Properties

Label 2112.2.a.y
Level $2112$
Weight $2$
Character orbit 2112.a
Self dual yes
Analytic conductor $16.864$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2112 = 2^{6} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2112.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(16.8644049069\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 264)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} + 2q^{5} - 4q^{7} + q^{9} + O(q^{10}) \) \( q + q^{3} + 2q^{5} - 4q^{7} + q^{9} - q^{11} - 6q^{13} + 2q^{15} + 6q^{17} - 8q^{19} - 4q^{21} - q^{25} + q^{27} + 6q^{29} - q^{33} - 8q^{35} - 6q^{37} - 6q^{39} - 10q^{41} - 8q^{43} + 2q^{45} + 9q^{49} + 6q^{51} - 6q^{53} - 2q^{55} - 8q^{57} + 4q^{59} + 2q^{61} - 4q^{63} - 12q^{65} - 12q^{67} + 8q^{71} + 2q^{73} - q^{75} + 4q^{77} + 4q^{79} + q^{81} - 12q^{83} + 12q^{85} + 6q^{87} - 6q^{89} + 24q^{91} - 16q^{95} + 2q^{97} - q^{99} + O(q^{100}) \)

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
0 1.00000 0 2.00000 0 −4.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(11\) \(1\)

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 2112.2.a.y 1
3.b odd 2 1 6336.2.a.o 1
4.b odd 2 1 2112.2.a.m 1
8.b even 2 1 528.2.a.b 1
8.d odd 2 1 264.2.a.b 1
12.b even 2 1 6336.2.a.v 1
24.f even 2 1 792.2.a.f 1
24.h odd 2 1 1584.2.a.n 1
40.e odd 2 1 6600.2.a.a 1
40.k even 4 2 6600.2.d.n 2
88.b odd 2 1 5808.2.a.f 1
88.g even 2 1 2904.2.a.i 1
264.p odd 2 1 8712.2.a.r 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
264.2.a.b 1 8.d odd 2 1
528.2.a.b 1 8.b even 2 1
792.2.a.f 1 24.f even 2 1
1584.2.a.n 1 24.h odd 2 1
2112.2.a.m 1 4.b odd 2 1
2112.2.a.y 1 1.a even 1 1 trivial
2904.2.a.i 1 88.g even 2 1
5808.2.a.f 1 88.b odd 2 1
6336.2.a.o 1 3.b odd 2 1
6336.2.a.v 1 12.b even 2 1
6600.2.a.a 1 40.e odd 2 1
6600.2.d.n 2 40.k even 4 2
8712.2.a.r 1 264.p odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2112))\):

\( T_{5} - 2 \)
\( T_{7} + 4 \)
\( T_{13} + 6 \)
\( T_{17} - 6 \)
\( T_{19} + 8 \)
\( T_{23} \)