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

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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: \(1\)
Dimension: \(40\)
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.

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

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:
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Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

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

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6025))\):

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