↑

Properties

Label 6025.2.a.p
Level $6025$
Weight $2$
Character orbit 6025.a
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $46$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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: \(1\)
Dimension: \(46\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 46 q + 34 q^{4} - 4 q^{6} + 34 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 46 q + 34 q^{4} - 4 q^{6} + 34 q^{9} - 64 q^{11} - 66 q^{14} + 22 q^{16} - 14 q^{21} - 50 q^{24} - 60 q^{26} - 36 q^{29} - 36 q^{31} + 12 q^{34} - 34 q^{36} - 88 q^{39} - 76 q^{41} - 100 q^{44} - 12 q^{46} + 22 q^{49} - 112 q^{51} - 26 q^{54} - 120 q^{56} - 84 q^{59} - 78 q^{61} + 28 q^{64} - 2 q^{66} - 24 q^{69} - 172 q^{71} - 16 q^{74} - 18 q^{76} - 54 q^{79} - 42 q^{81} + 44 q^{84} - 80 q^{86} - 86 q^{89} - 88 q^{91} + 4 q^{94} - 122 q^{96} - 148 q^{99}+O(q^{100}) \) 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 −2.68673 2.58072 5.21850 0 −6.93370 1.24945 −8.64724 3.66013 0
1.2 −2.67602 −0.199289 5.16108 0 0.533301 2.87374 −8.45912 −2.96028 0
1.3 −2.49572 −1.66439 4.22863 0 4.15385 4.24911 −5.56203 −0.229807 0
1.4 −2.44838 0.992209 3.99457 0 −2.42931 −0.744704 −4.88345 −2.01552 0
1.5 −2.36215 2.05253 3.57974 0 −4.84838 3.07728 −3.73158 1.21289 0
1.6 −1.95888 0.350465 1.83721 0 −0.686519 1.14869 0.318879 −2.87717 0
1.7 −1.92263 0.557567 1.69651 0 −1.07200 −0.976687 0.583491 −2.68912 0
1.8 −1.88286 −2.55671 1.54517 0 4.81392 3.51799 0.856390 3.53675 0
1.9 −1.84209 −1.69681 1.39329 0 3.12567 1.54055 1.11761 −0.120844 0
1.10 −1.83307 −2.40621 1.36013 0 4.41073 −0.302396 1.17293 2.78983 0
1.11 −1.70963 −1.38336 0.922819 0 2.36503 −5.05937 1.84158 −1.08631 0
1.12 −1.49203 3.12646 0.226139 0 −4.66475 4.66024 2.64665 6.77474 0
1.13 −1.45267 2.41257 0.110263 0 −3.50468 −1.25057 2.74517 2.82049 0
1.14 −1.30874 −1.88426 −0.287190 0 2.46601 1.28779 2.99335 0.550432 0
1.15 −1.09514 −0.223927 −0.800662 0 0.245232 −2.26365 3.06713 −2.94986 0
1.16 −0.930197 1.32621 −1.13473 0 −1.23364 −4.33497 2.91592 −1.24116 0
1.17 −0.779313 −2.96208 −1.39267 0 2.30839 −0.937135 2.64395 5.77395 0
1.18 −0.760721 1.12938 −1.42130 0 −0.859145 2.53853 2.60266 −1.72450 0
1.19 −0.636788 2.24729 −1.59450 0 −1.43105 1.14493 2.28894 2.05030 0
1.20 −0.434323 −1.75836 −1.81136 0 0.763695 2.56007 1.65536 0.0918227 0
See all 46 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.46
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.p 46
5.b even 2 1 inner 6025.2.a.p 46
5.c odd 4 2 1205.2.b.c ✓ 46
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1205.2.b.c ✓ 46 5.c odd 4 2
6025.2.a.p 46 1.a even 1 1 trivial
6025.2.a.p 46 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6025))\):

\( T_{2}^{46} - 63 T_{2}^{44} + 1836 T_{2}^{42} - 32871 T_{2}^{40} + 404962 T_{2}^{38} - 3644147 T_{2}^{36} + \cdots - 625 \) Copy content Toggle raw display
\( T_{3}^{46} - 86 T_{3}^{44} + 3425 T_{3}^{42} - 83933 T_{3}^{40} + 1418431 T_{3}^{38} - 17557300 T_{3}^{36} + \cdots - 1136356 \) Copy content Toggle raw display