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Properties

Label 6025.2.a.q
Level $6025$
Weight $2$
Character orbit 6025.a
Self dual yes
Analytic conductor $48.110$
Analytic rank $0$
Dimension $66$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6025,2,Mod(1,6025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6025, 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("6025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.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: \(48.1098672178\)
Analytic rank: \(0\)
Dimension: \(66\)
Twist minimal: no (minimal twist has level 1205)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 66 q + 78 q^{4} + 16 q^{6} + 90 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 66 q + 78 q^{4} + 16 q^{6} + 90 q^{9} + 48 q^{11} + 30 q^{14} + 98 q^{16} + 12 q^{19} + 18 q^{21} + 42 q^{24} + 48 q^{26} + 56 q^{29} + 48 q^{31} + 8 q^{34} + 158 q^{36} + 84 q^{39} + 56 q^{41} + 144 q^{44} + 36 q^{46} + 98 q^{49} + 44 q^{51} + 86 q^{54} + 104 q^{56} + 108 q^{59} + 22 q^{61} + 136 q^{64} + 74 q^{66} + 20 q^{69} + 212 q^{71} + 84 q^{74} + 6 q^{76} + 66 q^{79} + 162 q^{81} - 52 q^{84} + 100 q^{86} + 54 q^{89} + 72 q^{91} - 96 q^{94} + 122 q^{96} + 112 q^{99}+O(q^{100}) \) 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 −2.81437 0.650611 5.92068 0 −1.83106 −2.61686 −11.0342 −2.57671 0
1.2 −2.73687 −1.37229 5.49044 0 3.75578 −0.639768 −9.55288 −1.11681 0
1.3 −2.70326 −3.35528 5.30763 0 9.07021 3.43095 −8.94141 8.25791 0
1.4 −2.60935 2.94245 4.80870 0 −7.67788 2.28979 −7.32887 5.65803 0
1.5 −2.55975 2.19931 4.55230 0 −5.62967 −4.06530 −6.53325 1.83695 0
1.6 −2.48606 −2.54168 4.18051 0 6.31876 −3.51286 −5.42088 3.46011 0
1.7 −2.48219 −1.89252 4.16124 0 4.69758 −3.72710 −5.36461 0.581628 0
1.8 −2.37391 0.703313 3.63543 0 −1.66960 4.47866 −3.88235 −2.50535 0
1.9 −2.33352 1.59052 3.44531 0 −3.71151 −3.91727 −3.37267 −0.470249 0
1.10 −2.31942 −2.66924 3.37972 0 6.19110 0.0358936 −3.20016 4.12486 0
1.11 −2.20997 −2.26852 2.88397 0 5.01336 0.372373 −1.95355 2.14617 0
1.12 −2.06213 2.32228 2.25239 0 −4.78886 3.49367 −0.520471 2.39299 0
1.13 −1.90752 0.479938 1.63863 0 −0.915491 1.00580 0.689327 −2.76966 0
1.14 −1.85162 0.305536 1.42851 0 −0.565737 −2.51443 1.05818 −2.90665 0
1.15 −1.85071 2.57343 1.42511 0 −4.76266 −3.52351 1.06395 3.62254 0
1.16 −1.67685 3.17567 0.811815 0 −5.32511 0.164609 1.99240 7.08488 0
1.17 −1.64329 −3.10101 0.700400 0 5.09585 −0.459168 2.13562 6.61624 0
1.18 −1.54552 −0.0372080 0.388631 0 0.0575057 5.06287 2.49040 −2.99862 0
1.19 −1.47177 −1.07414 0.166115 0 1.58089 −3.64779 2.69906 −1.84623 0
1.20 −1.38861 −0.0366779 −0.0717484 0 0.0509315 3.69082 2.87686 −2.99865 0
See all 66 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.66
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(241\) \(1\)

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 6025.2.a.q 66
5.b even 2 1 inner 6025.2.a.q 66
5.c odd 4 2 1205.2.b.d ✓ 66
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1205.2.b.d ✓ 66 5.c odd 4 2
6025.2.a.q 66 1.a even 1 1 trivial
6025.2.a.q 66 5.b even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6025))\):

\( T_{2}^{66} - 105 T_{2}^{64} + 5239 T_{2}^{62} - 165314 T_{2}^{60} + 3703934 T_{2}^{58} - 62721100 T_{2}^{56} + \cdots - 1841449 \) Copy content Toggle raw display
\( T_{3}^{66} - 144 T_{3}^{64} + 9828 T_{3}^{62} - 423019 T_{3}^{60} + 12889773 T_{3}^{58} - 295883613 T_{3}^{56} + \cdots - 262144 \) Copy content Toggle raw display