Properties

Label 1900.3.g.d
Level $1900$
Weight $3$
Character orbit 1900.g
Analytic conductor $51.771$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1900.g (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(51.7712502285\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 28q + 104q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 28q + 104q^{9} + 8q^{11} + 58q^{19} + 112q^{39} - 276q^{49} - 100q^{61} + 132q^{81} - 184q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
949.1 0 −5.26531 0 0 0 12.1735i 0 18.7235 0
949.2 0 −5.26531 0 0 0 12.1735i 0 18.7235 0
949.3 0 −4.84257 0 0 0 6.85668i 0 14.4504 0
949.4 0 −4.84257 0 0 0 6.85668i 0 14.4504 0
949.5 0 −4.58743 0 0 0 1.52935i 0 12.0445 0
949.6 0 −4.58743 0 0 0 1.52935i 0 12.0445 0
949.7 0 −2.93221 0 0 0 5.62705i 0 −0.402160 0
949.8 0 −2.93221 0 0 0 5.62705i 0 −0.402160 0
949.9 0 −2.16913 0 0 0 8.18099i 0 −4.29489 0
949.10 0 −2.16913 0 0 0 8.18099i 0 −4.29489 0
949.11 0 −1.84332 0 0 0 10.5375i 0 −5.60216 0
949.12 0 −1.84332 0 0 0 10.5375i 0 −5.60216 0
949.13 0 −0.284180 0 0 0 2.19606i 0 −8.91924 0
949.14 0 −0.284180 0 0 0 2.19606i 0 −8.91924 0
949.15 0 0.284180 0 0 0 2.19606i 0 −8.91924 0
949.16 0 0.284180 0 0 0 2.19606i 0 −8.91924 0
949.17 0 1.84332 0 0 0 10.5375i 0 −5.60216 0
949.18 0 1.84332 0 0 0 10.5375i 0 −5.60216 0
949.19 0 2.16913 0 0 0 8.18099i 0 −4.29489 0
949.20 0 2.16913 0 0 0 8.18099i 0 −4.29489 0
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 949.28
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
19.b odd 2 1 inner
95.d odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1900.3.g.d 28
5.b even 2 1 inner 1900.3.g.d 28
5.c odd 4 1 1900.3.e.g 14
5.c odd 4 1 1900.3.e.h yes 14
19.b odd 2 1 inner 1900.3.g.d 28
95.d odd 2 1 inner 1900.3.g.d 28
95.g even 4 1 1900.3.e.g 14
95.g even 4 1 1900.3.e.h yes 14
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1900.3.e.g 14 5.c odd 4 1
1900.3.e.g 14 95.g even 4 1
1900.3.e.h yes 14 5.c odd 4 1
1900.3.e.h yes 14 95.g even 4 1
1900.3.g.d 28 1.a even 1 1 trivial
1900.3.g.d 28 5.b even 2 1 inner
1900.3.g.d 28 19.b odd 2 1 inner
1900.3.g.d 28 95.d odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{14} - 89 T_{3}^{12} + 3026 T_{3}^{10} - 49092 T_{3}^{8} + 390297 T_{3}^{6} - 1440495 T_{3}^{4} + 1994425 T_{3}^{2} - 151875 \) acting on \(S_{3}^{\mathrm{new}}(1900, [\chi])\).