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 Inner twists 1

Related objects

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.

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

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 −2.77437 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: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

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.l 40
5.b even 2 1 6025.2.a.o yes 40

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6025.2.a.l 40 1.a even 1 1 trivial
6025.2.a.o yes 40 5.b even 2 1

Atkin-Lehner signs

$$p$$ Sign
$$5$$ $$1$$
$$241$$ $$1$$

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