Properties

Label 4410.2.a.c
Level $4410$
Weight $2$
Character orbit 4410.a
Self dual yes
Analytic conductor $35.214$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Newspace parameters

Level: \( N \) \(=\) \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4410.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(35.2140272914\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{5} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 3q^{11} - 5q^{13} + q^{16} + 6q^{17} + q^{19} - q^{20} + 3q^{22} - 3q^{23} + q^{25} + 5q^{26} + 6q^{29} + 4q^{31} - q^{32} - 6q^{34} + 11q^{37} - q^{38} + q^{40} + 3q^{41} - 10q^{43} - 3q^{44} + 3q^{46} + 3q^{47} - q^{50} - 5q^{52} - 3q^{53} + 3q^{55} - 6q^{58} + 4q^{61} - 4q^{62} + q^{64} + 5q^{65} - 4q^{67} + 6q^{68} - 12q^{71} + 4q^{73} - 11q^{74} + q^{76} - 10q^{79} - q^{80} - 3q^{82} - 12q^{83} - 6q^{85} + 10q^{86} + 3q^{88} + 6q^{89} - 3q^{92} - 3q^{94} - q^{95} - 14q^{97} + O(q^{100}) \)

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 0 1.00000 −1.00000 0 0 −1.00000 0 1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(-1\)
\(5\) \(1\)
\(7\) \(-1\)

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 4410.2.a.c 1
3.b odd 2 1 490.2.a.j 1
7.b odd 2 1 4410.2.a.m 1
7.d odd 6 2 630.2.k.e 2
12.b even 2 1 3920.2.a.g 1
15.d odd 2 1 2450.2.a.f 1
15.e even 4 2 2450.2.c.p 2
21.c even 2 1 490.2.a.g 1
21.g even 6 2 70.2.e.b 2
21.h odd 6 2 490.2.e.a 2
84.h odd 2 1 3920.2.a.be 1
84.j odd 6 2 560.2.q.d 2
105.g even 2 1 2450.2.a.p 1
105.k odd 4 2 2450.2.c.f 2
105.p even 6 2 350.2.e.h 2
105.w odd 12 4 350.2.j.a 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
70.2.e.b 2 21.g even 6 2
350.2.e.h 2 105.p even 6 2
350.2.j.a 4 105.w odd 12 4
490.2.a.g 1 21.c even 2 1
490.2.a.j 1 3.b odd 2 1
490.2.e.a 2 21.h odd 6 2
560.2.q.d 2 84.j odd 6 2
630.2.k.e 2 7.d odd 6 2
2450.2.a.f 1 15.d odd 2 1
2450.2.a.p 1 105.g even 2 1
2450.2.c.f 2 105.k odd 4 2
2450.2.c.p 2 15.e even 4 2
3920.2.a.g 1 12.b even 2 1
3920.2.a.be 1 84.h odd 2 1
4410.2.a.c 1 1.a even 1 1 trivial
4410.2.a.m 1 7.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4410))\):

\( T_{11} + 3 \)
\( T_{13} + 5 \)
\( T_{17} - 6 \)
\( T_{19} - 1 \)
\( T_{29} - 6 \)
\( T_{31} - 4 \)