Properties

Label 63.4.a.b
Level $63$
Weight $4$
Character orbit 63.a
Self dual yes
Analytic conductor $3.717$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(3.71712033036\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 7)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - 7q^{4} - 16q^{5} - 7q^{7} - 15q^{8} + O(q^{10}) \) \( q + q^{2} - 7q^{4} - 16q^{5} - 7q^{7} - 15q^{8} - 16q^{10} + 8q^{11} + 28q^{13} - 7q^{14} + 41q^{16} - 54q^{17} - 110q^{19} + 112q^{20} + 8q^{22} - 48q^{23} + 131q^{25} + 28q^{26} + 49q^{28} + 110q^{29} + 12q^{31} + 161q^{32} - 54q^{34} + 112q^{35} - 246q^{37} - 110q^{38} + 240q^{40} - 182q^{41} + 128q^{43} - 56q^{44} - 48q^{46} - 324q^{47} + 49q^{49} + 131q^{50} - 196q^{52} + 162q^{53} - 128q^{55} + 105q^{56} + 110q^{58} - 810q^{59} - 488q^{61} + 12q^{62} - 167q^{64} - 448q^{65} + 244q^{67} + 378q^{68} + 112q^{70} + 768q^{71} - 702q^{73} - 246q^{74} + 770q^{76} - 56q^{77} + 440q^{79} - 656q^{80} - 182q^{82} + 1302q^{83} + 864q^{85} + 128q^{86} - 120q^{88} - 730q^{89} - 196q^{91} + 336q^{92} - 324q^{94} + 1760q^{95} + 294q^{97} + 49q^{98} + O(q^{100}) \)

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 −7.00000 −16.0000 0 −7.00000 −15.0000 0 −16.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 63.4.a.b 1
3.b odd 2 1 7.4.a.a 1
4.b odd 2 1 1008.4.a.c 1
5.b even 2 1 1575.4.a.e 1
7.b odd 2 1 441.4.a.i 1
7.c even 3 2 441.4.e.h 2
7.d odd 6 2 441.4.e.e 2
12.b even 2 1 112.4.a.f 1
15.d odd 2 1 175.4.a.b 1
15.e even 4 2 175.4.b.b 2
21.c even 2 1 49.4.a.b 1
21.g even 6 2 49.4.c.b 2
21.h odd 6 2 49.4.c.c 2
24.f even 2 1 448.4.a.e 1
24.h odd 2 1 448.4.a.i 1
33.d even 2 1 847.4.a.b 1
39.d odd 2 1 1183.4.a.b 1
51.c odd 2 1 2023.4.a.a 1
84.h odd 2 1 784.4.a.g 1
105.g even 2 1 1225.4.a.j 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
7.4.a.a 1 3.b odd 2 1
49.4.a.b 1 21.c even 2 1
49.4.c.b 2 21.g even 6 2
49.4.c.c 2 21.h odd 6 2
63.4.a.b 1 1.a even 1 1 trivial
112.4.a.f 1 12.b even 2 1
175.4.a.b 1 15.d odd 2 1
175.4.b.b 2 15.e even 4 2
441.4.a.i 1 7.b odd 2 1
441.4.e.e 2 7.d odd 6 2
441.4.e.h 2 7.c even 3 2
448.4.a.e 1 24.f even 2 1
448.4.a.i 1 24.h odd 2 1
784.4.a.g 1 84.h odd 2 1
847.4.a.b 1 33.d even 2 1
1008.4.a.c 1 4.b odd 2 1
1183.4.a.b 1 39.d odd 2 1
1225.4.a.j 1 105.g even 2 1
1575.4.a.e 1 5.b even 2 1
2023.4.a.a 1 51.c odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 1 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(63))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( T \)
$5$ \( 16 + T \)
$7$ \( 7 + T \)
$11$ \( -8 + T \)
$13$ \( -28 + T \)
$17$ \( 54 + T \)
$19$ \( 110 + T \)
$23$ \( 48 + T \)
$29$ \( -110 + T \)
$31$ \( -12 + T \)
$37$ \( 246 + T \)
$41$ \( 182 + T \)
$43$ \( -128 + T \)
$47$ \( 324 + T \)
$53$ \( -162 + T \)
$59$ \( 810 + T \)
$61$ \( 488 + T \)
$67$ \( -244 + T \)
$71$ \( -768 + T \)
$73$ \( 702 + T \)
$79$ \( -440 + T \)
$83$ \( -1302 + T \)
$89$ \( 730 + T \)
$97$ \( -294 + T \)
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