Properties

Label 210.2.a.c
Level 210
Weight 2
Character orbit 210.a
Self dual Yes
Analytic conductor 1.677
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 210.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.67685844245\)
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

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{7} + q^{8} + q^{9} + q^{10} + 4q^{11} - q^{12} - 2q^{13} + q^{14} - q^{15} + q^{16} + 2q^{17} + q^{18} - 4q^{19} + q^{20} - q^{21} + 4q^{22} - 8q^{23} - q^{24} + q^{25} - 2q^{26} - q^{27} + q^{28} + 6q^{29} - q^{30} - 8q^{31} + q^{32} - 4q^{33} + 2q^{34} + q^{35} + q^{36} - 2q^{37} - 4q^{38} + 2q^{39} + q^{40} + 2q^{41} - q^{42} - 12q^{43} + 4q^{44} + q^{45} - 8q^{46} - 8q^{47} - q^{48} + q^{49} + q^{50} - 2q^{51} - 2q^{52} + 6q^{53} - q^{54} + 4q^{55} + q^{56} + 4q^{57} + 6q^{58} + 4q^{59} - q^{60} - 2q^{61} - 8q^{62} + q^{63} + q^{64} - 2q^{65} - 4q^{66} + 12q^{67} + 2q^{68} + 8q^{69} + q^{70} + 8q^{71} + q^{72} - 14q^{73} - 2q^{74} - q^{75} - 4q^{76} + 4q^{77} + 2q^{78} + q^{80} + q^{81} + 2q^{82} + 12q^{83} - q^{84} + 2q^{85} - 12q^{86} - 6q^{87} + 4q^{88} + 2q^{89} + q^{90} - 2q^{91} - 8q^{92} + 8q^{93} - 8q^{94} - 4q^{95} - q^{96} + 10q^{97} + q^{98} + 4q^{99} + O(q^{100}) \)

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 1.00000 −1.00000 1.00000 1.00000 1.00000 1.00000
\(n\): 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
\(2\) \(-1\)
\(3\) \(1\)
\(5\) \(-1\)
\(7\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(210))\):

\( T_{11} - 4 \)
\( T_{17} - 2 \)
\( T_{19} + 4 \)