Properties

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

Related objects

Downloads

Learn more about

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: \(1\)
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 −2.80490 0.485560 5.86748 0 −1.36195 4.89210 −10.8479 −2.76423 0
1.2 −2.72336 −1.81872 5.41670 0 4.95303 −1.94325 −9.30491 0.307738 0
1.3 −2.67715 1.88460 5.16713 0 −5.04535 −1.59154 −8.47889 0.551710 0
1.4 −2.61751 −2.91594 4.85138 0 7.63252 2.00988 −7.46353 5.50273 0
1.5 −2.47202 −1.05364 4.11086 0 2.60461 −3.75256 −5.21808 −1.88985 0
1.6 −2.30867 −1.94403 3.32995 0 4.48812 −0.292911 −3.07041 0.779258 0
1.7 −2.16066 −3.21615 2.66843 0 6.94900 −3.61887 −1.44426 7.34365 0
1.8 −2.15543 0.792453 2.64590 0 −1.70808 −4.02126 −1.39219 −2.37202 0
1.9 −2.14986 1.70160 2.62188 0 −3.65820 3.86024 −1.33695 −0.104549 0
1.10 −1.98624 2.93351 1.94516 0 −5.82666 −3.87755 0.108919 5.60547 0
1.11 −1.73371 −1.68845 1.00575 0 2.92728 1.46765 1.72373 −0.149147 0
1.12 −1.58708 1.81144 0.518823 0 −2.87490 0.0644914 2.35075 0.281309 0
1.13 −1.58658 2.51389 0.517252 0 −3.98850 −3.57092 2.35251 3.31964 0
1.14 −1.41467 −0.773938 0.00129837 0 1.09487 2.74877 2.82751 −2.40102 0
1.15 −1.00174 2.95041 −0.996521 0 −2.95554 −1.49397 3.00173 5.70493 0
1.16 −0.863616 −1.78313 −1.25417 0 1.53994 −4.46828 2.81035 0.179539 0
1.17 −0.833391 −0.371715 −1.30546 0 0.309784 3.36045 2.75474 −2.86183 0
1.18 −0.811989 −3.20147 −1.34067 0 2.59956 1.14623 2.71259 7.24939 0
1.19 −0.645204 −2.49795 −1.58371 0 1.61169 −3.74088 2.31222 3.23976 0
1.20 −0.333070 −1.03111 −1.88906 0 0.343432 2.91492 1.29533 −1.93681 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.m 40
5.b even 2 1 6025.2.a.n yes 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6025.2.a.m 40 1.a even 1 1 trivial
6025.2.a.n yes 40 5.b even 2 1

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