2
841.2.d.m 24 1.a even 1 1 trivial
841.2.d.m 24 29.b even 2 1 inner
841.2.d.m 24 29.d even 7 1 inner
841.2.d.m 24 29.e even 14 1 inner
841.2.e.a 12 29.f odd 28 2
841.2.e.e 12 29.f odd 28 2
841.2.e.f 12 29.f odd 28 2
841.2.e.h 12 29.f odd 28 2
841.2.e.i 12 29.c odd 4 1
841.2.e.i 12 29.f odd 28 1
7569.2.a.bp 12 87.h odd 14 1
7569.2.a.bp 12 87.j odd 14 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{24} + 3 T_{2}^{22} + 5 T_{2}^{20} + 206 T_{2}^{18} + 1620 T_{2}^{16} + 4449 T_{2}^{14} + 12992 T_{2}^{12} + \cdots + 1 \) acting on \(S_{2}^{\mathrm{new}}(841, [\chi])\). Copy content Toggle raw display