Properties

Label 5054.2.a.c
Level $5054$
Weight $2$
Character orbit 5054.a
Self dual yes
Analytic conductor $40.356$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5054.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(40.3563931816\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} + q^{7} + q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} + q^{7} + q^{8} + q^{9} + 2 q^{12} + 4 q^{13} + q^{14} + q^{16} + 6 q^{17} + q^{18} + 2 q^{21} + 2 q^{24} - 5 q^{25} + 4 q^{26} - 4 q^{27} + q^{28} + 6 q^{29} + 4 q^{31} + q^{32} + 6 q^{34} + q^{36} - 2 q^{37} + 8 q^{39} - 6 q^{41} + 2 q^{42} + 8 q^{43} - 12 q^{47} + 2 q^{48} + q^{49} - 5 q^{50} + 12 q^{51} + 4 q^{52} - 6 q^{53} - 4 q^{54} + q^{56} + 6 q^{58} + 6 q^{59} + 8 q^{61} + 4 q^{62} + q^{63} + q^{64} + 4 q^{67} + 6 q^{68} + q^{72} + 2 q^{73} - 2 q^{74} - 10 q^{75} + 8 q^{78} - 8 q^{79} - 11 q^{81} - 6 q^{82} - 6 q^{83} + 2 q^{84} + 8 q^{86} + 12 q^{87} + 6 q^{89} + 4 q^{91} + 8 q^{93} - 12 q^{94} + 2 q^{96} + 10 q^{97} + q^{98}+O(q^{100}) \) Copy content Toggle raw display

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(7\) \(-1\)
\(19\) \(-1\)

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 5054.2.a.c 1
19.b odd 2 1 14.2.a.a 1
57.d even 2 1 126.2.a.b 1
76.d even 2 1 112.2.a.c 1
95.d odd 2 1 350.2.a.f 1
95.g even 4 2 350.2.c.d 2
133.c even 2 1 98.2.a.a 1
133.o even 6 2 98.2.c.a 2
133.r odd 6 2 98.2.c.b 2
152.b even 2 1 448.2.a.a 1
152.g odd 2 1 448.2.a.g 1
171.l even 6 2 1134.2.f.f 2
171.o odd 6 2 1134.2.f.l 2
209.d even 2 1 1694.2.a.e 1
228.b odd 2 1 1008.2.a.h 1
247.d odd 2 1 2366.2.a.j 1
247.i even 4 2 2366.2.d.b 2
285.b even 2 1 3150.2.a.i 1
285.j odd 4 2 3150.2.g.j 2
304.j odd 4 2 1792.2.b.c 2
304.m even 4 2 1792.2.b.g 2
323.c odd 2 1 4046.2.a.f 1
380.d even 2 1 2800.2.a.g 1
380.j odd 4 2 2800.2.g.h 2
399.h odd 2 1 882.2.a.i 1
399.s odd 6 2 882.2.g.d 2
399.w even 6 2 882.2.g.c 2
437.b even 2 1 7406.2.a.a 1
456.l odd 2 1 4032.2.a.r 1
456.p even 2 1 4032.2.a.w 1
532.b odd 2 1 784.2.a.b 1
532.t even 6 2 784.2.i.c 2
532.bh odd 6 2 784.2.i.i 2
665.g even 2 1 2450.2.a.t 1
665.n odd 4 2 2450.2.c.c 2
1064.f even 2 1 3136.2.a.e 1
1064.p odd 2 1 3136.2.a.z 1
1596.p even 2 1 7056.2.a.bd 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
14.2.a.a 1 19.b odd 2 1
98.2.a.a 1 133.c even 2 1
98.2.c.a 2 133.o even 6 2
98.2.c.b 2 133.r odd 6 2
112.2.a.c 1 76.d even 2 1
126.2.a.b 1 57.d even 2 1
350.2.a.f 1 95.d odd 2 1
350.2.c.d 2 95.g even 4 2
448.2.a.a 1 152.b even 2 1
448.2.a.g 1 152.g odd 2 1
784.2.a.b 1 532.b odd 2 1
784.2.i.c 2 532.t even 6 2
784.2.i.i 2 532.bh odd 6 2
882.2.a.i 1 399.h odd 2 1
882.2.g.c 2 399.w even 6 2
882.2.g.d 2 399.s odd 6 2
1008.2.a.h 1 228.b odd 2 1
1134.2.f.f 2 171.l even 6 2
1134.2.f.l 2 171.o odd 6 2
1694.2.a.e 1 209.d even 2 1
1792.2.b.c 2 304.j odd 4 2
1792.2.b.g 2 304.m even 4 2
2366.2.a.j 1 247.d odd 2 1
2366.2.d.b 2 247.i even 4 2
2450.2.a.t 1 665.g even 2 1
2450.2.c.c 2 665.n odd 4 2
2800.2.a.g 1 380.d even 2 1
2800.2.g.h 2 380.j odd 4 2
3136.2.a.e 1 1064.f even 2 1
3136.2.a.z 1 1064.p odd 2 1
3150.2.a.i 1 285.b even 2 1
3150.2.g.j 2 285.j odd 4 2
4032.2.a.r 1 456.l odd 2 1
4032.2.a.w 1 456.p even 2 1
4046.2.a.f 1 323.c odd 2 1
5054.2.a.c 1 1.a even 1 1 trivial
7056.2.a.bd 1 1596.p even 2 1
7406.2.a.a 1 437.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5054))\):

\( T_{3} - 2 \) Copy content Toggle raw display
\( T_{5} \) Copy content Toggle raw display
\( T_{13} - 4 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 1 \) Copy content Toggle raw display
$3$ \( T - 2 \) Copy content Toggle raw display
$5$ \( T \) Copy content Toggle raw display
$7$ \( T - 1 \) Copy content Toggle raw display
$11$ \( T \) Copy content Toggle raw display
$13$ \( T - 4 \) Copy content Toggle raw display
$17$ \( T - 6 \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T \) Copy content Toggle raw display
$29$ \( T - 6 \) Copy content Toggle raw display
$31$ \( T - 4 \) Copy content Toggle raw display
$37$ \( T + 2 \) Copy content Toggle raw display
$41$ \( T + 6 \) Copy content Toggle raw display
$43$ \( T - 8 \) Copy content Toggle raw display
$47$ \( T + 12 \) Copy content Toggle raw display
$53$ \( T + 6 \) Copy content Toggle raw display
$59$ \( T - 6 \) Copy content Toggle raw display
$61$ \( T - 8 \) Copy content Toggle raw display
$67$ \( T - 4 \) Copy content Toggle raw display
$71$ \( T \) Copy content Toggle raw display
$73$ \( T - 2 \) Copy content Toggle raw display
$79$ \( T + 8 \) Copy content Toggle raw display
$83$ \( T + 6 \) Copy content Toggle raw display
$89$ \( T - 6 \) Copy content Toggle raw display
$97$ \( T - 10 \) Copy content Toggle raw display
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