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Properties

Label 6025.2.a.k
Level $6025$
Weight $2$
Character orbit 6025.a
Self dual yes
Analytic conductor $48.110$
Analytic rank $0$
Dimension $25$
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] = [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: \(25\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 25 q + 4 q^{2} - 9 q^{3} + 36 q^{4} + 7 q^{6} - 7 q^{7} + 15 q^{8} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 25 q + 4 q^{2} - 9 q^{3} + 36 q^{4} + 7 q^{6} - 7 q^{7} + 15 q^{8} + 36 q^{9} + 10 q^{11} - 22 q^{12} - 10 q^{13} + 13 q^{14} + 54 q^{16} - q^{17} + 13 q^{18} + 50 q^{19} + 9 q^{21} - 11 q^{22} + 31 q^{23} + 22 q^{24} + 8 q^{26} - 42 q^{27} - 14 q^{28} + 4 q^{29} + 34 q^{31} + 44 q^{32} - 28 q^{33} + 33 q^{34} + 83 q^{36} - 14 q^{37} + 10 q^{38} + 23 q^{39} + 11 q^{41} - 23 q^{42} - 49 q^{43} + 20 q^{44} + 27 q^{46} + 28 q^{47} - 30 q^{48} + 66 q^{49} + 49 q^{51} - 39 q^{52} + 16 q^{53} + 5 q^{54} + 51 q^{56} - 10 q^{57} + 8 q^{58} + 30 q^{59} + 35 q^{61} + 18 q^{62} + 73 q^{64} - 13 q^{66} - 37 q^{67} - 11 q^{68} - 4 q^{69} + 12 q^{71} + 90 q^{72} - 36 q^{73} - 12 q^{74} + 57 q^{76} + 31 q^{77} + 9 q^{78} + 16 q^{79} + 65 q^{81} + 11 q^{82} - 43 q^{83} - 62 q^{84} - 9 q^{86} + 22 q^{87} - 20 q^{88} + 38 q^{89} + 86 q^{91} + 119 q^{92} - 10 q^{93} - 18 q^{94} - 34 q^{96} - 17 q^{97} + 32 q^{98} + 26 q^{99}+O(q^{100}) \) 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 −2.63003 1.40060 4.91705 0 −3.68362 −1.05429 −7.67192 −1.03832 0
1.2 −2.57160 −2.27367 4.61314 0 5.84699 2.96482 −6.71996 2.16959 0
1.3 −2.45442 −2.63869 4.02420 0 6.47646 −2.50490 −4.96823 3.96267 0
1.4 −2.36481 −0.380137 3.59233 0 0.898952 −4.83015 −3.76557 −2.85550 0
1.5 −1.96258 −3.23511 1.85173 0 6.34917 1.21428 0.290989 7.46593 0
1.6 −1.67265 2.12506 0.797742 0 −3.55448 2.13130 2.01095 1.51590 0
1.7 −1.54117 −2.24256 0.375203 0 3.45617 −3.95910 2.50409 2.02910 0
1.8 −1.32584 2.02466 −0.242137 0 −2.68439 −3.04433 2.97272 1.09926 0
1.9 −0.895481 0.415795 −1.19811 0 −0.372337 −2.78281 2.86385 −2.82711 0
1.10 −0.747372 2.67711 −1.44143 0 −2.00080 3.83700 2.57203 4.16691 0
1.11 −0.355815 −0.886461 −1.87340 0 0.315416 4.33523 1.37821 −2.21419 0
1.12 −0.193339 −2.50161 −1.96262 0 0.483659 0.166000 0.766131 3.25804 0
1.13 0.410249 0.0956416 −1.83170 0 0.0392369 2.86768 −1.57195 −2.99085 0
1.14 0.430350 −3.17127 −1.81480 0 −1.36476 −2.65145 −1.64170 7.05698 0
1.15 0.954311 0.726487 −1.08929 0 0.693295 1.92977 −2.94814 −2.47222 0
1.16 1.07842 2.50766 −0.837004 0 2.70432 −4.80516 −3.05949 3.28838 0
1.17 1.27704 −0.753956 −0.369177 0 −0.962829 −3.52652 −3.02553 −2.43155 0
1.18 1.43128 −1.25448 0.0485743 0 −1.79552 2.72576 −2.79304 −1.42627 0
1.19 2.06740 −3.16922 2.27415 0 −6.55204 −3.93807 0.566773 7.04394 0
1.20 2.13812 3.12674 2.57154 0 6.68533 0.919039 1.22201 6.77651 0
See all 25 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.25
Significant digits:
Format:

Atkin-Lehner signs

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

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 6025.2.a.k 25
5.b even 2 1 1205.2.a.d ✓ 25
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1205.2.a.d ✓ 25 5.b even 2 1
6025.2.a.k 25 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6025))\):

\( T_{2}^{25} - 4 T_{2}^{24} - 35 T_{2}^{23} + 151 T_{2}^{22} + 515 T_{2}^{21} - 2465 T_{2}^{20} + \cdots - 2031 \) Copy content Toggle raw display
\( T_{3}^{25} + 9 T_{3}^{24} - 15 T_{3}^{23} - 346 T_{3}^{22} - 356 T_{3}^{21} + 5451 T_{3}^{20} + \cdots - 688 \) Copy content Toggle raw display