Properties

Label 7350.2.a.br
Level 7350
Weight 2
Character orbit 7350.a
Self dual yes
Analytic conductor 58.690
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7350.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(58.6900454856\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 294)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} - 4q^{11} - q^{12} + 4q^{13} + q^{16} + q^{18} - 4q^{19} - 4q^{22} - q^{24} + 4q^{26} - q^{27} + 2q^{29} - 8q^{31} + q^{32} + 4q^{33} + q^{36} + 6q^{37} - 4q^{38} - 4q^{39} - 4q^{43} - 4q^{44} - 8q^{47} - q^{48} + 4q^{52} + 10q^{53} - q^{54} + 4q^{57} + 2q^{58} - 4q^{59} + 4q^{61} - 8q^{62} + q^{64} + 4q^{66} - 4q^{67} + 8q^{71} + q^{72} - 16q^{73} + 6q^{74} - 4q^{76} - 4q^{78} - 8q^{79} + q^{81} - 12q^{83} - 4q^{86} - 2q^{87} - 4q^{88} - 8q^{89} + 8q^{93} - 8q^{94} - q^{96} + 8q^{97} - 4q^{99} + O(q^{100}) \)

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
1.00000 −1.00000 1.00000 0 −1.00000 0 1.00000 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

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 7350.2.a.br 1
5.b even 2 1 294.2.a.c yes 1
7.b odd 2 1 7350.2.a.cj 1
15.d odd 2 1 882.2.a.l 1
20.d odd 2 1 2352.2.a.b 1
35.c odd 2 1 294.2.a.b 1
35.i odd 6 2 294.2.e.e 2
35.j even 6 2 294.2.e.d 2
40.e odd 2 1 9408.2.a.de 1
40.f even 2 1 9408.2.a.bo 1
60.h even 2 1 7056.2.a.ca 1
105.g even 2 1 882.2.a.f 1
105.o odd 6 2 882.2.g.a 2
105.p even 6 2 882.2.g.f 2
140.c even 2 1 2352.2.a.y 1
140.p odd 6 2 2352.2.q.y 2
140.s even 6 2 2352.2.q.a 2
280.c odd 2 1 9408.2.a.br 1
280.n even 2 1 9408.2.a.b 1
420.o odd 2 1 7056.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
294.2.a.b 1 35.c odd 2 1
294.2.a.c yes 1 5.b even 2 1
294.2.e.d 2 35.j even 6 2
294.2.e.e 2 35.i odd 6 2
882.2.a.f 1 105.g even 2 1
882.2.a.l 1 15.d odd 2 1
882.2.g.a 2 105.o odd 6 2
882.2.g.f 2 105.p even 6 2
2352.2.a.b 1 20.d odd 2 1
2352.2.a.y 1 140.c even 2 1
2352.2.q.a 2 140.s even 6 2
2352.2.q.y 2 140.p odd 6 2
7056.2.a.a 1 420.o odd 2 1
7056.2.a.ca 1 60.h even 2 1
7350.2.a.br 1 1.a even 1 1 trivial
7350.2.a.cj 1 7.b odd 2 1
9408.2.a.b 1 280.n even 2 1
9408.2.a.bo 1 40.f even 2 1
9408.2.a.br 1 280.c odd 2 1
9408.2.a.de 1 40.e odd 2 1

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(1\)
\(5\) \(1\)
\(7\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7350))\):

\( T_{11} + 4 \)
\( T_{13} - 4 \)
\( T_{17} \)
\( T_{19} + 4 \)
\( T_{23} \)
\( T_{31} + 8 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - T \)
$3$ \( 1 + T \)
$5$ 1
$7$ 1
$11$ \( 1 + 4 T + 11 T^{2} \)
$13$ \( 1 - 4 T + 13 T^{2} \)
$17$ \( 1 + 17 T^{2} \)
$19$ \( 1 + 4 T + 19 T^{2} \)
$23$ \( 1 + 23 T^{2} \)
$29$ \( 1 - 2 T + 29 T^{2} \)
$31$ \( 1 + 8 T + 31 T^{2} \)
$37$ \( 1 - 6 T + 37 T^{2} \)
$41$ \( 1 + 41 T^{2} \)
$43$ \( 1 + 4 T + 43 T^{2} \)
$47$ \( 1 + 8 T + 47 T^{2} \)
$53$ \( 1 - 10 T + 53 T^{2} \)
$59$ \( 1 + 4 T + 59 T^{2} \)
$61$ \( 1 - 4 T + 61 T^{2} \)
$67$ \( 1 + 4 T + 67 T^{2} \)
$71$ \( 1 - 8 T + 71 T^{2} \)
$73$ \( 1 + 16 T + 73 T^{2} \)
$79$ \( 1 + 8 T + 79 T^{2} \)
$83$ \( 1 + 12 T + 83 T^{2} \)
$89$ \( 1 + 8 T + 89 T^{2} \)
$97$ \( 1 - 8 T + 97 T^{2} \)
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