Properties

Label 882.2.a.j
Level $882$
Weight $2$
Character orbit 882.a
Self dual yes
Analytic conductor $7.043$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{4} + 3q^{5} + q^{8} + O(q^{10}) \) \( q + q^{2} + q^{4} + 3q^{5} + q^{8} + 3q^{10} - 3q^{11} + 2q^{13} + q^{16} + 6q^{17} + 2q^{19} + 3q^{20} - 3q^{22} - 6q^{23} + 4q^{25} + 2q^{26} + 9q^{29} - 7q^{31} + q^{32} + 6q^{34} - 10q^{37} + 2q^{38} + 3q^{40} - 4q^{43} - 3q^{44} - 6q^{46} + 12q^{47} + 4q^{50} + 2q^{52} - 3q^{53} - 9q^{55} + 9q^{58} - 3q^{59} - 4q^{61} - 7q^{62} + q^{64} + 6q^{65} + 2q^{67} + 6q^{68} + 2q^{73} - 10q^{74} + 2q^{76} + 5q^{79} + 3q^{80} + 9q^{83} + 18q^{85} - 4q^{86} - 3q^{88} - 6q^{89} - 6q^{92} + 12q^{94} + 6q^{95} - 13q^{97} + O(q^{100}) \)

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 3.00000 0 0 1.00000 0 3.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 882.2.a.j 1
3.b odd 2 1 882.2.a.a 1
4.b odd 2 1 7056.2.a.by 1
7.b odd 2 1 882.2.a.h 1
7.c even 3 2 126.2.g.a 2
7.d odd 6 2 882.2.g.e 2
12.b even 2 1 7056.2.a.e 1
21.c even 2 1 882.2.a.e 1
21.g even 6 2 882.2.g.g 2
21.h odd 6 2 126.2.g.d yes 2
28.d even 2 1 7056.2.a.h 1
28.g odd 6 2 1008.2.s.b 2
63.g even 3 2 1134.2.h.f 2
63.h even 3 2 1134.2.e.k 2
63.j odd 6 2 1134.2.e.g 2
63.n odd 6 2 1134.2.h.j 2
84.h odd 2 1 7056.2.a.bx 1
84.n even 6 2 1008.2.s.o 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
126.2.g.a 2 7.c even 3 2
126.2.g.d yes 2 21.h odd 6 2
882.2.a.a 1 3.b odd 2 1
882.2.a.e 1 21.c even 2 1
882.2.a.h 1 7.b odd 2 1
882.2.a.j 1 1.a even 1 1 trivial
882.2.g.e 2 7.d odd 6 2
882.2.g.g 2 21.g even 6 2
1008.2.s.b 2 28.g odd 6 2
1008.2.s.o 2 84.n even 6 2
1134.2.e.g 2 63.j odd 6 2
1134.2.e.k 2 63.h even 3 2
1134.2.h.f 2 63.g even 3 2
1134.2.h.j 2 63.n odd 6 2
7056.2.a.e 1 12.b even 2 1
7056.2.a.h 1 28.d even 2 1
7056.2.a.bx 1 84.h odd 2 1
7056.2.a.by 1 4.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(882))\):

\( T_{5} - 3 \)
\( T_{11} + 3 \)
\( T_{13} - 2 \)