Properties

Label 5915.2.a.f
Level $5915$
Weight $2$
Character orbit 5915.a
Self dual yes
Analytic conductor $47.232$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 5915 = 5 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5915.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.2315127956\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} - 2 q^{4} + q^{5} - q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{3} - 2 q^{4} + q^{5} - q^{7} - 2 q^{9} + 3 q^{11} - 2 q^{12} + q^{15} + 4 q^{16} + 3 q^{17} - 2 q^{19} - 2 q^{20} - q^{21} - 6 q^{23} + q^{25} - 5 q^{27} + 2 q^{28} + 3 q^{29} + 4 q^{31} + 3 q^{33} - q^{35} + 4 q^{36} - 2 q^{37} + 12 q^{41} - 10 q^{43} - 6 q^{44} - 2 q^{45} - 9 q^{47} + 4 q^{48} + q^{49} + 3 q^{51} + 12 q^{53} + 3 q^{55} - 2 q^{57} - 2 q^{60} + 8 q^{61} + 2 q^{63} - 8 q^{64} + 4 q^{67} - 6 q^{68} - 6 q^{69} - 2 q^{73} + q^{75} + 4 q^{76} - 3 q^{77} - q^{79} + 4 q^{80} + q^{81} - 12 q^{83} + 2 q^{84} + 3 q^{85} + 3 q^{87} + 12 q^{89} + 12 q^{92} + 4 q^{93} - 2 q^{95} + q^{97} - 6 q^{99}+O(q^{100}) \) 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 −2.00000 1.00000 0 −1.00000 0 −2.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(7\) \(1\)
\(13\) \(1\)

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 5915.2.a.f 1
13.b even 2 1 35.2.a.a 1
39.d odd 2 1 315.2.a.b 1
52.b odd 2 1 560.2.a.b 1
65.d even 2 1 175.2.a.b 1
65.h odd 4 2 175.2.b.a 2
91.b odd 2 1 245.2.a.c 1
91.r even 6 2 245.2.e.a 2
91.s odd 6 2 245.2.e.b 2
104.e even 2 1 2240.2.a.k 1
104.h odd 2 1 2240.2.a.u 1
143.d odd 2 1 4235.2.a.c 1
156.h even 2 1 5040.2.a.v 1
195.e odd 2 1 1575.2.a.f 1
195.s even 4 2 1575.2.d.c 2
260.g odd 2 1 2800.2.a.z 1
260.p even 4 2 2800.2.g.l 2
273.g even 2 1 2205.2.a.e 1
364.h even 2 1 3920.2.a.ba 1
455.h odd 2 1 1225.2.a.e 1
455.s even 4 2 1225.2.b.d 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
35.2.a.a 1 13.b even 2 1
175.2.a.b 1 65.d even 2 1
175.2.b.a 2 65.h odd 4 2
245.2.a.c 1 91.b odd 2 1
245.2.e.a 2 91.r even 6 2
245.2.e.b 2 91.s odd 6 2
315.2.a.b 1 39.d odd 2 1
560.2.a.b 1 52.b odd 2 1
1225.2.a.e 1 455.h odd 2 1
1225.2.b.d 2 455.s even 4 2
1575.2.a.f 1 195.e odd 2 1
1575.2.d.c 2 195.s even 4 2
2205.2.a.e 1 273.g even 2 1
2240.2.a.k 1 104.e even 2 1
2240.2.a.u 1 104.h odd 2 1
2800.2.a.z 1 260.g odd 2 1
2800.2.g.l 2 260.p even 4 2
3920.2.a.ba 1 364.h even 2 1
4235.2.a.c 1 143.d odd 2 1
5040.2.a.v 1 156.h even 2 1
5915.2.a.f 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5915))\):

\( T_{2} \) Copy content Toggle raw display
\( T_{3} - 1 \) 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
$5$ \( T - 1 \) Copy content Toggle raw display
$7$ \( T + 1 \) Copy content Toggle raw display
$11$ \( T - 3 \) Copy content Toggle raw display
$13$ \( T \) Copy content Toggle raw display
$17$ \( T - 3 \) Copy content Toggle raw display
$19$ \( T + 2 \) Copy content Toggle raw display
$23$ \( T + 6 \) Copy content Toggle raw display
$29$ \( T - 3 \) Copy content Toggle raw display
$31$ \( T - 4 \) Copy content Toggle raw display
$37$ \( T + 2 \) Copy content Toggle raw display
$41$ \( T - 12 \) Copy content Toggle raw display
$43$ \( T + 10 \) Copy content Toggle raw display
$47$ \( T + 9 \) Copy content Toggle raw display
$53$ \( T - 12 \) Copy content Toggle raw display
$59$ \( T \) Copy content Toggle raw display
$61$ \( T - 8 \) Copy content Toggle raw display
$67$ \( T - 4 \) Copy content Toggle raw display
$71$ \( T \) Copy content Toggle raw display
$73$ \( T + 2 \) Copy content Toggle raw display
$79$ \( T + 1 \) Copy content Toggle raw display
$83$ \( T + 12 \) Copy content Toggle raw display
$89$ \( T - 12 \) Copy content Toggle raw display
$97$ \( T - 1 \) Copy content Toggle raw display
show more
show less