Properties

Label 6010.2.a.i
Level 6010
Weight 2
Character orbit 6010.a
Self dual Yes
Analytic conductor 47.990
Analytic rank 1
Dimension 29
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: \(1\)
Dimension: \(29\)
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.

\(\operatorname{Tr}(f)(q) = \) \(29q \) \(\mathstrut -\mathstrut 29q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 29q^{4} \) \(\mathstrut -\mathstrut 29q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 29q^{8} \) \(\mathstrut +\mathstrut 29q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(29q \) \(\mathstrut -\mathstrut 29q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 29q^{4} \) \(\mathstrut -\mathstrut 29q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 29q^{8} \) \(\mathstrut +\mathstrut 29q^{9} \) \(\mathstrut +\mathstrut 29q^{10} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 29q^{16} \) \(\mathstrut -\mathstrut 23q^{17} \) \(\mathstrut -\mathstrut 29q^{18} \) \(\mathstrut +\mathstrut q^{19} \) \(\mathstrut -\mathstrut 29q^{20} \) \(\mathstrut +\mathstrut 2q^{21} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 29q^{25} \) \(\mathstrut +\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 43q^{27} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut -\mathstrut 29q^{32} \) \(\mathstrut -\mathstrut 19q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 29q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut -\mathstrut q^{38} \) \(\mathstrut +\mathstrut 18q^{39} \) \(\mathstrut +\mathstrut 29q^{40} \) \(\mathstrut -\mathstrut 17q^{41} \) \(\mathstrut -\mathstrut 2q^{42} \) \(\mathstrut -\mathstrut 19q^{43} \) \(\mathstrut -\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 9q^{46} \) \(\mathstrut -\mathstrut 21q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 45q^{49} \) \(\mathstrut -\mathstrut 29q^{50} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 4q^{52} \) \(\mathstrut -\mathstrut 53q^{53} \) \(\mathstrut +\mathstrut 43q^{54} \) \(\mathstrut -\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 5q^{58} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 16q^{61} \) \(\mathstrut -\mathstrut 21q^{62} \) \(\mathstrut -\mathstrut 17q^{63} \) \(\mathstrut +\mathstrut 29q^{64} \) \(\mathstrut +\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 23q^{68} \) \(\mathstrut +\mathstrut 13q^{69} \) \(\mathstrut +\mathstrut 2q^{71} \) \(\mathstrut -\mathstrut 29q^{72} \) \(\mathstrut -\mathstrut q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 10q^{75} \) \(\mathstrut +\mathstrut q^{76} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut -\mathstrut 18q^{78} \) \(\mathstrut +\mathstrut 26q^{79} \) \(\mathstrut -\mathstrut 29q^{80} \) \(\mathstrut +\mathstrut 33q^{81} \) \(\mathstrut +\mathstrut 17q^{82} \) \(\mathstrut -\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 2q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut +\mathstrut 19q^{86} \) \(\mathstrut -\mathstrut 56q^{87} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 29q^{90} \) \(\mathstrut +\mathstrut 27q^{91} \) \(\mathstrut -\mathstrut 9q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 21q^{94} \) \(\mathstrut -\mathstrut q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 15q^{97} \) \(\mathstrut -\mathstrut 45q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.35701 1.00000 −1.00000 3.35701 1.93749 −1.00000 8.26955 1.00000
1.2 −1.00000 −3.28561 1.00000 −1.00000 3.28561 −1.57080 −1.00000 7.79525 1.00000
1.3 −1.00000 −3.13073 1.00000 −1.00000 3.13073 1.27896 −1.00000 6.80148 1.00000
1.4 −1.00000 −3.11389 1.00000 −1.00000 3.11389 −3.05168 −1.00000 6.69634 1.00000
1.5 −1.00000 −2.56402 1.00000 −1.00000 2.56402 3.60827 −1.00000 3.57419 1.00000
1.6 −1.00000 −2.49423 1.00000 −1.00000 2.49423 −3.71754 −1.00000 3.22119 1.00000
1.7 −1.00000 −2.19430 1.00000 −1.00000 2.19430 −4.31508 −1.00000 1.81494 1.00000
1.8 −1.00000 −1.98688 1.00000 −1.00000 1.98688 4.00516 −1.00000 0.947682 1.00000
1.9 −1.00000 −1.83240 1.00000 −1.00000 1.83240 1.88309 −1.00000 0.357691 1.00000
1.10 −1.00000 −1.48145 1.00000 −1.00000 1.48145 4.09967 −1.00000 −0.805307 1.00000
1.11 −1.00000 −1.46035 1.00000 −1.00000 1.46035 −4.07873 −1.00000 −0.867392 1.00000
1.12 −1.00000 −1.21765 1.00000 −1.00000 1.21765 0.502953 −1.00000 −1.51732 1.00000
1.13 −1.00000 −0.796611 1.00000 −1.00000 0.796611 −0.409995 −1.00000 −2.36541 1.00000
1.14 −1.00000 −0.774267 1.00000 −1.00000 0.774267 −0.164549 −1.00000 −2.40051 1.00000
1.15 −1.00000 −0.302339 1.00000 −1.00000 0.302339 2.70786 −1.00000 −2.90859 1.00000
1.16 −1.00000 −0.296108 1.00000 −1.00000 0.296108 −4.13577 −1.00000 −2.91232 1.00000
1.17 −1.00000 −0.0910206 1.00000 −1.00000 0.0910206 3.58336 −1.00000 −2.99172 1.00000
1.18 −1.00000 0.225876 1.00000 −1.00000 −0.225876 −5.00303 −1.00000 −2.94898 1.00000
1.19 −1.00000 0.876968 1.00000 −1.00000 −0.876968 0.528754 −1.00000 −2.23093 1.00000
1.20 −1.00000 0.937103 1.00000 −1.00000 −0.937103 −1.92879 −1.00000 −2.12184 1.00000
See all 29 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.29
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 \(T_{3}^{29} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6010))\).