Properties

Label 7623.2.a.g
Level 7623
Weight 2
Character orbit 7623.a
Self dual yes
Analytic conductor 60.870
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 7623.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(60.8699614608\)
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

\(f(q)\) \(=\) \( q - q^{2} - q^{4} + 2q^{5} + q^{7} + 3q^{8} + O(q^{10}) \) \( q - q^{2} - q^{4} + 2q^{5} + q^{7} + 3q^{8} - 2q^{10} + 2q^{13} - q^{14} - q^{16} - 6q^{17} - 4q^{19} - 2q^{20} - q^{25} - 2q^{26} - q^{28} - 2q^{29} - 5q^{32} + 6q^{34} + 2q^{35} + 6q^{37} + 4q^{38} + 6q^{40} + 2q^{41} + 4q^{43} + q^{49} + q^{50} - 2q^{52} - 6q^{53} + 3q^{56} + 2q^{58} - 12q^{59} + 2q^{61} + 7q^{64} + 4q^{65} + 4q^{67} + 6q^{68} - 2q^{70} + 6q^{73} - 6q^{74} + 4q^{76} + 16q^{79} - 2q^{80} - 2q^{82} - 12q^{83} - 12q^{85} - 4q^{86} + 14q^{89} + 2q^{91} - 8q^{95} + 18q^{97} - q^{98} + O(q^{100}) \)

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 0 −1.00000 2.00000 0 1.00000 3.00000 0 −2.00000
\(n\): 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 7623.2.a.g 1
3.b odd 2 1 2541.2.a.j 1
11.b odd 2 1 63.2.a.a 1
33.d even 2 1 21.2.a.a 1
44.c even 2 1 1008.2.a.l 1
55.d odd 2 1 1575.2.a.c 1
55.e even 4 2 1575.2.d.a 2
77.b even 2 1 441.2.a.f 1
77.h odd 6 2 441.2.e.a 2
77.i even 6 2 441.2.e.b 2
88.b odd 2 1 4032.2.a.h 1
88.g even 2 1 4032.2.a.k 1
99.g even 6 2 567.2.f.g 2
99.h odd 6 2 567.2.f.b 2
132.d odd 2 1 336.2.a.a 1
165.d even 2 1 525.2.a.d 1
165.l odd 4 2 525.2.d.a 2
231.h odd 2 1 147.2.a.a 1
231.k odd 6 2 147.2.e.c 2
231.l even 6 2 147.2.e.b 2
264.m even 2 1 1344.2.a.g 1
264.p odd 2 1 1344.2.a.s 1
308.g odd 2 1 7056.2.a.p 1
429.e even 2 1 3549.2.a.c 1
528.s odd 4 2 5376.2.c.l 2
528.x even 4 2 5376.2.c.r 2
561.h even 2 1 6069.2.a.b 1
627.b odd 2 1 7581.2.a.d 1
660.g odd 2 1 8400.2.a.bn 1
924.n even 2 1 2352.2.a.v 1
924.y even 6 2 2352.2.q.e 2
924.z odd 6 2 2352.2.q.x 2
1155.e odd 2 1 3675.2.a.n 1
1848.b odd 2 1 9408.2.a.bv 1
1848.e even 2 1 9408.2.a.m 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
21.2.a.a 1 33.d even 2 1
63.2.a.a 1 11.b odd 2 1
147.2.a.a 1 231.h odd 2 1
147.2.e.b 2 231.l even 6 2
147.2.e.c 2 231.k odd 6 2
336.2.a.a 1 132.d odd 2 1
441.2.a.f 1 77.b even 2 1
441.2.e.a 2 77.h odd 6 2
441.2.e.b 2 77.i even 6 2
525.2.a.d 1 165.d even 2 1
525.2.d.a 2 165.l odd 4 2
567.2.f.b 2 99.h odd 6 2
567.2.f.g 2 99.g even 6 2
1008.2.a.l 1 44.c even 2 1
1344.2.a.g 1 264.m even 2 1
1344.2.a.s 1 264.p odd 2 1
1575.2.a.c 1 55.d odd 2 1
1575.2.d.a 2 55.e even 4 2
2352.2.a.v 1 924.n even 2 1
2352.2.q.e 2 924.y even 6 2
2352.2.q.x 2 924.z odd 6 2
2541.2.a.j 1 3.b odd 2 1
3549.2.a.c 1 429.e even 2 1
3675.2.a.n 1 1155.e odd 2 1
4032.2.a.h 1 88.b odd 2 1
4032.2.a.k 1 88.g even 2 1
5376.2.c.l 2 528.s odd 4 2
5376.2.c.r 2 528.x even 4 2
6069.2.a.b 1 561.h even 2 1
7056.2.a.p 1 308.g odd 2 1
7581.2.a.d 1 627.b odd 2 1
7623.2.a.g 1 1.a even 1 1 trivial
8400.2.a.bn 1 660.g odd 2 1
9408.2.a.m 1 1848.e even 2 1
9408.2.a.bv 1 1848.b odd 2 1

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(7\) \(-1\)
\(11\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7623))\):

\( T_{2} + 1 \)
\( T_{5} - 2 \)
\( T_{13} - 2 \)