Properties

Label 1800.2.a.t
Level 1800
Weight 2
Character orbit 1800.a
Self dual yes
Analytic conductor 14.373
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.3730723638\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 600)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 3q^{7} + O(q^{10}) \) \( q + 3q^{7} - 2q^{11} - 3q^{13} - 6q^{17} - 7q^{19} - 6q^{23} + 2q^{29} - 5q^{31} + 10q^{37} - 12q^{41} + 3q^{43} + 10q^{47} + 2q^{49} + 6q^{59} - 13q^{61} + 7q^{67} + 4q^{71} - 6q^{73} - 6q^{77} - 8q^{79} + 6q^{83} - 16q^{89} - 9q^{91} - 7q^{97} + O(q^{100}) \)

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 0 0 0 0 3.00000 0 0 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 1800.2.a.t 1
3.b odd 2 1 600.2.a.i yes 1
4.b odd 2 1 3600.2.a.i 1
5.b even 2 1 1800.2.a.e 1
5.c odd 4 2 1800.2.f.e 2
12.b even 2 1 1200.2.a.b 1
15.d odd 2 1 600.2.a.b 1
15.e even 4 2 600.2.f.d 2
20.d odd 2 1 3600.2.a.bl 1
20.e even 4 2 3600.2.f.o 2
24.f even 2 1 4800.2.a.bs 1
24.h odd 2 1 4800.2.a.bc 1
60.h even 2 1 1200.2.a.q 1
60.l odd 4 2 1200.2.f.c 2
120.i odd 2 1 4800.2.a.bp 1
120.m even 2 1 4800.2.a.bd 1
120.q odd 4 2 4800.2.f.z 2
120.w even 4 2 4800.2.f.k 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
600.2.a.b 1 15.d odd 2 1
600.2.a.i yes 1 3.b odd 2 1
600.2.f.d 2 15.e even 4 2
1200.2.a.b 1 12.b even 2 1
1200.2.a.q 1 60.h even 2 1
1200.2.f.c 2 60.l odd 4 2
1800.2.a.e 1 5.b even 2 1
1800.2.a.t 1 1.a even 1 1 trivial
1800.2.f.e 2 5.c odd 4 2
3600.2.a.i 1 4.b odd 2 1
3600.2.a.bl 1 20.d odd 2 1
3600.2.f.o 2 20.e even 4 2
4800.2.a.bc 1 24.h odd 2 1
4800.2.a.bd 1 120.m even 2 1
4800.2.a.bp 1 120.i odd 2 1
4800.2.a.bs 1 24.f even 2 1
4800.2.f.k 2 120.w even 4 2
4800.2.f.z 2 120.q odd 4 2

Atkin-Lehner signs

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

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1800))\):

\( T_{7} - 3 \)
\( T_{11} + 2 \)
\( T_{13} + 3 \)