Properties

Label 6025.2.a.o
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.

\(\operatorname{Tr}(f)(q) = \) \( 40q + 11q^{2} + 8q^{3} + 41q^{4} + 3q^{6} + 16q^{7} + 33q^{8} + 38q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 40q + 11q^{2} + 8q^{3} + 41q^{4} + 3q^{6} + 16q^{7} + 33q^{8} + 38q^{9} + q^{11} + 14q^{12} + 9q^{13} - q^{14} + 43q^{16} + 12q^{17} + 42q^{18} + 2q^{21} + 5q^{22} + 77q^{23} - 2q^{24} + 2q^{26} + 38q^{27} + 42q^{28} + 2q^{29} + q^{31} + 72q^{32} + 20q^{33} + 5q^{34} + 32q^{36} + 28q^{37} + 23q^{38} - 2q^{39} - 2q^{41} + 37q^{42} + 31q^{43} + 3q^{44} + 14q^{46} + 96q^{47} + 13q^{48} + 40q^{49} - 10q^{51} + 42q^{52} + 54q^{53} + 4q^{54} - 15q^{56} + 37q^{57} + 27q^{58} + q^{59} + 5q^{61} + 39q^{62} + 70q^{63} + 65q^{64} - 52q^{66} + 34q^{67} + 52q^{68} + 21q^{69} - 9q^{71} + 70q^{72} + 25q^{73} + 22q^{74} - 47q^{76} + 54q^{77} + 58q^{78} + 13q^{79} + 12q^{81} - 5q^{82} + 63q^{83} + 95q^{84} - 18q^{86} + 47q^{87} + 13q^{88} + 19q^{89} - 31q^{91} + 137q^{92} + 52q^{93} + 120q^{94} - 49q^{96} + 36q^{97} + 64q^{98} + 16q^{99} + O(q^{100}) \)

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 −2.56709 −0.178555 4.58996 0 0.458367 0.233097 −6.64865 −2.96812 0
1.2 −2.41430 3.26436 3.82885 0 −7.88114 1.16921 −4.41538 7.65603 0
1.3 −2.30206 0.621403 3.29948 0 −1.43051 0.210935 −2.99147 −2.61386 0
1.4 −2.25059 −0.826129 3.06516 0 1.85928 0.537315 −2.39723 −2.31751 0
1.5 −2.24247 −1.80227 3.02866 0 4.04153 5.11796 −2.30673 0.248182 0
1.6 −2.06849 2.17142 2.27866 0 −4.49155 2.39120 −0.576402 1.71504 0
1.7 −1.77260 −0.796316 1.14211 0 1.41155 −3.30701 1.52069 −2.36588 0
1.8 −1.44334 −2.75896 0.0832441 0 3.98213 1.64702 2.76654 4.61187 0
1.9 −1.43804 0.465580 0.0679498 0 −0.669521 1.05447 2.77836 −2.78324 0
1.10 −1.38463 −1.64656 −0.0828005 0 2.27988 −2.06195 2.88391 −0.288826 0
1.11 −1.33622 1.40541 −0.214528 0 −1.87793 −0.850787 2.95909 −1.02483 0
1.12 −0.859912 1.32501 −1.26055 0 −1.13939 0.529848 2.80379 −1.24436 0
1.13 −0.810170 2.88822 −1.34362 0 −2.33995 3.73380 2.70891 5.34179 0
1.14 −0.625313 0.793037 −1.60898 0 −0.495897 −2.86756 2.25675 −2.37109 0
1.15 −0.607027 −2.70729 −1.63152 0 1.64340 4.13328 2.20443 4.32942 0
1.16 −0.568441 −1.77259 −1.67687 0 1.00761 −2.89075 2.09009 0.142065 0
1.17 −0.447066 2.52995 −1.80013 0 −1.13106 −3.76816 1.69891 3.40066 0
1.18 −0.410308 1.14046 −1.83165 0 −0.467941 3.98049 1.57216 −1.69935 0
1.19 0.232950 1.45187 −1.94573 0 0.338212 −4.96346 −0.919157 −0.892086 0
1.20 0.394755 2.83806 −1.84417 0 1.12034 −0.914717 −1.51750 5.05456 0
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.40
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.o yes 40
5.b even 2 1 6025.2.a.l 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6025.2.a.l 40 5.b even 2 1
6025.2.a.o 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