Properties

Label 2178.2.a.m
Level 2178
Weight 2
Character orbit 2178.a
Self dual yes
Analytic conductor 17.391
Analytic rank 0
Dimension 1
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 2178 = 2 \cdot 3^{2} \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2178.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(17.3914175602\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 66)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{4} + 4q^{5} + 2q^{7} + q^{8} + O(q^{10}) \) \( q + q^{2} + q^{4} + 4q^{5} + 2q^{7} + q^{8} + 4q^{10} - 4q^{13} + 2q^{14} + q^{16} - 2q^{17} + 4q^{20} + 6q^{23} + 11q^{25} - 4q^{26} + 2q^{28} + 10q^{29} - 8q^{31} + q^{32} - 2q^{34} + 8q^{35} - 2q^{37} + 4q^{40} + 2q^{41} - 4q^{43} + 6q^{46} + 2q^{47} - 3q^{49} + 11q^{50} - 4q^{52} - 4q^{53} + 2q^{56} + 10q^{58} + 8q^{61} - 8q^{62} + q^{64} - 16q^{65} - 12q^{67} - 2q^{68} + 8q^{70} - 2q^{71} + 6q^{73} - 2q^{74} - 10q^{79} + 4q^{80} + 2q^{82} + 4q^{83} - 8q^{85} - 4q^{86} - 10q^{89} - 8q^{91} + 6q^{92} + 2q^{94} - 2q^{97} - 3q^{98} + O(q^{100}) \)

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 1.00000 4.00000 0 2.00000 1.00000 0 4.00000
\(n\): 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 2178.2.a.m 1
3.b odd 2 1 726.2.a.d 1
11.b odd 2 1 198.2.a.c 1
12.b even 2 1 5808.2.a.b 1
33.d even 2 1 66.2.a.c 1
33.f even 10 4 726.2.e.e 4
33.h odd 10 4 726.2.e.m 4
44.c even 2 1 1584.2.a.s 1
55.d odd 2 1 4950.2.a.bo 1
55.e even 4 2 4950.2.c.d 2
77.b even 2 1 9702.2.a.a 1
88.b odd 2 1 6336.2.a.c 1
88.g even 2 1 6336.2.a.d 1
99.g even 6 2 1782.2.e.l 2
99.h odd 6 2 1782.2.e.n 2
132.d odd 2 1 528.2.a.a 1
165.d even 2 1 1650.2.a.c 1
165.l odd 4 2 1650.2.c.m 2
231.h odd 2 1 3234.2.a.s 1
264.m even 2 1 2112.2.a.n 1
264.p odd 2 1 2112.2.a.bd 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
66.2.a.c 1 33.d even 2 1
198.2.a.c 1 11.b odd 2 1
528.2.a.a 1 132.d odd 2 1
726.2.a.d 1 3.b odd 2 1
726.2.e.e 4 33.f even 10 4
726.2.e.m 4 33.h odd 10 4
1584.2.a.s 1 44.c even 2 1
1650.2.a.c 1 165.d even 2 1
1650.2.c.m 2 165.l odd 4 2
1782.2.e.l 2 99.g even 6 2
1782.2.e.n 2 99.h odd 6 2
2112.2.a.n 1 264.m even 2 1
2112.2.a.bd 1 264.p odd 2 1
2178.2.a.m 1 1.a even 1 1 trivial
3234.2.a.s 1 231.h odd 2 1
4950.2.a.bo 1 55.d odd 2 1
4950.2.c.d 2 55.e even 4 2
5808.2.a.b 1 12.b even 2 1
6336.2.a.c 1 88.b odd 2 1
6336.2.a.d 1 88.g even 2 1
9702.2.a.a 1 77.b even 2 1

Atkin-Lehner signs

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

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2178))\):

\( T_{5} - 4 \)
\( T_{7} - 2 \)
\( T_{13} + 4 \)
\( T_{17} + 2 \)

Hecke Characteristic Polynomials

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