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

Downloads

Learn more about

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: \( 1 \)
Twist minimal: yes
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.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 35.2.a.a 1
3.b odd 2 1 315.2.a.b 1
4.b odd 2 1 560.2.a.b 1
5.b even 2 1 175.2.a.b 1
5.c odd 4 2 175.2.b.a 2
7.b odd 2 1 245.2.a.c 1
7.c even 3 2 245.2.e.a 2
7.d odd 6 2 245.2.e.b 2
8.b even 2 1 2240.2.a.k 1
8.d odd 2 1 2240.2.a.u 1
11.b odd 2 1 4235.2.a.c 1
12.b even 2 1 5040.2.a.v 1
13.b even 2 1 5915.2.a.f 1
15.d odd 2 1 1575.2.a.f 1
15.e even 4 2 1575.2.d.c 2
20.d odd 2 1 2800.2.a.z 1
20.e even 4 2 2800.2.g.l 2
21.c even 2 1 2205.2.a.e 1
28.d even 2 1 3920.2.a.ba 1
35.c odd 2 1 1225.2.a.e 1
35.f even 4 2 1225.2.b.d 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
35.2.a.a 1 1.a even 1 1 trivial
175.2.a.b 1 5.b even 2 1
175.2.b.a 2 5.c odd 4 2
245.2.a.c 1 7.b odd 2 1
245.2.e.a 2 7.c even 3 2
245.2.e.b 2 7.d odd 6 2
315.2.a.b 1 3.b odd 2 1
560.2.a.b 1 4.b odd 2 1
1225.2.a.e 1 35.c odd 2 1
1225.2.b.d 2 35.f even 4 2
1575.2.a.f 1 15.d odd 2 1
1575.2.d.c 2 15.e even 4 2
2205.2.a.e 1 21.c even 2 1
2240.2.a.k 1 8.b even 2 1
2240.2.a.u 1 8.d odd 2 1
2800.2.a.z 1 20.d odd 2 1
2800.2.g.l 2 20.e even 4 2
3920.2.a.ba 1 28.d even 2 1
4235.2.a.c 1 11.b odd 2 1
5040.2.a.v 1 12.b even 2 1
5915.2.a.f 1 13.b even 2 1

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)
\(7\) \(-1\)

Hecke kernels

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