Properties

Label 2366.2.a.j
Level 2366
Weight 2
Character orbit 2366.a
Self dual yes
Analytic conductor 18.893
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2366.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(18.8926051182\)
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

\(f(q)\) \(=\) \( q + q^{2} - 2q^{3} + q^{4} - 2q^{6} - q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - 2q^{3} + q^{4} - 2q^{6} - q^{7} + q^{8} + q^{9} - 2q^{12} - q^{14} + q^{16} + 6q^{17} + q^{18} - 2q^{19} + 2q^{21} - 2q^{24} - 5q^{25} + 4q^{27} - q^{28} - 6q^{29} + 4q^{31} + q^{32} + 6q^{34} + q^{36} - 2q^{37} - 2q^{38} - 6q^{41} + 2q^{42} + 8q^{43} + 12q^{47} - 2q^{48} + q^{49} - 5q^{50} - 12q^{51} + 6q^{53} + 4q^{54} - q^{56} + 4q^{57} - 6q^{58} + 6q^{59} + 8q^{61} + 4q^{62} - q^{63} + q^{64} + 4q^{67} + 6q^{68} + q^{72} - 2q^{73} - 2q^{74} + 10q^{75} - 2q^{76} + 8q^{79} - 11q^{81} - 6q^{82} + 6q^{83} + 2q^{84} + 8q^{86} + 12q^{87} + 6q^{89} - 8q^{93} + 12q^{94} - 2q^{96} + 10q^{97} + q^{98} + O(q^{100}) \)

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 −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:

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 2366.2.a.j 1
13.b even 2 1 14.2.a.a 1
13.d odd 4 2 2366.2.d.b 2
39.d odd 2 1 126.2.a.b 1
52.b odd 2 1 112.2.a.c 1
65.d even 2 1 350.2.a.f 1
65.h odd 4 2 350.2.c.d 2
91.b odd 2 1 98.2.a.a 1
91.r even 6 2 98.2.c.b 2
91.s odd 6 2 98.2.c.a 2
104.e even 2 1 448.2.a.g 1
104.h odd 2 1 448.2.a.a 1
117.n odd 6 2 1134.2.f.f 2
117.t even 6 2 1134.2.f.l 2
143.d odd 2 1 1694.2.a.e 1
156.h even 2 1 1008.2.a.h 1
195.e odd 2 1 3150.2.a.i 1
195.s even 4 2 3150.2.g.j 2
208.o odd 4 2 1792.2.b.g 2
208.p even 4 2 1792.2.b.c 2
221.b even 2 1 4046.2.a.f 1
247.d odd 2 1 5054.2.a.c 1
260.g odd 2 1 2800.2.a.g 1
260.p even 4 2 2800.2.g.h 2
273.g even 2 1 882.2.a.i 1
273.w odd 6 2 882.2.g.c 2
273.ba even 6 2 882.2.g.d 2
299.c odd 2 1 7406.2.a.a 1
312.b odd 2 1 4032.2.a.w 1
312.h even 2 1 4032.2.a.r 1
364.h even 2 1 784.2.a.b 1
364.x even 6 2 784.2.i.i 2
364.bl odd 6 2 784.2.i.c 2
455.h odd 2 1 2450.2.a.t 1
455.s even 4 2 2450.2.c.c 2
728.b even 2 1 3136.2.a.z 1
728.l odd 2 1 3136.2.a.e 1
1092.d odd 2 1 7056.2.a.bd 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
14.2.a.a 1 13.b even 2 1
98.2.a.a 1 91.b odd 2 1
98.2.c.a 2 91.s odd 6 2
98.2.c.b 2 91.r even 6 2
112.2.a.c 1 52.b odd 2 1
126.2.a.b 1 39.d odd 2 1
350.2.a.f 1 65.d even 2 1
350.2.c.d 2 65.h odd 4 2
448.2.a.a 1 104.h odd 2 1
448.2.a.g 1 104.e even 2 1
784.2.a.b 1 364.h even 2 1
784.2.i.c 2 364.bl odd 6 2
784.2.i.i 2 364.x even 6 2
882.2.a.i 1 273.g even 2 1
882.2.g.c 2 273.w odd 6 2
882.2.g.d 2 273.ba even 6 2
1008.2.a.h 1 156.h even 2 1
1134.2.f.f 2 117.n odd 6 2
1134.2.f.l 2 117.t even 6 2
1694.2.a.e 1 143.d odd 2 1
1792.2.b.c 2 208.p even 4 2
1792.2.b.g 2 208.o odd 4 2
2366.2.a.j 1 1.a even 1 1 trivial
2366.2.d.b 2 13.d odd 4 2
2450.2.a.t 1 455.h odd 2 1
2450.2.c.c 2 455.s even 4 2
2800.2.a.g 1 260.g odd 2 1
2800.2.g.h 2 260.p even 4 2
3136.2.a.e 1 728.l odd 2 1
3136.2.a.z 1 728.b even 2 1
3150.2.a.i 1 195.e odd 2 1
3150.2.g.j 2 195.s even 4 2
4032.2.a.r 1 312.h even 2 1
4032.2.a.w 1 312.b odd 2 1
4046.2.a.f 1 221.b even 2 1
5054.2.a.c 1 247.d odd 2 1
7056.2.a.bd 1 1092.d odd 2 1
7406.2.a.a 1 299.c odd 2 1

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(7\) \(1\)
\(13\) \(1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2366))\):

\( T_{3} + 2 \)
\( T_{5} \)

Hecke Characteristic Polynomials

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