Properties

Label 187.2.a.a
Level 187
Weight 2
Character orbit 187.a
Self dual Yes
Analytic conductor 1.493
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 187 = 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 187.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.4932025178\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} - 2q^{4} + 3q^{5} + 2q^{7} - 2q^{9} + O(q^{10}) \) \( q + q^{3} - 2q^{4} + 3q^{5} + 2q^{7} - 2q^{9} + q^{11} - 2q^{12} + 2q^{13} + 3q^{15} + 4q^{16} - q^{17} + 2q^{19} - 6q^{20} + 2q^{21} - 3q^{23} + 4q^{25} - 5q^{27} - 4q^{28} - 6q^{29} - 7q^{31} + q^{33} + 6q^{35} + 4q^{36} - 7q^{37} + 2q^{39} + 12q^{41} - 10q^{43} - 2q^{44} - 6q^{45} + 4q^{48} - 3q^{49} - q^{51} - 4q^{52} + 6q^{53} + 3q^{55} + 2q^{57} - 3q^{59} - 6q^{60} + 8q^{61} - 4q^{63} - 8q^{64} + 6q^{65} - 7q^{67} + 2q^{68} - 3q^{69} - 9q^{71} + 2q^{73} + 4q^{75} - 4q^{76} + 2q^{77} + 8q^{79} + 12q^{80} + q^{81} + 6q^{83} - 4q^{84} - 3q^{85} - 6q^{87} + 15q^{89} + 4q^{91} + 6q^{92} - 7q^{93} + 6q^{95} + 11q^{97} - 2q^{99} + O(q^{100}) \)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
0 1.00000 −2.00000 3.00000 0 2.00000 0 −2.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Atkin-Lehner signs

\( p \) Sign
\(11\) \(-1\)
\(17\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(187))\):

\( T_{2} \)
\( T_{3} - 1 \)