Properties

Label 6010.2.a.j
Level 6010
Weight 2
Character orbit 6010.a
Self dual Yes
Analytic conductor 47.990
Analytic rank 0
Dimension 33
CM No

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Newspace parameters

Level: \( N \) = \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9900916148\)
Analytic rank: \(0\)
Dimension: \(33\)
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.

\(\operatorname{Tr}(f)(q) = \) \(33q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 33q^{4} \) \(\mathstrut +\mathstrut 33q^{5} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 49q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(33q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 33q^{4} \) \(\mathstrut +\mathstrut 33q^{5} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 49q^{9} \) \(\mathstrut +\mathstrut 33q^{10} \) \(\mathstrut +\mathstrut 12q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 20q^{13} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 33q^{16} \) \(\mathstrut +\mathstrut 33q^{17} \) \(\mathstrut +\mathstrut 49q^{18} \) \(\mathstrut +\mathstrut 17q^{19} \) \(\mathstrut +\mathstrut 33q^{20} \) \(\mathstrut +\mathstrut 26q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 7q^{23} \) \(\mathstrut +\mathstrut 6q^{24} \) \(\mathstrut +\mathstrut 33q^{25} \) \(\mathstrut +\mathstrut 20q^{26} \) \(\mathstrut +\mathstrut 21q^{27} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut +\mathstrut 35q^{31} \) \(\mathstrut +\mathstrut 33q^{32} \) \(\mathstrut +\mathstrut 25q^{33} \) \(\mathstrut +\mathstrut 33q^{34} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 49q^{36} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 17q^{38} \) \(\mathstrut +\mathstrut 22q^{39} \) \(\mathstrut +\mathstrut 33q^{40} \) \(\mathstrut +\mathstrut 39q^{41} \) \(\mathstrut +\mathstrut 26q^{42} \) \(\mathstrut -\mathstrut 3q^{43} \) \(\mathstrut +\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 49q^{45} \) \(\mathstrut +\mathstrut 7q^{46} \) \(\mathstrut +\mathstrut 19q^{47} \) \(\mathstrut +\mathstrut 6q^{48} \) \(\mathstrut +\mathstrut 69q^{49} \) \(\mathstrut +\mathstrut 33q^{50} \) \(\mathstrut +\mathstrut 21q^{51} \) \(\mathstrut +\mathstrut 20q^{52} \) \(\mathstrut +\mathstrut 41q^{53} \) \(\mathstrut +\mathstrut 21q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 4q^{56} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 30q^{61} \) \(\mathstrut +\mathstrut 35q^{62} \) \(\mathstrut -\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut 33q^{64} \) \(\mathstrut +\mathstrut 20q^{65} \) \(\mathstrut +\mathstrut 25q^{66} \) \(\mathstrut -\mathstrut 9q^{67} \) \(\mathstrut +\mathstrut 33q^{68} \) \(\mathstrut +\mathstrut 23q^{69} \) \(\mathstrut +\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 36q^{71} \) \(\mathstrut +\mathstrut 49q^{72} \) \(\mathstrut +\mathstrut 35q^{73} \) \(\mathstrut +\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 6q^{75} \) \(\mathstrut +\mathstrut 17q^{76} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut +\mathstrut 22q^{78} \) \(\mathstrut +\mathstrut 32q^{79} \) \(\mathstrut +\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 53q^{81} \) \(\mathstrut +\mathstrut 39q^{82} \) \(\mathstrut +\mathstrut 24q^{83} \) \(\mathstrut +\mathstrut 26q^{84} \) \(\mathstrut +\mathstrut 33q^{85} \) \(\mathstrut -\mathstrut 3q^{86} \) \(\mathstrut +\mathstrut 12q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 40q^{89} \) \(\mathstrut +\mathstrut 49q^{90} \) \(\mathstrut +\mathstrut 5q^{91} \) \(\mathstrut +\mathstrut 7q^{92} \) \(\mathstrut +\mathstrut 18q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 17q^{95} \) \(\mathstrut +\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut +\mathstrut 69q^{98} \) \(\mathstrut +\mathstrut 3q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 1.00000 −3.20038 1.00000 1.00000 −3.20038 −3.69470 1.00000 7.24241 1.00000
1.2 1.00000 −3.13566 1.00000 1.00000 −3.13566 3.51903 1.00000 6.83234 1.00000
1.3 1.00000 −2.97405 1.00000 1.00000 −2.97405 −4.80622 1.00000 5.84500 1.00000
1.4 1.00000 −2.94052 1.00000 1.00000 −2.94052 1.02542 1.00000 5.64669 1.00000
1.5 1.00000 −2.70935 1.00000 1.00000 −2.70935 2.38883 1.00000 4.34059 1.00000
1.6 1.00000 −2.12592 1.00000 1.00000 −2.12592 −2.80754 1.00000 1.51952 1.00000
1.7 1.00000 −1.86907 1.00000 1.00000 −1.86907 −0.450739 1.00000 0.493433 1.00000
1.8 1.00000 −1.57998 1.00000 1.00000 −1.57998 −4.21564 1.00000 −0.503648 1.00000
1.9 1.00000 −1.55579 1.00000 1.00000 −1.55579 2.74607 1.00000 −0.579528 1.00000
1.10 1.00000 −1.52452 1.00000 1.00000 −1.52452 3.34647 1.00000 −0.675836 1.00000
1.11 1.00000 −1.48456 1.00000 1.00000 −1.48456 −3.64737 1.00000 −0.796082 1.00000
1.12 1.00000 −0.800428 1.00000 1.00000 −0.800428 2.44913 1.00000 −2.35931 1.00000
1.13 1.00000 −0.635616 1.00000 1.00000 −0.635616 −1.32070 1.00000 −2.59599 1.00000
1.14 1.00000 −0.552487 1.00000 1.00000 −0.552487 2.28822 1.00000 −2.69476 1.00000
1.15 1.00000 −0.489009 1.00000 1.00000 −0.489009 −2.03673 1.00000 −2.76087 1.00000
1.16 1.00000 −0.361555 1.00000 1.00000 −0.361555 4.32690 1.00000 −2.86928 1.00000
1.17 1.00000 0.162499 1.00000 1.00000 0.162499 −4.01770 1.00000 −2.97359 1.00000
1.18 1.00000 0.351716 1.00000 1.00000 0.351716 −0.0941576 1.00000 −2.87630 1.00000
1.19 1.00000 0.649976 1.00000 1.00000 0.649976 1.95740 1.00000 −2.57753 1.00000
1.20 1.00000 0.828443 1.00000 1.00000 0.828443 4.24055 1.00000 −2.31368 1.00000
See all 33 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.33
Significant digits:
Format:

Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(-1\)
\(601\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{3}^{33} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6010))\).