Properties

Label 6025.2.a.k
Level 6025
Weight 2
Character orbit 6025.a
Self dual Yes
Analytic conductor 48.110
Analytic rank 0
Dimension 25
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: \(0\)
Dimension: \(25\)
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.

\(\operatorname{Tr}(f)(q) = \) \(25q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 36q^{4} \) \(\mathstrut +\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 36q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(25q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 36q^{4} \) \(\mathstrut +\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 36q^{9} \) \(\mathstrut +\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 22q^{12} \) \(\mathstrut -\mathstrut 10q^{13} \) \(\mathstrut +\mathstrut 13q^{14} \) \(\mathstrut +\mathstrut 54q^{16} \) \(\mathstrut -\mathstrut q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 50q^{19} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut -\mathstrut 11q^{22} \) \(\mathstrut +\mathstrut 31q^{23} \) \(\mathstrut +\mathstrut 22q^{24} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut -\mathstrut 42q^{27} \) \(\mathstrut -\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 4q^{29} \) \(\mathstrut +\mathstrut 34q^{31} \) \(\mathstrut +\mathstrut 44q^{32} \) \(\mathstrut -\mathstrut 28q^{33} \) \(\mathstrut +\mathstrut 33q^{34} \) \(\mathstrut +\mathstrut 83q^{36} \) \(\mathstrut -\mathstrut 14q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut +\mathstrut 23q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut -\mathstrut 23q^{42} \) \(\mathstrut -\mathstrut 49q^{43} \) \(\mathstrut +\mathstrut 20q^{44} \) \(\mathstrut +\mathstrut 27q^{46} \) \(\mathstrut +\mathstrut 28q^{47} \) \(\mathstrut -\mathstrut 30q^{48} \) \(\mathstrut +\mathstrut 66q^{49} \) \(\mathstrut +\mathstrut 49q^{51} \) \(\mathstrut -\mathstrut 39q^{52} \) \(\mathstrut +\mathstrut 16q^{53} \) \(\mathstrut +\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 51q^{56} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 8q^{58} \) \(\mathstrut +\mathstrut 30q^{59} \) \(\mathstrut +\mathstrut 35q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 73q^{64} \) \(\mathstrut -\mathstrut 13q^{66} \) \(\mathstrut -\mathstrut 37q^{67} \) \(\mathstrut -\mathstrut 11q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 12q^{71} \) \(\mathstrut +\mathstrut 90q^{72} \) \(\mathstrut -\mathstrut 36q^{73} \) \(\mathstrut -\mathstrut 12q^{74} \) \(\mathstrut +\mathstrut 57q^{76} \) \(\mathstrut +\mathstrut 31q^{77} \) \(\mathstrut +\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 65q^{81} \) \(\mathstrut +\mathstrut 11q^{82} \) \(\mathstrut -\mathstrut 43q^{83} \) \(\mathstrut -\mathstrut 62q^{84} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 20q^{88} \) \(\mathstrut +\mathstrut 38q^{89} \) \(\mathstrut +\mathstrut 86q^{91} \) \(\mathstrut +\mathstrut 119q^{92} \) \(\mathstrut -\mathstrut 10q^{93} \) \(\mathstrut -\mathstrut 18q^{94} \) \(\mathstrut -\mathstrut 34q^{96} \) \(\mathstrut -\mathstrut 17q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.63003 1.40060 4.91705 0 −3.68362 −1.05429 −7.67192 −1.03832 0
1.2 −2.57160 −2.27367 4.61314 0 5.84699 2.96482 −6.71996 2.16959 0
1.3 −2.45442 −2.63869 4.02420 0 6.47646 −2.50490 −4.96823 3.96267 0
1.4 −2.36481 −0.380137 3.59233 0 0.898952 −4.83015 −3.76557 −2.85550 0
1.5 −1.96258 −3.23511 1.85173 0 6.34917 1.21428 0.290989 7.46593 0
1.6 −1.67265 2.12506 0.797742 0 −3.55448 2.13130 2.01095 1.51590 0
1.7 −1.54117 −2.24256 0.375203 0 3.45617 −3.95910 2.50409 2.02910 0
1.8 −1.32584 2.02466 −0.242137 0 −2.68439 −3.04433 2.97272 1.09926 0
1.9 −0.895481 0.415795 −1.19811 0 −0.372337 −2.78281 2.86385 −2.82711 0
1.10 −0.747372 2.67711 −1.44143 0 −2.00080 3.83700 2.57203 4.16691 0
1.11 −0.355815 −0.886461 −1.87340 0 0.315416 4.33523 1.37821 −2.21419 0
1.12 −0.193339 −2.50161 −1.96262 0 0.483659 0.166000 0.766131 3.25804 0
1.13 0.410249 0.0956416 −1.83170 0 0.0392369 2.86768 −1.57195 −2.99085 0
1.14 0.430350 −3.17127 −1.81480 0 −1.36476 −2.65145 −1.64170 7.05698 0
1.15 0.954311 0.726487 −1.08929 0 0.693295 1.92977 −2.94814 −2.47222 0
1.16 1.07842 2.50766 −0.837004 0 2.70432 −4.80516 −3.05949 3.28838 0
1.17 1.27704 −0.753956 −0.369177 0 −0.962829 −3.52652 −3.02553 −2.43155 0
1.18 1.43128 −1.25448 0.0485743 0 −1.79552 2.72576 −2.79304 −1.42627 0
1.19 2.06740 −3.16922 2.27415 0 −6.55204 −3.93807 0.566773 7.04394 0
1.20 2.13812 3.12674 2.57154 0 6.68533 0.919039 1.22201 6.77651 0
See all 25 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.25
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6025))\):

\(T_{2}^{25} - \cdots\)
\(T_{3}^{25} + \cdots\)