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Properties

Label 4925.2.a.s
Level $4925$
Weight $2$
Character orbit 4925.a
Self dual yes
Analytic conductor $39.326$
Analytic rank $0$
Dimension $49$
CM no
Inner twists $1$

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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] = [4925,2,Mod(1,4925)] 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("4925.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4925, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 4925 = 5^{2} \cdot 197 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4925.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [49,5,22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(39.3263229955\)
Analytic rank: \(0\)
Dimension: \(49\)
Twist minimal: no (minimal twist has level 985)
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.

\(\operatorname{Tr}(f)(q) = \) \( 49 q + 5 q^{2} + 22 q^{3} + 49 q^{4} + 2 q^{6} + 32 q^{7} + 15 q^{8} + 51 q^{9} - 2 q^{11} + 44 q^{12} + 32 q^{13} - 8 q^{14} + 49 q^{16} + 14 q^{17} + 25 q^{18} + 4 q^{19} + 10 q^{21} + 38 q^{22} + 24 q^{23}+ \cdots + 22 q^{99}+O(q^{100}) \) 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 −2.70890 2.78915 5.33816 0 −7.55553 4.77774 −9.04275 4.77934 0
1.2 −2.64077 −0.517715 4.97367 0 1.36717 2.42998 −7.85277 −2.73197 0
1.3 −2.59262 1.74428 4.72170 0 −4.52227 3.15048 −7.05633 0.0425277 0
1.4 −2.45849 1.81153 4.04418 0 −4.45363 −2.66745 −5.02561 0.281635 0
1.5 −2.25387 −1.45500 3.07992 0 3.27937 3.79411 −2.43401 −0.882988 0
1.6 −2.16949 0.257883 2.70667 0 −0.559474 0.876810 −1.53312 −2.93350 0
1.7 −2.09155 2.86206 2.37458 0 −5.98614 −0.362555 −0.783458 5.19139 0
1.8 −2.02231 −1.02633 2.08973 0 2.07555 −1.36812 −0.181465 −1.94666 0
1.9 −1.86955 1.20234 1.49520 0 −2.24784 −0.699733 0.943741 −1.55437 0
1.10 −1.80911 −2.24718 1.27287 0 4.06540 2.84950 1.31546 2.04984 0
1.11 −1.79195 −1.17236 1.21107 0 2.10080 −2.36413 1.41371 −1.62558 0
1.12 −1.56500 −2.82019 0.449238 0 4.41362 4.08560 2.42695 4.95350 0
1.13 −1.38665 2.47348 −0.0772027 0 −3.42985 1.44878 2.88035 3.11809 0
1.14 −1.32369 2.49883 −0.247834 0 −3.30769 −4.44135 2.97544 3.24415 0
1.15 −1.27211 −0.681648 −0.381746 0 0.867129 2.83290 3.02983 −2.53536 0
1.16 −1.18293 0.672647 −0.600670 0 −0.795696 −3.32812 3.07642 −2.54755 0
1.17 −0.961463 3.28021 −1.07559 0 −3.15380 3.71558 2.95706 7.75980 0
1.18 −0.870537 1.92866 −1.24217 0 −1.67897 4.43166 2.82242 0.719722 0
1.19 −0.599062 3.23257 −1.64112 0 −1.93651 −4.00419 2.18126 7.44950 0
1.20 −0.420000 −2.34519 −1.82360 0 0.984980 −1.96792 1.60591 2.49993 0
See all 49 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.49
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \( -1 \)
\(197\) \( +1 \)

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 4925.2.a.s 49
5.b even 2 1 4925.2.a.r 49
5.c odd 4 2 985.2.b.a ✓ 98
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
985.2.b.a ✓ 98 5.c odd 4 2
4925.2.a.r 49 5.b even 2 1
4925.2.a.s 49 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4925))\):

\( T_{2}^{49} - 5 T_{2}^{48} - 61 T_{2}^{47} + 335 T_{2}^{46} + 1683 T_{2}^{45} - 10421 T_{2}^{44} + \cdots - 16732 \) Copy content Toggle raw display
\( T_{3}^{49} - 22 T_{3}^{48} + 143 T_{3}^{47} + 330 T_{3}^{46} - 8029 T_{3}^{45} + 21618 T_{3}^{44} + \cdots + 54784 \) Copy content Toggle raw display