↑

Properties

Label 7203.2.a.k
Level $7203$
Weight $2$
Character orbit 7203.a
Self dual yes
Analytic conductor $57.516$
Analytic rank $1$
Dimension $24$
CM no
Inner twists $1$

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] = [7203,2,Mod(1,7203)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7203, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) 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("7203.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 7203 = 3 \cdot 7^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7203.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,-6,24,18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(57.5162445759\)
Analytic rank: \(1\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 147)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 6 q^{2} + 24 q^{3} + 18 q^{4} - 6 q^{6} - 18 q^{8} + 24 q^{9} - 12 q^{10} - 12 q^{11} + 18 q^{12} - 14 q^{13} + 6 q^{16} + 2 q^{17} - 6 q^{18} - 26 q^{19} + 6 q^{20} - 24 q^{22} - 24 q^{23} - 18 q^{24}+ \cdots - 12 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.76937 1.00000 5.66944 −0.158853 −2.76937 0 −10.1620 1.00000 0.439924
1.2 −2.59513 1.00000 4.73469 3.53982 −2.59513 0 −7.09686 1.00000 −9.18628
1.3 −2.35187 1.00000 3.53127 −0.557059 −2.35187 0 −3.60134 1.00000 1.31013
1.4 −2.23534 1.00000 2.99674 1.56164 −2.23534 0 −2.22804 1.00000 −3.49078
1.5 −2.16475 1.00000 2.68616 −2.35627 −2.16475 0 −1.48537 1.00000 5.10075
1.6 −1.95099 1.00000 1.80636 3.02702 −1.95099 0 0.377796 1.00000 −5.90568
1.7 −1.73436 1.00000 1.00799 −2.45117 −1.73436 0 1.72050 1.00000 4.25120
1.8 −1.30793 1.00000 −0.289308 −1.06184 −1.30793 0 2.99426 1.00000 1.38882
1.9 −0.871253 1.00000 −1.24092 −4.24654 −0.871253 0 2.82366 1.00000 3.69981
1.10 −0.839793 1.00000 −1.29475 1.55513 −0.839793 0 2.76691 1.00000 −1.30599
1.11 −0.777469 1.00000 −1.39554 1.98233 −0.777469 0 2.63993 1.00000 −1.54120
1.12 −0.635256 1.00000 −1.59645 2.16973 −0.635256 0 2.28467 1.00000 −1.37833
1.13 −0.411506 1.00000 −1.83066 −1.75068 −0.411506 0 1.57634 1.00000 0.720416
1.14 0.0536083 1.00000 −1.99713 2.17062 0.0536083 0 −0.214279 1.00000 0.116363
1.15 0.544156 1.00000 −1.70389 −1.49980 0.544156 0 −2.01550 1.00000 −0.816125
1.16 0.671730 1.00000 −1.54878 0.375440 0.671730 0 −2.38382 1.00000 0.252195
1.17 0.804104 1.00000 −1.35342 1.35338 0.804104 0 −2.69650 1.00000 1.08826
1.18 1.06836 1.00000 −0.858601 −2.14514 1.06836 0 −3.05402 1.00000 −2.29179
1.19 1.33627 1.00000 −0.214387 3.76441 1.33627 0 −2.95902 1.00000 5.03026
1.20 1.76319 1.00000 1.10884 −3.70870 1.76319 0 −1.57128 1.00000 −6.53915
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(7\) \( -1 \)

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 7203.2.a.k 24
7.b odd 2 1 7203.2.a.i 24
49.h odd 42 2 147.2.m.a ✓ 48
147.o even 42 2 441.2.bb.c 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
147.2.m.a ✓ 48 49.h odd 42 2
441.2.bb.c 48 147.o even 42 2
7203.2.a.i 24 7.b odd 2 1
7203.2.a.k 24 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(7203))\):

\( T_{2}^{24} + 6 T_{2}^{23} - 15 T_{2}^{22} - 148 T_{2}^{21} + 12 T_{2}^{20} + 1536 T_{2}^{19} + 1162 T_{2}^{18} + \cdots - 41 \) Copy content Toggle raw display
\( T_{5}^{24} - 60 T_{5}^{22} + 8 T_{5}^{21} + 1506 T_{5}^{20} - 344 T_{5}^{19} - 20845 T_{5}^{18} + \cdots + 33013 \) Copy content Toggle raw display