Properties

Label 6025.2.a.l
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.

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

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 −2.77437 2.60911 5.69713 0 −7.23863 1.40482 −10.2572 3.80744 0
1.2 −2.74359 −0.0877195 5.52727 0 0.240666 −1.38863 −9.67736 −2.99231 0
1.3 −2.67635 −2.41547 5.16285 0 6.46465 −0.976502 −8.46490 2.83451 0
1.4 −2.60048 −3.03019 4.76251 0 7.87996 −1.49919 −7.18385 6.18207 0
1.5 −2.50972 −0.136405 4.29867 0 0.342337 −4.91163 −5.76901 −2.98139 0
1.6 −2.49478 2.89336 4.22391 0 −7.21828 0.185663 −5.54817 5.37152 0
1.7 −2.40563 −2.30634 3.78704 0 5.54820 4.72754 −4.29895 2.31922 0
1.8 −2.17490 0.995168 2.73018 0 −2.16439 3.57474 −1.58807 −2.00964 0
1.9 −2.06779 0.977473 2.27574 0 −2.02121 −1.48726 −0.570172 −2.04455 0
1.10 −1.92684 −1.97893 1.71272 0 3.81308 −3.74943 0.553547 0.916158 0
1.11 −1.60847 −3.19065 0.587161 0 5.13204 −4.87921 2.27250 7.18022 0
1.12 −1.59175 0.0342835 0.533671 0 −0.0545707 −1.01795 2.33403 −2.99882 0
1.13 −1.55382 2.23966 0.414344 0 −3.48002 1.09916 2.46382 2.01608 0
1.14 −1.26445 0.637501 −0.401165 0 −0.806088 3.31632 3.03615 −2.59359 0
1.15 −1.23402 −3.02124 −0.477193 0 3.72827 0.346766 3.05691 6.12789 0
1.16 −1.19733 −1.42352 −0.566401 0 1.70442 1.72539 3.07283 −0.973586 0
1.17 −1.14940 0.361587 −0.678878 0 −0.415609 −3.63700 3.07910 −2.86925 0
1.18 −0.679522 2.20024 −1.53825 0 −1.49511 −5.10754 2.40432 1.84107 0
1.19 −0.667714 2.21224 −1.55416 0 −1.47714 −0.972247 2.37316 1.89399 0
1.20 −0.599456 2.83593 −1.64065 0 −1.70002 0.360434 2.18241 5.04251 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6025))\):

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