Properties

Label 4410.2.a.d
Level $4410$
Weight $2$
Character orbit 4410.a
Self dual yes
Analytic conductor $35.214$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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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: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{5} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 2q^{11} + 2q^{13} + q^{16} - 2q^{17} + 6q^{19} - q^{20} + 2q^{22} + 4q^{23} + q^{25} - 2q^{26} - 2q^{31} - q^{32} + 2q^{34} + 2q^{37} - 6q^{38} + q^{40} - 10q^{41} - 8q^{43} - 2q^{44} - 4q^{46} + 8q^{47} - q^{50} + 2q^{52} + 2q^{53} + 2q^{55} - 4q^{59} + 8q^{61} + 2q^{62} + q^{64} - 2q^{65} - 4q^{67} - 2q^{68} - 6q^{71} - 2q^{73} - 2q^{74} + 6q^{76} - 8q^{79} - q^{80} + 10q^{82} - 4q^{83} + 2q^{85} + 8q^{86} + 2q^{88} + 10q^{89} + 4q^{92} - 8q^{94} - 6q^{95} + 18q^{97} + O(q^{100}) \)

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.d 1
3.b odd 2 1 4410.2.a.bk yes 1
7.b odd 2 1 4410.2.a.o yes 1
21.c even 2 1 4410.2.a.bb yes 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4410.2.a.d 1 1.a even 1 1 trivial
4410.2.a.o yes 1 7.b odd 2 1
4410.2.a.bb yes 1 21.c even 2 1
4410.2.a.bk yes 1 3.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4410))\):

\( T_{11} + 2 \)
\( T_{13} - 2 \)
\( T_{17} + 2 \)
\( T_{19} - 6 \)
\( T_{29} \)
\( T_{31} + 2 \)