Properties

Label 4704.2.a.v
Level $4704$
Weight $2$
Character orbit 4704.a
Self dual yes
Analytic conductor $37.562$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4704 = 2^{5} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4704.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.5616291108\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 672)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} - 2q^{5} + q^{9} + O(q^{10}) \) \( q + q^{3} - 2q^{5} + q^{9} - 2q^{13} - 2q^{15} - 2q^{17} - 4q^{19} - q^{25} + q^{27} + 6q^{29} + 6q^{37} - 2q^{39} + 6q^{41} + 8q^{43} - 2q^{45} - 8q^{47} - 2q^{51} + 6q^{53} - 4q^{57} + 12q^{59} - 10q^{61} + 4q^{65} + 16q^{67} - 8q^{71} + 6q^{73} - q^{75} + 8q^{79} + q^{81} + 12q^{83} + 4q^{85} + 6q^{87} + 14q^{89} + 8q^{95} + 6q^{97} + O(q^{100}) \)

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
0 1.00000 0 −2.00000 0 0 0 1.00000 0
\(n\): 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 4704.2.a.v 1
4.b odd 2 1 4704.2.a.c 1
7.b odd 2 1 672.2.a.d 1
8.b even 2 1 9408.2.a.bd 1
8.d odd 2 1 9408.2.a.cz 1
21.c even 2 1 2016.2.a.a 1
28.d even 2 1 672.2.a.h yes 1
56.e even 2 1 1344.2.a.d 1
56.h odd 2 1 1344.2.a.l 1
84.h odd 2 1 2016.2.a.b 1
112.j even 4 2 5376.2.c.o 2
112.l odd 4 2 5376.2.c.u 2
168.e odd 2 1 4032.2.a.bi 1
168.i even 2 1 4032.2.a.bd 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
672.2.a.d 1 7.b odd 2 1
672.2.a.h yes 1 28.d even 2 1
1344.2.a.d 1 56.e even 2 1
1344.2.a.l 1 56.h odd 2 1
2016.2.a.a 1 21.c even 2 1
2016.2.a.b 1 84.h odd 2 1
4032.2.a.bd 1 168.i even 2 1
4032.2.a.bi 1 168.e odd 2 1
4704.2.a.c 1 4.b odd 2 1
4704.2.a.v 1 1.a even 1 1 trivial
5376.2.c.o 2 112.j even 4 2
5376.2.c.u 2 112.l odd 4 2
9408.2.a.bd 1 8.b even 2 1
9408.2.a.cz 1 8.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4704))\):

\( T_{5} + 2 \)
\( T_{11} \)
\( T_{13} + 2 \)
\( T_{19} + 4 \)
\( T_{31} \)