Properties

Label 187.2.a.b
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

Related objects

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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

\(f(q)\) \(=\) \( q + 2q^{2} + 2q^{4} + 4q^{5} - 5q^{7} - 3q^{9} + O(q^{10}) \) \( q + 2q^{2} + 2q^{4} + 4q^{5} - 5q^{7} - 3q^{9} + 8q^{10} - q^{11} + 4q^{13} - 10q^{14} - 4q^{16} + q^{17} - 6q^{18} + 2q^{19} + 8q^{20} - 2q^{22} - 2q^{23} + 11q^{25} + 8q^{26} - 10q^{28} - 3q^{29} + 4q^{31} - 8q^{32} + 2q^{34} - 20q^{35} - 6q^{36} - 2q^{37} + 4q^{38} - 3q^{41} - 2q^{43} - 2q^{44} - 12q^{45} - 4q^{46} + 3q^{47} + 18q^{49} + 22q^{50} + 8q^{52} + 9q^{53} - 4q^{55} - 6q^{58} - 3q^{59} - 10q^{61} + 8q^{62} + 15q^{63} - 8q^{64} + 16q^{65} + 7q^{67} + 2q^{68} - 40q^{70} + 2q^{71} - 3q^{73} - 4q^{74} + 4q^{76} + 5q^{77} - 16q^{80} + 9q^{81} - 6q^{82} + 14q^{83} + 4q^{85} - 4q^{86} + q^{89} - 24q^{90} - 20q^{91} - 4q^{92} + 6q^{94} + 8q^{95} - 10q^{97} + 36q^{98} + 3q^{99} + O(q^{100}) \)

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
2.00000 0 2.00000 4.00000 0 −5.00000 0 −3.00000 8.00000
\(n\): 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(187))\):

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