Properties

Label 7436.2.a.d
Level $7436$
Weight $2$
Character orbit 7436.a
Self dual yes
Analytic conductor $59.377$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 7436 = 2^{2} \cdot 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7436.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(59.3767589430\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 44)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} + 3 q^{5} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{3} + 3 q^{5} - 2 q^{7} - 2 q^{9} + q^{11} + 3 q^{15} + 6 q^{17} - 8 q^{19} - 2 q^{21} - 3 q^{23} + 4 q^{25} - 5 q^{27} - 5 q^{31} + q^{33} - 6 q^{35} + q^{37} - 10 q^{43} - 6 q^{45} - 3 q^{49} + 6 q^{51} - 6 q^{53} + 3 q^{55} - 8 q^{57} - 3 q^{59} - 4 q^{61} + 4 q^{63} + q^{67} - 3 q^{69} - 15 q^{71} + 4 q^{73} + 4 q^{75} - 2 q^{77} + 2 q^{79} + q^{81} - 6 q^{83} + 18 q^{85} + 9 q^{89} - 5 q^{93} - 24 q^{95} + 7 q^{97} - 2 q^{99}+O(q^{100}) \) 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
0 1.00000 0 3.00000 0 −2.00000 0 −2.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(11\) \(-1\)
\(13\) \(1\)

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 7436.2.a.d 1
13.b even 2 1 44.2.a.a 1
39.d odd 2 1 396.2.a.c 1
52.b odd 2 1 176.2.a.a 1
65.d even 2 1 1100.2.a.b 1
65.h odd 4 2 1100.2.b.c 2
91.b odd 2 1 2156.2.a.a 1
91.r even 6 2 2156.2.i.b 2
91.s odd 6 2 2156.2.i.c 2
104.e even 2 1 704.2.a.f 1
104.h odd 2 1 704.2.a.i 1
117.n odd 6 2 3564.2.i.a 2
117.t even 6 2 3564.2.i.j 2
143.d odd 2 1 484.2.a.a 1
143.l odd 10 4 484.2.e.b 4
143.n even 10 4 484.2.e.a 4
156.h even 2 1 1584.2.a.p 1
195.e odd 2 1 9900.2.a.h 1
195.s even 4 2 9900.2.c.g 2
208.o odd 4 2 2816.2.c.k 2
208.p even 4 2 2816.2.c.e 2
260.g odd 2 1 4400.2.a.v 1
260.p even 4 2 4400.2.b.k 2
312.b odd 2 1 6336.2.a.j 1
312.h even 2 1 6336.2.a.i 1
364.h even 2 1 8624.2.a.w 1
429.e even 2 1 4356.2.a.j 1
572.b even 2 1 1936.2.a.c 1
1144.h odd 2 1 7744.2.a.m 1
1144.o even 2 1 7744.2.a.bc 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
44.2.a.a 1 13.b even 2 1
176.2.a.a 1 52.b odd 2 1
396.2.a.c 1 39.d odd 2 1
484.2.a.a 1 143.d odd 2 1
484.2.e.a 4 143.n even 10 4
484.2.e.b 4 143.l odd 10 4
704.2.a.f 1 104.e even 2 1
704.2.a.i 1 104.h odd 2 1
1100.2.a.b 1 65.d even 2 1
1100.2.b.c 2 65.h odd 4 2
1584.2.a.p 1 156.h even 2 1
1936.2.a.c 1 572.b even 2 1
2156.2.a.a 1 91.b odd 2 1
2156.2.i.b 2 91.r even 6 2
2156.2.i.c 2 91.s odd 6 2
2816.2.c.e 2 208.p even 4 2
2816.2.c.k 2 208.o odd 4 2
3564.2.i.a 2 117.n odd 6 2
3564.2.i.j 2 117.t even 6 2
4356.2.a.j 1 429.e even 2 1
4400.2.a.v 1 260.g odd 2 1
4400.2.b.k 2 260.p even 4 2
6336.2.a.i 1 312.h even 2 1
6336.2.a.j 1 312.b odd 2 1
7436.2.a.d 1 1.a even 1 1 trivial
7744.2.a.m 1 1144.h odd 2 1
7744.2.a.bc 1 1144.o even 2 1
8624.2.a.w 1 364.h even 2 1
9900.2.a.h 1 195.e odd 2 1
9900.2.c.g 2 195.s even 4 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7436))\):

\( T_{3} - 1 \) Copy content Toggle raw display
\( T_{5} - 3 \) Copy content Toggle raw display
\( T_{7} + 2 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T - 1 \) Copy content Toggle raw display
$5$ \( T - 3 \) Copy content Toggle raw display
$7$ \( T + 2 \) Copy content Toggle raw display
$11$ \( T - 1 \) Copy content Toggle raw display
$13$ \( T \) Copy content Toggle raw display
$17$ \( T - 6 \) Copy content Toggle raw display
$19$ \( T + 8 \) Copy content Toggle raw display
$23$ \( T + 3 \) Copy content Toggle raw display
$29$ \( T \) Copy content Toggle raw display
$31$ \( T + 5 \) Copy content Toggle raw display
$37$ \( T - 1 \) Copy content Toggle raw display
$41$ \( T \) Copy content Toggle raw display
$43$ \( T + 10 \) Copy content Toggle raw display
$47$ \( T \) Copy content Toggle raw display
$53$ \( T + 6 \) Copy content Toggle raw display
$59$ \( T + 3 \) Copy content Toggle raw display
$61$ \( T + 4 \) Copy content Toggle raw display
$67$ \( T - 1 \) Copy content Toggle raw display
$71$ \( T + 15 \) Copy content Toggle raw display
$73$ \( T - 4 \) Copy content Toggle raw display
$79$ \( T - 2 \) Copy content Toggle raw display
$83$ \( T + 6 \) Copy content Toggle raw display
$89$ \( T - 9 \) Copy content Toggle raw display
$97$ \( T - 7 \) Copy content Toggle raw display
show more
show less