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Properties

Label 4925.2.a.r
Level $4925$
Weight $2$
Character orbit 4925.a
Self dual yes
Analytic conductor $39.326$
Analytic rank $1$
Dimension $49$
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] = [4925,2,Mod(1,4925)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
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")
 
//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);
 
Level: \( N \) \(=\) \( 4925 = 5^{2} \cdot 197 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4925.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: \(39.3263229955\)
Analytic rank: \(1\)
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.

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 −2.79089 0.406400 5.78908 0 −1.13422 −1.50513 −10.5749 −2.83484 0
1.2 −2.63405 −1.88963 4.93820 0 4.97737 0.201886 −7.73937 0.570696 0
1.3 −2.59061 2.33246 4.71127 0 −6.04251 −4.16518 −7.02386 2.44038 0
1.4 −2.58552 −3.08353 4.68492 0 7.97252 3.10556 −6.94192 6.50813 0
1.5 −2.51668 −3.09870 4.33369 0 7.79844 −2.79664 −5.87315 6.60194 0
1.6 −2.46587 0.597412 4.08052 0 −1.47314 −1.55114 −5.13031 −2.64310 0
1.7 −2.33154 −1.66088 3.43607 0 3.87240 −1.15133 −3.34826 −0.241482 0
1.8 −2.32198 −2.63224 3.39157 0 6.11200 −5.08302 −3.23120 3.92870 0
1.9 −2.16529 0.704498 2.68847 0 −1.52544 4.65089 −1.49074 −2.50368 0
1.10 −1.97563 2.19256 1.90311 0 −4.33169 2.78164 0.191426 1.80734 0
1.11 −1.83076 2.81413 1.35169 0 −5.15201 −2.14355 1.18690 4.91935 0
1.12 −1.74510 −2.11665 1.04537 0 3.69377 −2.11819 1.66592 1.48022 0
1.13 −1.61100 1.75987 0.595328 0 −2.83515 1.48382 2.26293 0.0971430 0
1.14 −1.45182 −0.257058 0.107768 0 0.373200 −4.95623 2.74717 −2.93392 0
1.15 −1.34195 −0.0980382 −0.199165 0 0.131563 0.0228448 2.95117 −2.99039 0
1.16 −1.29247 −1.51932 −0.329522 0 1.96368 2.88465 3.01084 −0.691664 0
1.17 −1.27373 −3.21433 −0.377621 0 4.09418 0.234977 3.02844 7.33194 0
1.18 −1.01022 0.344075 −0.979461 0 −0.347590 0.0648861 3.00990 −2.88161 0
1.19 −0.949495 1.30028 −1.09846 0 −1.23461 1.82879 2.94197 −1.30928 0
1.20 −0.862325 −3.33083 −1.25639 0 2.87226 −3.93497 2.80807 8.09446 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.r 49
5.b even 2 1 4925.2.a.s 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 1.a even 1 1 trivial
4925.2.a.s 49 5.b even 2 1

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