Properties

Label 4410.2.a.a
Level $4410$
Weight $2$
Character orbit 4410.a
Self dual yes
Analytic conductor $35.214$
Analytic rank $0$
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: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 630)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{5} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 4q^{11} - 6q^{13} + q^{16} - 4q^{17} - 6q^{19} - q^{20} + 4q^{22} + q^{25} + 6q^{26} - 6q^{29} + 4q^{31} - q^{32} + 4q^{34} + 8q^{37} + 6q^{38} + q^{40} - 10q^{41} - 2q^{43} - 4q^{44} - 10q^{47} - q^{50} - 6q^{52} + 14q^{53} + 4q^{55} + 6q^{58} + 4q^{59} + 8q^{61} - 4q^{62} + q^{64} + 6q^{65} + 6q^{67} - 4q^{68} - 2q^{71} + 10q^{73} - 8q^{74} - 6q^{76} + 16q^{79} - q^{80} + 10q^{82} + 8q^{83} + 4q^{85} + 2q^{86} + 4q^{88} - 2q^{89} + 10q^{94} + 6q^{95} - 2q^{97} + O(q^{100}) \)

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.a 1
3.b odd 2 1 4410.2.a.bl 1
7.b odd 2 1 630.2.a.e 1
21.c even 2 1 630.2.a.g yes 1
28.d even 2 1 5040.2.a.bp 1
35.c odd 2 1 3150.2.a.bh 1
35.f even 4 2 3150.2.g.b 2
84.h odd 2 1 5040.2.a.n 1
105.g even 2 1 3150.2.a.s 1
105.k odd 4 2 3150.2.g.s 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
630.2.a.e 1 7.b odd 2 1
630.2.a.g yes 1 21.c even 2 1
3150.2.a.s 1 105.g even 2 1
3150.2.a.bh 1 35.c odd 2 1
3150.2.g.b 2 35.f even 4 2
3150.2.g.s 2 105.k odd 4 2
4410.2.a.a 1 1.a even 1 1 trivial
4410.2.a.bl 1 3.b odd 2 1
5040.2.a.n 1 84.h odd 2 1
5040.2.a.bp 1 28.d even 2 1

Hecke kernels

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

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