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Properties

Label 3283.2.a.bc
Level $3283$
Weight $2$
Character orbit 3283.a
Self dual yes
Analytic conductor $26.215$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3283,2,Mod(1,3283)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3283, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3283.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3283 = 7^{2} \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3283.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(26.2148869836\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: no (minimal twist has level 469)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 22 q + 6 q^{3} + 22 q^{4} + 17 q^{5} + 10 q^{6} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 22 q + 6 q^{3} + 22 q^{4} + 17 q^{5} + 10 q^{6} + 24 q^{9} + 6 q^{10} - q^{11} + 13 q^{12} + 22 q^{13} + q^{15} + 18 q^{16} + 35 q^{17} - 14 q^{18} + 12 q^{19} + 17 q^{20} + 14 q^{22} - q^{23} + 40 q^{24} + 13 q^{25} + 25 q^{26} + 12 q^{27} + 12 q^{29} + 2 q^{30} + 6 q^{31} - 25 q^{32} + 27 q^{33} - 14 q^{34} + 64 q^{36} + 32 q^{38} - 3 q^{39} + 8 q^{40} + 20 q^{41} + 5 q^{43} - 17 q^{44} + 56 q^{45} - 68 q^{46} + 51 q^{47} - 13 q^{48} + 25 q^{50} - 9 q^{51} + 55 q^{52} - 11 q^{53} + 43 q^{54} + 6 q^{55} + 28 q^{57} - 11 q^{58} + 33 q^{59} - 94 q^{60} + 29 q^{61} + 30 q^{62} + 50 q^{64} + 18 q^{65} + 22 q^{66} + 22 q^{67} + 92 q^{68} + 12 q^{69} - 2 q^{71} - 25 q^{72} + 40 q^{73} - 21 q^{74} + 25 q^{75} - 13 q^{76} + 134 q^{78} - 21 q^{79} + 23 q^{80} + 26 q^{81} + 3 q^{82} + 49 q^{83} + 25 q^{85} - 26 q^{86} - 32 q^{87} - 46 q^{88} + 69 q^{89} - 99 q^{90} + 21 q^{92} - 21 q^{93} + 18 q^{95} + 84 q^{96} + q^{97} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.78042 −1.37650 5.73076 0.302794 3.82727 0 −10.3731 −1.10524 −0.841896
1.2 −2.51119 2.50933 4.30606 −1.21275 −6.30140 0 −5.79094 3.29674 3.04545
1.3 −2.40892 −3.24321 3.80290 3.68371 7.81264 0 −4.34304 7.51842 −8.87377
1.4 −1.93800 1.14978 1.75585 −2.09629 −2.22828 0 0.473155 −1.67800 4.06262
1.5 −1.67678 3.15252 0.811582 3.56232 −5.28607 0 1.99271 6.93838 −5.97322
1.6 −1.46434 −2.28205 0.144293 −1.60101 3.34169 0 2.71739 2.20773 2.34442
1.7 −1.26426 2.25439 −0.401657 0.478393 −2.85013 0 3.03631 2.08229 −0.604811
1.8 −1.22435 0.976949 −0.500961 2.37395 −1.19613 0 3.06206 −2.04557 −2.90655
1.9 −0.884213 −1.94453 −1.21817 0.305132 1.71938 0 2.84555 0.781215 −0.269801
1.10 −0.479433 −0.172560 −1.77014 −2.14931 0.0827308 0 1.80753 −2.97022 1.03045
1.11 −0.350827 0.769811 −1.87692 1.37484 −0.270070 0 1.36013 −2.40739 −0.482332
1.12 0.220187 0.855982 −1.95152 3.79041 0.188476 0 −0.870072 −2.26729 0.834599
1.13 0.233650 −2.47683 −1.94541 1.24003 −0.578711 0 −0.921843 3.13471 0.289732
1.14 1.10056 2.64108 −0.788778 4.44815 2.90665 0 −3.06920 3.97529 4.89543
1.15 1.22119 −1.46345 −0.508686 −1.14293 −1.78715 0 −3.06359 −0.858323 −1.39574
1.16 1.31642 −0.188848 −0.267033 −2.84537 −0.248604 0 −2.98437 −2.96434 −3.74571
1.17 1.49896 2.95879 0.246872 −1.02495 4.43509 0 −2.62786 5.75442 −1.53636
1.18 1.81562 −0.554974 1.29647 1.45659 −1.00762 0 −1.27735 −2.69200 2.64461
1.19 2.00018 −2.62781 2.00071 3.65304 −5.25609 0 0.00141588 3.90539 7.30673
1.20 2.49458 3.09667 4.22294 −1.96538 7.72490 0 5.54531 6.58937 −4.90281
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.22
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(7\) \( +1 \)
\(67\) \( -1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 3283.2.a.bc 22
7.b odd 2 1 3283.2.a.bb 22
7.c even 3 2 469.2.f.c ✓ 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
469.2.f.c ✓ 44 7.c even 3 2
3283.2.a.bb 22 7.b odd 2 1
3283.2.a.bc 22 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(3283))\):

\( T_{2}^{22} - 33 T_{2}^{20} + 463 T_{2}^{18} + 5 T_{2}^{17} - 3617 T_{2}^{16} - 114 T_{2}^{15} + \cdots - 147 \) Copy content Toggle raw display
\( T_{3}^{22} - 6 T_{3}^{21} - 27 T_{3}^{20} + 218 T_{3}^{19} + 193 T_{3}^{18} - 3220 T_{3}^{17} + \cdots + 577 \) Copy content Toggle raw display