Properties

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

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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 1470)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{5} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 2q^{11} + 2q^{13} + q^{16} + 4q^{17} - q^{20} + 2q^{22} - 8q^{23} + q^{25} - 2q^{26} - 2q^{31} - q^{32} - 4q^{34} + 8q^{37} + q^{40} + 2q^{41} - 2q^{43} - 2q^{44} + 8q^{46} - 10q^{47} - q^{50} + 2q^{52} + 2q^{53} + 2q^{55} - 4q^{59} - 10q^{61} + 2q^{62} + q^{64} - 2q^{65} + 2q^{67} + 4q^{68} + 12q^{71} + 10q^{73} - 8q^{74} + 16q^{79} - q^{80} - 2q^{82} - 16q^{83} - 4q^{85} + 2q^{86} + 2q^{88} - 14q^{89} - 8q^{92} + 10q^{94} + 6q^{97} + O(q^{100}) \)

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.e 1
3.b odd 2 1 1470.2.a.n 1
7.b odd 2 1 4410.2.a.n 1
15.d odd 2 1 7350.2.a.bh 1
21.c even 2 1 1470.2.a.p yes 1
21.g even 6 2 1470.2.i.c 2
21.h odd 6 2 1470.2.i.g 2
105.g even 2 1 7350.2.a.o 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1470.2.a.n 1 3.b odd 2 1
1470.2.a.p yes 1 21.c even 2 1
1470.2.i.c 2 21.g even 6 2
1470.2.i.g 2 21.h odd 6 2
4410.2.a.e 1 1.a even 1 1 trivial
4410.2.a.n 1 7.b odd 2 1
7350.2.a.o 1 105.g even 2 1
7350.2.a.bh 1 15.d odd 2 1

Hecke kernels

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

\( T_{11} + 2 \)
\( T_{13} - 2 \)
\( T_{17} - 4 \)
\( T_{19} \)
\( T_{29} \)
\( T_{31} + 2 \)