Properties

Label 1210.2.a.b
Level $1210$
Weight $2$
Character orbit 1210.a
Self dual yes
Analytic conductor $9.662$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1210 = 2 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1210.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(9.66189864457\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 110)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - 3 q^{7} - q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - 3 q^{7} - q^{8} - 2 q^{9} - q^{10} - q^{12} + 6 q^{13} + 3 q^{14} - q^{15} + q^{16} + 7 q^{17} + 2 q^{18} - 5 q^{19} + q^{20} + 3 q^{21} - 6 q^{23} + q^{24} + q^{25} - 6 q^{26} + 5 q^{27} - 3 q^{28} - 5 q^{29} + q^{30} - 3 q^{31} - q^{32} - 7 q^{34} - 3 q^{35} - 2 q^{36} + 3 q^{37} + 5 q^{38} - 6 q^{39} - q^{40} - 2 q^{41} - 3 q^{42} - 4 q^{43} - 2 q^{45} + 6 q^{46} - 2 q^{47} - q^{48} + 2 q^{49} - q^{50} - 7 q^{51} + 6 q^{52} - q^{53} - 5 q^{54} + 3 q^{56} + 5 q^{57} + 5 q^{58} - 10 q^{59} - q^{60} - 7 q^{61} + 3 q^{62} + 6 q^{63} + q^{64} + 6 q^{65} + 8 q^{67} + 7 q^{68} + 6 q^{69} + 3 q^{70} + 7 q^{71} + 2 q^{72} - 14 q^{73} - 3 q^{74} - q^{75} - 5 q^{76} + 6 q^{78} - 10 q^{79} + q^{80} + q^{81} + 2 q^{82} + 6 q^{83} + 3 q^{84} + 7 q^{85} + 4 q^{86} + 5 q^{87} - 15 q^{89} + 2 q^{90} - 18 q^{91} - 6 q^{92} + 3 q^{93} + 2 q^{94} - 5 q^{95} + q^{96} - 12 q^{97} - 2 q^{98}+O(q^{100}) \) 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 −1.00000 1.00000 1.00000 1.00000 −3.00000 −1.00000 −2.00000 −1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(5\) \(-1\)
\(11\) \(-1\)

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 1210.2.a.b 1
4.b odd 2 1 9680.2.a.x 1
5.b even 2 1 6050.2.a.bj 1
11.b odd 2 1 110.2.a.b 1
33.d even 2 1 990.2.a.d 1
44.c even 2 1 880.2.a.i 1
55.d odd 2 1 550.2.a.f 1
55.e even 4 2 550.2.b.a 2
77.b even 2 1 5390.2.a.bf 1
88.b odd 2 1 3520.2.a.y 1
88.g even 2 1 3520.2.a.h 1
132.d odd 2 1 7920.2.a.d 1
165.d even 2 1 4950.2.a.bc 1
165.l odd 4 2 4950.2.c.m 2
220.g even 2 1 4400.2.a.l 1
220.i odd 4 2 4400.2.b.i 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
110.2.a.b 1 11.b odd 2 1
550.2.a.f 1 55.d odd 2 1
550.2.b.a 2 55.e even 4 2
880.2.a.i 1 44.c even 2 1
990.2.a.d 1 33.d even 2 1
1210.2.a.b 1 1.a even 1 1 trivial
3520.2.a.h 1 88.g even 2 1
3520.2.a.y 1 88.b odd 2 1
4400.2.a.l 1 220.g even 2 1
4400.2.b.i 2 220.i odd 4 2
4950.2.a.bc 1 165.d even 2 1
4950.2.c.m 2 165.l odd 4 2
5390.2.a.bf 1 77.b even 2 1
6050.2.a.bj 1 5.b even 2 1
7920.2.a.d 1 132.d odd 2 1
9680.2.a.x 1 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1210))\):

\( T_{3} + 1 \) Copy content Toggle raw display
\( T_{7} + 3 \) Copy content Toggle raw display
\( T_{13} - 6 \) Copy content Toggle raw display
\( T_{17} - 7 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 1 \) Copy content Toggle raw display
$3$ \( T + 1 \) Copy content Toggle raw display
$5$ \( T - 1 \) Copy content Toggle raw display
$7$ \( T + 3 \) Copy content Toggle raw display
$11$ \( T \) Copy content Toggle raw display
$13$ \( T - 6 \) Copy content Toggle raw display
$17$ \( T - 7 \) Copy content Toggle raw display
$19$ \( T + 5 \) Copy content Toggle raw display
$23$ \( T + 6 \) Copy content Toggle raw display
$29$ \( T + 5 \) Copy content Toggle raw display
$31$ \( T + 3 \) Copy content Toggle raw display
$37$ \( T - 3 \) Copy content Toggle raw display
$41$ \( T + 2 \) Copy content Toggle raw display
$43$ \( T + 4 \) Copy content Toggle raw display
$47$ \( T + 2 \) Copy content Toggle raw display
$53$ \( T + 1 \) Copy content Toggle raw display
$59$ \( T + 10 \) Copy content Toggle raw display
$61$ \( T + 7 \) Copy content Toggle raw display
$67$ \( T - 8 \) Copy content Toggle raw display
$71$ \( T - 7 \) Copy content Toggle raw display
$73$ \( T + 14 \) Copy content Toggle raw display
$79$ \( T + 10 \) Copy content Toggle raw display
$83$ \( T - 6 \) Copy content Toggle raw display
$89$ \( T + 15 \) Copy content Toggle raw display
$97$ \( T + 12 \) Copy content Toggle raw display
show more
show less