Properties

Label 441.2.a.b
Level $441$
Weight $2$
Character orbit 441.a
Self dual yes
Analytic conductor $3.521$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2 q^{2} + 2 q^{4} + 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( q - 2 q^{2} + 2 q^{4} + 2 q^{5} - 4 q^{10} + 2 q^{11} + q^{13} - 4 q^{16} + q^{19} + 4 q^{20} - 4 q^{22} - q^{25} - 2 q^{26} - 4 q^{29} + 9 q^{31} + 8 q^{32} + 3 q^{37} - 2 q^{38} + 10 q^{41} + 5 q^{43} + 4 q^{44} + 6 q^{47} + 2 q^{50} + 2 q^{52} - 12 q^{53} + 4 q^{55} + 8 q^{58} + 12 q^{59} + 10 q^{61} - 18 q^{62} - 8 q^{64} + 2 q^{65} - 5 q^{67} + 6 q^{71} - 3 q^{73} - 6 q^{74} + 2 q^{76} - q^{79} - 8 q^{80} - 20 q^{82} - 6 q^{83} - 10 q^{86} - 16 q^{89} - 12 q^{94} + 2 q^{95} - 6 q^{97}+O(q^{100}) \) 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
−2.00000 0 2.00000 2.00000 0 0 0 0 −4.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(7\) \(1\)

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 441.2.a.b 1
3.b odd 2 1 147.2.a.c 1
4.b odd 2 1 7056.2.a.bp 1
7.b odd 2 1 441.2.a.a 1
7.c even 3 2 63.2.e.b 2
7.d odd 6 2 441.2.e.e 2
12.b even 2 1 2352.2.a.d 1
15.d odd 2 1 3675.2.a.a 1
21.c even 2 1 147.2.a.b 1
21.g even 6 2 147.2.e.a 2
21.h odd 6 2 21.2.e.a 2
24.f even 2 1 9408.2.a.cv 1
24.h odd 2 1 9408.2.a.bg 1
28.d even 2 1 7056.2.a.m 1
28.g odd 6 2 1008.2.s.d 2
63.g even 3 2 567.2.g.f 2
63.h even 3 2 567.2.h.a 2
63.j odd 6 2 567.2.h.f 2
63.n odd 6 2 567.2.g.a 2
84.h odd 2 1 2352.2.a.w 1
84.j odd 6 2 2352.2.q.c 2
84.n even 6 2 336.2.q.f 2
105.g even 2 1 3675.2.a.c 1
105.o odd 6 2 525.2.i.e 2
105.x even 12 4 525.2.r.e 4
168.e odd 2 1 9408.2.a.k 1
168.i even 2 1 9408.2.a.bz 1
168.s odd 6 2 1344.2.q.m 2
168.v even 6 2 1344.2.q.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
21.2.e.a 2 21.h odd 6 2
63.2.e.b 2 7.c even 3 2
147.2.a.b 1 21.c even 2 1
147.2.a.c 1 3.b odd 2 1
147.2.e.a 2 21.g even 6 2
336.2.q.f 2 84.n even 6 2
441.2.a.a 1 7.b odd 2 1
441.2.a.b 1 1.a even 1 1 trivial
441.2.e.e 2 7.d odd 6 2
525.2.i.e 2 105.o odd 6 2
525.2.r.e 4 105.x even 12 4
567.2.g.a 2 63.n odd 6 2
567.2.g.f 2 63.g even 3 2
567.2.h.a 2 63.h even 3 2
567.2.h.f 2 63.j odd 6 2
1008.2.s.d 2 28.g odd 6 2
1344.2.q.c 2 168.v even 6 2
1344.2.q.m 2 168.s odd 6 2
2352.2.a.d 1 12.b even 2 1
2352.2.a.w 1 84.h odd 2 1
2352.2.q.c 2 84.j odd 6 2
3675.2.a.a 1 15.d odd 2 1
3675.2.a.c 1 105.g even 2 1
7056.2.a.m 1 28.d even 2 1
7056.2.a.bp 1 4.b odd 2 1
9408.2.a.k 1 168.e odd 2 1
9408.2.a.bg 1 24.h odd 2 1
9408.2.a.bz 1 168.i even 2 1
9408.2.a.cv 1 24.f even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(441))\):

\( T_{2} + 2 \) Copy content Toggle raw display
\( T_{5} - 2 \) Copy content Toggle raw display
\( T_{13} - 1 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 2 \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T - 2 \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T - 2 \) Copy content Toggle raw display
$13$ \( T - 1 \) Copy content Toggle raw display
$17$ \( T \) Copy content Toggle raw display
$19$ \( T - 1 \) Copy content Toggle raw display
$23$ \( T \) Copy content Toggle raw display
$29$ \( T + 4 \) Copy content Toggle raw display
$31$ \( T - 9 \) Copy content Toggle raw display
$37$ \( T - 3 \) Copy content Toggle raw display
$41$ \( T - 10 \) Copy content Toggle raw display
$43$ \( T - 5 \) Copy content Toggle raw display
$47$ \( T - 6 \) Copy content Toggle raw display
$53$ \( T + 12 \) Copy content Toggle raw display
$59$ \( T - 12 \) Copy content Toggle raw display
$61$ \( T - 10 \) Copy content Toggle raw display
$67$ \( T + 5 \) Copy content Toggle raw display
$71$ \( T - 6 \) Copy content Toggle raw display
$73$ \( T + 3 \) Copy content Toggle raw display
$79$ \( T + 1 \) Copy content Toggle raw display
$83$ \( T + 6 \) Copy content Toggle raw display
$89$ \( T + 16 \) Copy content Toggle raw display
$97$ \( T + 6 \) Copy content Toggle raw display
show more
show less