Properties

Label 6025.2.a.o
Level 6025
Weight 2
Character orbit 6025.a
Self dual Yes
Analytic conductor 48.110
Analytic rank 0
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: \(0\)
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 −2.56709 −0.178555 4.58996 0 0.458367 0.233097 −6.64865 −2.96812 0
1.2 −2.41430 3.26436 3.82885 0 −7.88114 1.16921 −4.41538 7.65603 0
1.3 −2.30206 0.621403 3.29948 0 −1.43051 0.210935 −2.99147 −2.61386 0
1.4 −2.25059 −0.826129 3.06516 0 1.85928 0.537315 −2.39723 −2.31751 0
1.5 −2.24247 −1.80227 3.02866 0 4.04153 5.11796 −2.30673 0.248182 0
1.6 −2.06849 2.17142 2.27866 0 −4.49155 2.39120 −0.576402 1.71504 0
1.7 −1.77260 −0.796316 1.14211 0 1.41155 −3.30701 1.52069 −2.36588 0
1.8 −1.44334 −2.75896 0.0832441 0 3.98213 1.64702 2.76654 4.61187 0
1.9 −1.43804 0.465580 0.0679498 0 −0.669521 1.05447 2.77836 −2.78324 0
1.10 −1.38463 −1.64656 −0.0828005 0 2.27988 −2.06195 2.88391 −0.288826 0
1.11 −1.33622 1.40541 −0.214528 0 −1.87793 −0.850787 2.95909 −1.02483 0
1.12 −0.859912 1.32501 −1.26055 0 −1.13939 0.529848 2.80379 −1.24436 0
1.13 −0.810170 2.88822 −1.34362 0 −2.33995 3.73380 2.70891 5.34179 0
1.14 −0.625313 0.793037 −1.60898 0 −0.495897 −2.86756 2.25675 −2.37109 0
1.15 −0.607027 −2.70729 −1.63152 0 1.64340 4.13328 2.20443 4.32942 0
1.16 −0.568441 −1.77259 −1.67687 0 1.00761 −2.89075 2.09009 0.142065 0
1.17 −0.447066 2.52995 −1.80013 0 −1.13106 −3.76816 1.69891 3.40066 0
1.18 −0.410308 1.14046 −1.83165 0 −0.467941 3.98049 1.57216 −1.69935 0
1.19 0.232950 1.45187 −1.94573 0 0.338212 −4.96346 −0.919157 −0.892086 0
1.20 0.394755 2.83806 −1.84417 0 1.12034 −0.914717 −1.51750 5.05456 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6025))\):

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