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Properties

Label 841.2.d.k
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,-12,2] 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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 12 q^{4} + 2 q^{5} - 8 q^{6} + 20 q^{7} - 36 q^{9} + 10 q^{13} + 32 q^{16} + 62 q^{20} + 50 q^{22} - 24 q^{23} + 62 q^{24} - 30 q^{25} - 24 q^{28} + 4 q^{30} + 6 q^{33} + 40 q^{34} + 18 q^{35} + 32 q^{36}+ \cdots + 108 q^{96}+O(q^{100}) \) 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 −1.39585 − 0.672206i 1.82973 − 2.29441i 0.249556 + 0.312934i 0.409335 + 0.197125i −4.09635 + 1.97270i 2.12813 − 2.66859i 0.551506 + 2.41630i −1.24884 − 5.47155i −0.438862 − 0.550315i
190.2 −1.04790 − 0.504643i 0.614018 − 0.769955i −0.403546 − 0.506030i −1.71127 − 0.824106i −1.03198 + 0.496977i 0.951284 − 1.19287i 0.685132 + 3.00176i 0.451751 + 1.97925i 1.37737 + 1.72716i
190.3 1.04790 + 0.504643i −0.614018 + 0.769955i −0.403546 − 0.506030i −1.71127 − 0.824106i −1.03198 + 0.496977i 0.951284 − 1.19287i −0.685132 − 3.00176i 0.451751 + 1.97925i −1.37737 − 1.72716i
190.4 1.39585 + 0.672206i −1.82973 + 2.29441i 0.249556 + 0.312934i 0.409335 + 0.197125i −4.09635 + 1.97270i 2.12813 − 2.66859i −0.551506 − 2.41630i −1.24884 − 5.47155i 0.438862 + 0.550315i
571.1 −1.39585 + 0.672206i 1.82973 + 2.29441i 0.249556 − 0.312934i 0.409335 − 0.197125i −4.09635 − 1.97270i 2.12813 + 2.66859i 0.551506 − 2.41630i −1.24884 + 5.47155i −0.438862 + 0.550315i
571.2 −1.04790 + 0.504643i 0.614018 + 0.769955i −0.403546 + 0.506030i −1.71127 + 0.824106i −1.03198 − 0.496977i 0.951284 + 1.19287i 0.685132 − 3.00176i 0.451751 − 1.97925i 1.37737 − 1.72716i
571.3 1.04790 − 0.504643i −0.614018 − 0.769955i −0.403546 + 0.506030i −1.71127 + 0.824106i −1.03198 − 0.496977i 0.951284 + 1.19287i −0.685132 + 3.00176i 0.451751 − 1.97925i −1.37737 + 1.72716i
571.4 1.39585 − 0.672206i −1.82973 − 2.29441i 0.249556 − 0.312934i 0.409335 − 0.197125i −4.09635 − 1.97270i 2.12813 + 2.66859i −0.551506 + 2.41630i −1.24884 + 5.47155i 0.438862 − 0.550315i
574.1 −1.41392 + 1.77300i 0.632086 − 2.76935i −0.699312 − 3.06388i 0.0360893 − 0.0452546i 4.01633 + 5.03632i 0.347569 − 1.52280i 2.33469 + 1.12433i −4.56686 − 2.19928i 0.0292089 + 0.127973i
574.2 −0.342842 + 0.429910i −0.438989 + 1.92334i 0.377760 + 1.65507i 1.71089 − 2.14539i −0.676359 − 0.848127i −0.995517 + 4.36165i −1.83189 − 0.882190i −0.803613 − 0.387000i 0.335760 + 1.47106i
574.3 0.342842 − 0.429910i 0.438989 − 1.92334i 0.377760 + 1.65507i 1.71089 − 2.14539i −0.676359 − 0.848127i −0.995517 + 4.36165i 1.83189 + 0.882190i −0.803613 − 0.387000i −0.335760 − 1.47106i
574.4 1.41392 − 1.77300i −0.632086 + 2.76935i −0.699312 − 3.06388i 0.0360893 − 0.0452546i 4.01633 + 5.03632i 0.347569 − 1.52280i −2.33469 − 1.12433i −4.56686 − 2.19928i −0.0292089 − 0.127973i
605.1 −0.579097 + 2.53719i −0.395831 + 0.190622i −4.30005 − 2.07079i −0.574198 + 2.51573i −0.254420 − 1.11469i −0.0676908 + 0.0325982i 4.49896 − 5.64151i −1.75012 + 2.19459i −6.05036 − 2.91370i
605.2 −0.0380532 + 0.166722i 1.01298 − 0.487826i 1.77559 + 0.855079i 0.629156 − 2.75651i 0.0427841 + 0.187449i 2.63622 − 1.26954i −0.423373 + 0.530892i −1.08231 + 1.35718i 0.435630 + 0.209788i
605.3 0.0380532 − 0.166722i −1.01298 + 0.487826i 1.77559 + 0.855079i 0.629156 − 2.75651i 0.0427841 + 0.187449i 2.63622 − 1.26954i 0.423373 − 0.530892i −1.08231 + 1.35718i −0.435630 − 0.209788i
605.4 0.579097 − 2.53719i 0.395831 − 0.190622i −4.30005 − 2.07079i −0.574198 + 2.51573i −0.254420 − 1.11469i −0.0676908 + 0.0325982i −4.49896 + 5.64151i −1.75012 + 2.19459i 6.05036 + 2.91370i
645.1 −0.579097 − 2.53719i −0.395831 − 0.190622i −4.30005 + 2.07079i −0.574198 − 2.51573i −0.254420 + 1.11469i −0.0676908 − 0.0325982i 4.49896 + 5.64151i −1.75012 − 2.19459i −6.05036 + 2.91370i
645.2 −0.0380532 − 0.166722i 1.01298 + 0.487826i 1.77559 − 0.855079i 0.629156 + 2.75651i 0.0427841 − 0.187449i 2.63622 + 1.26954i −0.423373 − 0.530892i −1.08231 − 1.35718i 0.435630 − 0.209788i
645.3 0.0380532 + 0.166722i −1.01298 − 0.487826i 1.77559 − 0.855079i 0.629156 + 2.75651i 0.0427841 − 0.187449i 2.63622 + 1.26954i 0.423373 + 0.530892i −1.08231 − 1.35718i −0.435630 + 0.209788i
645.4 0.579097 + 2.53719i 0.395831 + 0.190622i −4.30005 + 2.07079i −0.574198 − 2.51573i −0.254420 + 1.11469i −0.0676908 − 0.0325982i −4.49896 − 5.64151i −1.75012 − 2.19459i 6.05036 − 2.91370i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 190.4
Significant digits:
Format:

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.k 24
29.b even 2 1 inner 841.2.d.k 24
29.c odd 4 1 841.2.e.e 12
29.c odd 4 1 841.2.e.f 12
29.d even 7 1 841.2.a.k 12
29.d even 7 1 inner 841.2.d.k 24
29.d even 7 2 841.2.d.l 24
29.d even 7 2 841.2.d.m 24
29.e even 14 1 841.2.a.k 12
29.e even 14 1 inner 841.2.d.k 24
29.e even 14 2 841.2.d.l 24
29.e even 14 2 841.2.d.m 24
29.f odd 28 2 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 1 841.2.e.e 12
29.f odd 28 1 841.2.e.f 12
29.f odd 28 2 841.2.e.h 12
29.f odd 28 2 841.2.e.i 12
87.h odd 14 1 7569.2.a.bp 12
87.j odd 14 1 7569.2.a.bp 12
87.k even 28 2 261.2.o.a 12
116.l even 28 2 464.2.y.d 12
145.o even 28 2 725.2.p.a 24
145.s odd 28 2 725.2.q.a 12
145.t even 28 2 725.2.p.a 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
29.2.e.a ✓ 12 29.f odd 28 2
261.2.o.a 12 87.k even 28 2
464.2.y.d 12 116.l even 28 2
725.2.p.a 24 145.o even 28 2
725.2.p.a 24 145.t even 28 2
725.2.q.a 12 145.s odd 28 2
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 1.a even 1 1 trivial
841.2.d.k 24 29.b even 2 1 inner
841.2.d.k 24 29.d even 7 1 inner
841.2.d.k 24 29.e even 14 1 inner
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 29.d even 7 2
841.2.d.m 24 29.e even 14 2
841.2.e.a 12 29.f odd 28 2
841.2.e.e 12 29.c odd 4 1
841.2.e.e 12 29.f odd 28 1
841.2.e.f 12 29.c odd 4 1
841.2.e.f 12 29.f odd 28 1
841.2.e.h 12 29.f odd 28 2
841.2.e.i 12 29.f odd 28 2
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 \( T_{2}^{24} + 10 T_{2}^{22} + 47 T_{2}^{20} + 136 T_{2}^{18} + 297 T_{2}^{16} - 1578 T_{2}^{14} + \cdots + 1 \) acting on \(S_{2}^{\mathrm{new}}(841, [\chi])\). Copy content Toggle raw display