# 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 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: $$0$$ Dimension: $$25$$ Twist minimal: no (minimal twist has level 1205) 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.

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

## 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 −2.63003 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: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## 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.k 25
5.b even 2 1 1205.2.a.d 25

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1205.2.a.d 25 5.b even 2 1
6025.2.a.k 25 1.a even 1 1 trivial

## Hecke kernels

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

 $$T_{2}^{25} - \cdots$$ $$T_{3}^{25} + \cdots$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database