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Properties

Label 4925.2.a.n
Level $4925$
Weight $2$
Character orbit 4925.a
Self dual yes
Analytic conductor $39.326$
Analytic rank $1$
Dimension $28$
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: \(28\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q - q^{2} + 19 q^{4} - 11 q^{6} + 2 q^{7} - 3 q^{8} + 18 q^{9} - 19 q^{11} + q^{12} - q^{13} - 12 q^{14} + q^{16} + 2 q^{17} + 2 q^{18} - 50 q^{19} - 19 q^{21} + 11 q^{22} - 2 q^{23} - 35 q^{24}+ \cdots - 74 q^{99}+O(q^{100}) \) 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 −2.75023 2.06570 5.56379 0 −5.68116 0.630554 −9.80124 1.26711 0
1.2 −2.45160 −1.43029 4.01035 0 3.50651 4.61474 −4.92858 −0.954260 0
1.3 −2.24251 1.42145 3.02883 0 −3.18760 0.594424 −2.30715 −0.979491 0
1.4 −2.22908 −0.227670 2.96881 0 0.507496 0.282717 −2.15955 −2.94817 0
1.5 −1.93680 −0.393513 1.75119 0 0.762155 −4.57378 0.481897 −2.84515 0
1.6 −1.67893 2.40308 0.818811 0 −4.03461 −1.19974 1.98314 2.77479 0
1.7 −1.46699 −1.46182 0.152046 0 2.14446 0.952154 2.71092 −0.863094 0
1.8 −1.31537 1.42411 −0.269802 0 −1.87323 −4.10116 2.98563 −0.971904 0
1.9 −1.24774 2.40328 −0.443146 0 −2.99867 4.60847 3.04841 2.77575 0
1.10 −1.19691 −2.90286 −0.567418 0 3.47444 −2.09583 3.07296 5.42657 0
1.11 −1.15422 −2.58397 −0.667769 0 2.98248 3.27068 3.07920 3.67692 0
1.12 −0.711428 1.93338 −1.49387 0 −1.37546 −0.770983 2.48564 0.737949 0
1.13 −0.181210 3.35828 −1.96716 0 −0.608552 −3.58186 0.718889 8.27801 0
1.14 −0.0152697 −2.23603 −1.99977 0 0.0341434 3.76831 0.0610751 1.99983 0
1.15 0.0703727 −1.38425 −1.99505 0 −0.0974136 1.59777 −0.281142 −1.08385 0
1.16 0.209850 −1.23000 −1.95596 0 −0.258115 −2.44423 −0.830157 −1.48710 0
1.17 0.704371 1.37202 −1.50386 0 0.966412 2.73903 −2.46802 −1.11756 0
1.18 0.748949 0.351571 −1.43908 0 0.263309 3.81748 −2.57569 −2.87640 0
1.19 0.767474 −2.69467 −1.41098 0 −2.06809 −1.73345 −2.61784 4.26127 0
1.20 1.14380 −1.11714 −0.691731 0 −1.27778 −0.126560 −3.07879 −1.75200 0
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.28
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.n ✓ 28
5.b even 2 1 4925.2.a.o yes 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4925.2.a.n ✓ 28 1.a even 1 1 trivial
4925.2.a.o yes 28 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4925))\):

\( T_{2}^{28} + T_{2}^{27} - 37 T_{2}^{26} - 35 T_{2}^{25} + 602 T_{2}^{24} + 538 T_{2}^{23} - 5677 T_{2}^{22} + \cdots + 1 \) Copy content Toggle raw display
\( T_{3}^{28} - 51 T_{3}^{26} + T_{3}^{25} + 1135 T_{3}^{24} - 46 T_{3}^{23} - 14530 T_{3}^{22} + \cdots + 400 \) Copy content Toggle raw display