# Properties

 Label 6025.2.a.j Level $6025$ Weight $2$ Character orbit 6025.a Self dual yes Analytic conductor $48.110$ Analytic rank $1$ 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: $$1$$ 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.

 $$\operatorname{Tr}(f)(q) =$$ $$25q - 6q^{2} - 15q^{3} + 32q^{4} - q^{6} - 19q^{7} - 15q^{8} + 32q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$25q - 6q^{2} - 15q^{3} + 32q^{4} - q^{6} - 19q^{7} - 15q^{8} + 32q^{9} + 2q^{11} - 20q^{12} - 14q^{13} - 5q^{14} + 38q^{16} - 7q^{17} - 9q^{18} + 30q^{19} + q^{21} - q^{22} - 43q^{23} - 6q^{24} - 22q^{26} - 42q^{27} - 32q^{28} - 4q^{29} + 14q^{31} - 26q^{32} - 4q^{33} + 7q^{34} + 15q^{36} - 16q^{37} - 14q^{38} - 21q^{39} - q^{41} + 25q^{42} - 35q^{43} - 52q^{44} - 27q^{46} - 50q^{47} - 26q^{48} + 46q^{49} - 7q^{51} - 3q^{52} - 4q^{53} - 31q^{54} - 51q^{56} - 2q^{58} + 6q^{59} + 19q^{61} - 28q^{63} + 49q^{64} - 27q^{66} - 65q^{67} + 25q^{68} + 2q^{69} - 34q^{71} + 10q^{72} - 8q^{73} - 42q^{74} + 71q^{76} - q^{77} + 59q^{78} - 12q^{79} + 29q^{81} - 11q^{82} - 41q^{83} - 10q^{84} - 13q^{86} - 40q^{87} + 52q^{88} - 24q^{89} + 46q^{91} - 85q^{92} + 30q^{93} + 14q^{94} - 30q^{96} - 9q^{97} + 64q^{98} + 2q^{99} + O(q^{100})$$

## 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 −2.77603 −0.0161258 5.70635 0 0.0447656 −4.43454 −10.2889 −2.99974 0
1.2 −2.68235 −1.41400 5.19500 0 3.79283 3.05254 −8.57011 −1.00061 0
1.3 −2.52189 2.20014 4.35995 0 −5.54852 1.38484 −5.95156 1.84062 0
1.4 −2.43298 −3.08500 3.91941 0 7.50575 2.29332 −4.66990 6.51721 0
1.5 −2.31949 −0.405385 3.38004 0 0.940288 −1.18682 −3.20098 −2.83566 0
1.6 −2.03980 3.04377 2.16080 0 −6.20869 −3.73609 −0.327997 6.26453 0
1.7 −1.96718 −2.44636 1.86979 0 4.81242 −2.28114 0.256155 2.98466 0
1.8 −1.91059 −2.10440 1.65034 0 4.02063 −2.16427 0.668063 1.42849 0
1.9 −1.31571 0.792486 −0.268903 0 −1.04268 1.49796 2.98522 −2.37197 0
1.10 −1.05446 −2.79403 −0.888118 0 2.94619 1.63707 3.04540 4.80663 0
1.11 −0.782724 1.54504 −1.38734 0 −1.20934 2.90223 2.65136 −0.612841 0
1.12 −0.707449 −1.14949 −1.49952 0 0.813204 −1.94091 2.47573 −1.67868 0
1.13 −0.362712 −3.41577 −1.86844 0 1.23894 −3.34046 1.40313 8.66752 0
1.14 −0.300307 −0.482693 −1.90982 0 0.144956 −5.09571 1.17415 −2.76701 0
1.15 0.0694400 2.28670 −1.99518 0 0.158789 −0.976003 −0.277425 2.22902 0
1.16 0.566303 0.484852 −1.67930 0 0.274573 0.0113879 −2.08360 −2.76492 0
1.17 1.11717 −3.26371 −0.751931 0 −3.64612 3.89846 −3.07438 7.65181 0
1.18 1.16007 −2.40515 −0.654229 0 −2.79015 −1.39900 −3.07910 2.78474 0
1.19 1.25748 2.42991 −0.418732 0 3.05557 −3.44014 −3.04152 2.90444 0
1.20 1.58885 −2.11200 0.524458 0 −3.35566 −3.95616 −2.34442 1.46053 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.j 25
5.b even 2 1 1205.2.a.e 25

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1205.2.a.e 25 5.b even 2 1
6025.2.a.j 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 $$S_{2}^{\mathrm{new}}(\Gamma_0(6025))$$:

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