Properties

Label 7350.2.a.o
Level $7350$
Weight $2$
Character orbit 7350.a
Self dual yes
Analytic conductor $58.690$
Analytic rank $0$
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: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1470)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} + 2 q^{11} - q^{12} + 2 q^{13} + q^{16} - 4 q^{17} - q^{18} - 2 q^{22} - 8 q^{23} + q^{24} - 2 q^{26} - q^{27} + 2 q^{31} - q^{32} - 2 q^{33} + 4 q^{34} + q^{36} - 8 q^{37} - 2 q^{39} + 2 q^{41} + 2 q^{43} + 2 q^{44} + 8 q^{46} + 10 q^{47} - q^{48} + 4 q^{51} + 2 q^{52} + 2 q^{53} + q^{54} - 4 q^{59} + 10 q^{61} - 2 q^{62} + q^{64} + 2 q^{66} - 2 q^{67} - 4 q^{68} + 8 q^{69} - 12 q^{71} - q^{72} + 10 q^{73} + 8 q^{74} + 2 q^{78} + 16 q^{79} + q^{81} - 2 q^{82} + 16 q^{83} - 2 q^{86} - 2 q^{88} - 14 q^{89} - 8 q^{92} - 2 q^{93} - 10 q^{94} + q^{96} + 6 q^{97} + 2 q^{99}+O(q^{100}) \) 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
−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:

Atkin-Lehner signs

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

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 7350.2.a.o 1
5.b even 2 1 1470.2.a.p yes 1
7.b odd 2 1 7350.2.a.bh 1
15.d odd 2 1 4410.2.a.n 1
35.c odd 2 1 1470.2.a.n 1
35.i odd 6 2 1470.2.i.g 2
35.j even 6 2 1470.2.i.c 2
105.g even 2 1 4410.2.a.e 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1470.2.a.n 1 35.c odd 2 1
1470.2.a.p yes 1 5.b even 2 1
1470.2.i.c 2 35.j even 6 2
1470.2.i.g 2 35.i odd 6 2
4410.2.a.e 1 105.g even 2 1
4410.2.a.n 1 15.d odd 2 1
7350.2.a.o 1 1.a even 1 1 trivial
7350.2.a.bh 1 7.b odd 2 1

Hecke kernels

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

\( T_{11} - 2 \) Copy content Toggle raw display
\( T_{13} - 2 \) Copy content Toggle raw display
\( T_{17} + 4 \) Copy content Toggle raw display
\( T_{19} \) Copy content Toggle raw display
\( T_{23} + 8 \) Copy content Toggle raw display
\( T_{31} - 2 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 1 \) Copy content Toggle raw display
$3$ \( T + 1 \) Copy content Toggle raw display
$5$ \( T \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T - 2 \) Copy content Toggle raw display
$13$ \( T - 2 \) Copy content Toggle raw display
$17$ \( T + 4 \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T + 8 \) Copy content Toggle raw display
$29$ \( T \) Copy content Toggle raw display
$31$ \( T - 2 \) Copy content Toggle raw display
$37$ \( T + 8 \) Copy content Toggle raw display
$41$ \( T - 2 \) Copy content Toggle raw display
$43$ \( T - 2 \) Copy content Toggle raw display
$47$ \( T - 10 \) Copy content Toggle raw display
$53$ \( T - 2 \) Copy content Toggle raw display
$59$ \( T + 4 \) Copy content Toggle raw display
$61$ \( T - 10 \) Copy content Toggle raw display
$67$ \( T + 2 \) Copy content Toggle raw display
$71$ \( T + 12 \) Copy content Toggle raw display
$73$ \( T - 10 \) Copy content Toggle raw display
$79$ \( T - 16 \) Copy content Toggle raw display
$83$ \( T - 16 \) Copy content Toggle raw display
$89$ \( T + 14 \) Copy content Toggle raw display
$97$ \( T - 6 \) Copy content Toggle raw display
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