Properties

Label 102.2.a.c
Level 102
Weight 2
Character orbit 102.a
Self dual Yes
Analytic conductor 0.814
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 102 = 2 \cdot 3 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 102.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.814474100617\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} - 2q^{5} + q^{6} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} + q^{4} - 2q^{5} + q^{6} + q^{8} + q^{9} - 2q^{10} - 4q^{11} + q^{12} - 2q^{13} - 2q^{15} + q^{16} + q^{17} + q^{18} + 4q^{19} - 2q^{20} - 4q^{22} + q^{24} - q^{25} - 2q^{26} + q^{27} - 10q^{29} - 2q^{30} + 8q^{31} + q^{32} - 4q^{33} + q^{34} + q^{36} - 2q^{37} + 4q^{38} - 2q^{39} - 2q^{40} + 10q^{41} + 12q^{43} - 4q^{44} - 2q^{45} + q^{48} - 7q^{49} - q^{50} + q^{51} - 2q^{52} + 6q^{53} + q^{54} + 8q^{55} + 4q^{57} - 10q^{58} + 12q^{59} - 2q^{60} - 10q^{61} + 8q^{62} + q^{64} + 4q^{65} - 4q^{66} - 12q^{67} + q^{68} + q^{72} + 10q^{73} - 2q^{74} - q^{75} + 4q^{76} - 2q^{78} - 8q^{79} - 2q^{80} + q^{81} + 10q^{82} + 4q^{83} - 2q^{85} + 12q^{86} - 10q^{87} - 4q^{88} - 6q^{89} - 2q^{90} + 8q^{93} - 8q^{95} + q^{96} - 14q^{97} - 7q^{98} - 4q^{99} + O(q^{100}) \)

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
1.00000 1.00000 1.00000 −2.00000 1.00000 0 1.00000 1.00000 −2.00000
\(n\): 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
\(2\) \(-1\)
\(3\) \(-1\)
\(17\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{5} + 2 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(102))\).