Properties

Label 6025.2.a.n
Level 6025
Weight 2
Character orbit 6025.a
Self dual yes
Analytic conductor 48.110
Analytic rank 0
Dimension 40
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 40q + 9q^{2} + 8q^{3} + 41q^{4} + 3q^{6} + 20q^{7} + 27q^{8} + 38q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 40q + 9q^{2} + 8q^{3} + 41q^{4} + 3q^{6} + 20q^{7} + 27q^{8} + 38q^{9} + q^{11} + 26q^{12} + 11q^{13} - q^{14} + 43q^{16} + 20q^{17} + 18q^{18} + 2q^{21} + 23q^{22} + 79q^{23} - 2q^{24} + 2q^{26} + 26q^{27} + 30q^{28} + 2q^{29} + q^{31} + 68q^{32} + 20q^{33} + 5q^{34} + 32q^{36} + 16q^{37} + 45q^{38} - 2q^{39} - 2q^{41} + 19q^{42} + 25q^{43} + 3q^{44} + 14q^{46} + 88q^{47} + 75q^{48} + 40q^{49} - 10q^{51} + 18q^{52} + 34q^{53} + 4q^{54} - 15q^{56} + 51q^{57} + 53q^{58} + q^{59} + 9q^{61} + 39q^{62} + 110q^{63} + 17q^{64} + 26q^{66} + 30q^{67} + 44q^{68} - 7q^{69} + 5q^{71} + 18q^{72} + 23q^{73} - 18q^{74} + 43q^{76} + 30q^{77} + 46q^{78} + 5q^{79} + 44q^{81} + 5q^{82} + 65q^{83} - 65q^{84} + 40q^{86} + 33q^{87} + 71q^{88} - 9q^{89} + q^{91} + 117q^{92} + 68q^{93} - 72q^{94} + 83q^{96} - 8q^{97} + 76q^{98} - 40q^{99} + O(q^{100}) \)

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.

Label \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.56980 0.961984 4.60385 0 −2.47210 2.40958 −6.69138 −2.07459 0
1.2 −2.49215 0.300645 4.21080 0 −0.749251 2.12232 −5.50965 −2.90961 0
1.3 −2.35802 2.46294 3.56028 0 −5.80768 −4.19376 −3.67917 3.06609 0
1.4 −2.31444 −1.11942 3.35665 0 2.59084 1.28338 −3.13990 −1.74690 0
1.5 −2.11193 3.26338 2.46023 0 −6.89202 1.21893 −0.971967 7.64967 0
1.6 −1.94004 1.97205 1.76376 0 −3.82586 −2.17744 0.458324 0.888995 0
1.7 −1.93842 −1.97315 1.75746 0 3.82479 −0.0385515 0.470139 0.893333 0
1.8 −1.82970 −1.30801 1.34779 0 2.39326 2.38020 1.19335 −1.28911 0
1.9 −1.70335 −3.34921 0.901404 0 5.70487 4.14952 1.87129 8.21718 0
1.10 −1.43348 2.46422 0.0548683 0 −3.53241 5.17959 2.78831 3.07238 0
1.11 −1.35529 0.00323419 −0.163197 0 −0.00438325 −1.75164 2.93175 −2.99999 0
1.12 −1.11018 −0.936293 −0.767491 0 1.03946 −2.02452 3.07242 −2.12335 0
1.13 −0.785880 −0.0947217 −1.38239 0 0.0744399 3.94418 2.65816 −2.99103 0
1.14 −0.628757 −2.03617 −1.60466 0 1.28026 0.952044 2.26646 1.14599 0
1.15 −0.460717 3.13691 −1.78774 0 −1.44523 1.56377 1.74508 6.84020 0
1.16 −0.409457 −1.91892 −1.83235 0 0.785714 −3.66070 1.56918 0.682248 0
1.17 −0.337207 −2.44634 −1.88629 0 0.824921 −2.26789 1.31048 2.98457 0
1.18 −0.230402 1.04564 −1.94691 0 −0.240918 1.53080 0.909377 −1.90664 0
1.19 −0.0794983 0.864949 −1.99368 0 −0.0687619 −0.264036 0.317491 −2.25186 0
1.20 0.221853 −0.516508 −1.95078 0 −0.114589 −0.263042 −0.876492 −2.73322 0
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.40
Significant digits:
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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.n yes 40
5.b even 2 1 6025.2.a.m 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6025.2.a.m 40 5.b even 2 1
6025.2.a.n yes 40 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6025))\):

\(T_{2}^{40} - \cdots\)
\(T_{3}^{40} - \cdots\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database