Properties

Label 7514.2.a.i
Level $7514$
Weight $2$
Character orbit 7514.a
Self dual yes
Analytic conductor $60.000$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7514,2,Mod(1,7514)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7514, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7514.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7514 = 2 \cdot 13 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7514.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(59.9995920788\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 26)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q + q^{2} + 3 q^{3} + q^{4} + q^{5} + 3 q^{6} - q^{7} + q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + 3 q^{3} + q^{4} + q^{5} + 3 q^{6} - q^{7} + q^{8} + 6 q^{9} + q^{10} + 2 q^{11} + 3 q^{12} - q^{13} - q^{14} + 3 q^{15} + q^{16} + 6 q^{18} + 6 q^{19} + q^{20} - 3 q^{21} + 2 q^{22} + 4 q^{23} + 3 q^{24} - 4 q^{25} - q^{26} + 9 q^{27} - q^{28} - 2 q^{29} + 3 q^{30} - 4 q^{31} + q^{32} + 6 q^{33} - q^{35} + 6 q^{36} - 3 q^{37} + 6 q^{38} - 3 q^{39} + q^{40} - 3 q^{42} - 5 q^{43} + 2 q^{44} + 6 q^{45} + 4 q^{46} + 13 q^{47} + 3 q^{48} - 6 q^{49} - 4 q^{50} - q^{52} + 12 q^{53} + 9 q^{54} + 2 q^{55} - q^{56} + 18 q^{57} - 2 q^{58} - 10 q^{59} + 3 q^{60} + 8 q^{61} - 4 q^{62} - 6 q^{63} + q^{64} - q^{65} + 6 q^{66} - 2 q^{67} + 12 q^{69} - q^{70} + 5 q^{71} + 6 q^{72} + 10 q^{73} - 3 q^{74} - 12 q^{75} + 6 q^{76} - 2 q^{77} - 3 q^{78} + 4 q^{79} + q^{80} + 9 q^{81} - 3 q^{84} - 5 q^{86} - 6 q^{87} + 2 q^{88} + 6 q^{89} + 6 q^{90} + q^{91} + 4 q^{92} - 12 q^{93} + 13 q^{94} + 6 q^{95} + 3 q^{96} - 14 q^{97} - 6 q^{98} + 12 q^{99}+O(q^{100}) \) 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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
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 3.00000 1.00000 1.00000 3.00000 −1.00000 1.00000 6.00000 1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(13\) \( +1 \)
\(17\) \( +1 \)

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 7514.2.a.i 1
17.b even 2 1 26.2.a.b 1
51.c odd 2 1 234.2.a.b 1
68.d odd 2 1 208.2.a.d 1
85.c even 2 1 650.2.a.g 1
85.g odd 4 2 650.2.b.a 2
119.d odd 2 1 1274.2.a.o 1
119.h odd 6 2 1274.2.f.a 2
119.j even 6 2 1274.2.f.l 2
136.e odd 2 1 832.2.a.a 1
136.h even 2 1 832.2.a.j 1
153.h even 6 2 2106.2.e.h 2
153.i odd 6 2 2106.2.e.t 2
187.b odd 2 1 3146.2.a.a 1
204.h even 2 1 1872.2.a.m 1
221.b even 2 1 338.2.a.a 1
221.g odd 4 2 338.2.b.a 2
221.l even 6 2 338.2.c.c 2
221.n even 6 2 338.2.c.g 2
221.w odd 12 4 338.2.e.d 4
255.h odd 2 1 5850.2.a.bn 1
255.o even 4 2 5850.2.e.v 2
272.k odd 4 2 3328.2.b.k 2
272.r even 4 2 3328.2.b.g 2
323.c odd 2 1 9386.2.a.f 1
340.d odd 2 1 5200.2.a.c 1
408.b odd 2 1 7488.2.a.w 1
408.h even 2 1 7488.2.a.v 1
663.g odd 2 1 3042.2.a.l 1
663.q even 4 2 3042.2.b.f 2
884.h odd 2 1 2704.2.a.n 1
884.t even 4 2 2704.2.f.j 2
1105.h even 2 1 8450.2.a.y 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
26.2.a.b 1 17.b even 2 1
208.2.a.d 1 68.d odd 2 1
234.2.a.b 1 51.c odd 2 1
338.2.a.a 1 221.b even 2 1
338.2.b.a 2 221.g odd 4 2
338.2.c.c 2 221.l even 6 2
338.2.c.g 2 221.n even 6 2
338.2.e.d 4 221.w odd 12 4
650.2.a.g 1 85.c even 2 1
650.2.b.a 2 85.g odd 4 2
832.2.a.a 1 136.e odd 2 1
832.2.a.j 1 136.h even 2 1
1274.2.a.o 1 119.d odd 2 1
1274.2.f.a 2 119.h odd 6 2
1274.2.f.l 2 119.j even 6 2
1872.2.a.m 1 204.h even 2 1
2106.2.e.h 2 153.h even 6 2
2106.2.e.t 2 153.i odd 6 2
2704.2.a.n 1 884.h odd 2 1
2704.2.f.j 2 884.t even 4 2
3042.2.a.l 1 663.g odd 2 1
3042.2.b.f 2 663.q even 4 2
3146.2.a.a 1 187.b odd 2 1
3328.2.b.g 2 272.r even 4 2
3328.2.b.k 2 272.k odd 4 2
5200.2.a.c 1 340.d odd 2 1
5850.2.a.bn 1 255.h odd 2 1
5850.2.e.v 2 255.o even 4 2
7488.2.a.v 1 408.h even 2 1
7488.2.a.w 1 408.b odd 2 1
7514.2.a.i 1 1.a even 1 1 trivial
8450.2.a.y 1 1105.h even 2 1
9386.2.a.f 1 323.c odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7514))\):

\( T_{3} - 3 \) Copy content Toggle raw display
\( T_{5} - 1 \) Copy content Toggle raw display
\( T_{7} + 1 \) Copy content Toggle raw display

Hecke characteristic polynomials

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