Properties

Label 35.2.a.a
Level 35
Weight 2
Character orbit 35.a
Self dual Yes
Analytic conductor 0.279
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 35 = 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 35.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.279476407074\)
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

\(f(q)\) \(=\) \( q + q^{3} - 2q^{4} - q^{5} + q^{7} - 2q^{9} + O(q^{10}) \) \( q + q^{3} - 2q^{4} - q^{5} + q^{7} - 2q^{9} - 3q^{11} - 2q^{12} + 5q^{13} - q^{15} + 4q^{16} + 3q^{17} + 2q^{19} + 2q^{20} + q^{21} - 6q^{23} + q^{25} - 5q^{27} - 2q^{28} + 3q^{29} - 4q^{31} - 3q^{33} - q^{35} + 4q^{36} + 2q^{37} + 5q^{39} - 12q^{41} - 10q^{43} + 6q^{44} + 2q^{45} + 9q^{47} + 4q^{48} + q^{49} + 3q^{51} - 10q^{52} + 12q^{53} + 3q^{55} + 2q^{57} + 2q^{60} + 8q^{61} - 2q^{63} - 8q^{64} - 5q^{65} - 4q^{67} - 6q^{68} - 6q^{69} + 2q^{73} + q^{75} - 4q^{76} - 3q^{77} - q^{79} - 4q^{80} + q^{81} + 12q^{83} - 2q^{84} - 3q^{85} + 3q^{87} - 12q^{89} + 5q^{91} + 12q^{92} - 4q^{93} - 2q^{95} - q^{97} + 6q^{99} + O(q^{100}) \)

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 −1.00000 0 1.00000 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
\(5\) \(1\)
\(7\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{2} \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(35))\).