Properties

Label 2352.4.a.v
Level $2352$
Weight $4$
Character orbit 2352.a
Self dual yes
Analytic conductor $138.772$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2352.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(138.772492334\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 84)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 3q^{3} - 14q^{5} + 9q^{9} + O(q^{10}) \) \( q + 3q^{3} - 14q^{5} + 9q^{9} - 4q^{11} - 54q^{13} - 42q^{15} + 14q^{17} + 92q^{19} + 152q^{23} + 71q^{25} + 27q^{27} - 106q^{29} - 144q^{31} - 12q^{33} + 158q^{37} - 162q^{39} + 390q^{41} + 508q^{43} - 126q^{45} - 528q^{47} + 42q^{51} + 606q^{53} + 56q^{55} + 276q^{57} - 364q^{59} - 678q^{61} + 756q^{65} - 844q^{67} + 456q^{69} + 8q^{71} + 422q^{73} + 213q^{75} - 384q^{79} + 81q^{81} - 548q^{83} - 196q^{85} - 318q^{87} - 1194q^{89} - 432q^{93} - 1288q^{95} + 1502q^{97} - 36q^{99} + O(q^{100}) \)

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
0 3.00000 0 −14.0000 0 0 0 9.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(7\) \(-1\)

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 2352.4.a.v 1
4.b odd 2 1 588.4.a.a 1
7.b odd 2 1 336.4.a.e 1
12.b even 2 1 1764.4.a.l 1
21.c even 2 1 1008.4.a.d 1
28.d even 2 1 84.4.a.b 1
28.f even 6 2 588.4.i.a 2
28.g odd 6 2 588.4.i.h 2
56.e even 2 1 1344.4.a.b 1
56.h odd 2 1 1344.4.a.p 1
84.h odd 2 1 252.4.a.a 1
84.j odd 6 2 1764.4.k.n 2
84.n even 6 2 1764.4.k.c 2
140.c even 2 1 2100.4.a.g 1
140.j odd 4 2 2100.4.k.g 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
84.4.a.b 1 28.d even 2 1
252.4.a.a 1 84.h odd 2 1
336.4.a.e 1 7.b odd 2 1
588.4.a.a 1 4.b odd 2 1
588.4.i.a 2 28.f even 6 2
588.4.i.h 2 28.g odd 6 2
1008.4.a.d 1 21.c even 2 1
1344.4.a.b 1 56.e even 2 1
1344.4.a.p 1 56.h odd 2 1
1764.4.a.l 1 12.b even 2 1
1764.4.k.c 2 84.n even 6 2
1764.4.k.n 2 84.j odd 6 2
2100.4.a.g 1 140.c even 2 1
2100.4.k.g 2 140.j odd 4 2
2352.4.a.v 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 \(S_{4}^{\mathrm{new}}(\Gamma_0(2352))\):

\( T_{5} + 14 \)
\( T_{11} + 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( -3 + T \)
$5$ \( 14 + T \)
$7$ \( T \)
$11$ \( 4 + T \)
$13$ \( 54 + T \)
$17$ \( -14 + T \)
$19$ \( -92 + T \)
$23$ \( -152 + T \)
$29$ \( 106 + T \)
$31$ \( 144 + T \)
$37$ \( -158 + T \)
$41$ \( -390 + T \)
$43$ \( -508 + T \)
$47$ \( 528 + T \)
$53$ \( -606 + T \)
$59$ \( 364 + T \)
$61$ \( 678 + T \)
$67$ \( 844 + T \)
$71$ \( -8 + T \)
$73$ \( -422 + T \)
$79$ \( 384 + T \)
$83$ \( 548 + T \)
$89$ \( 1194 + T \)
$97$ \( -1502 + T \)
show more
show less