Properties

Label 1840.3.c.b
Level $1840$
Weight $3$
Character orbit 1840.c
Analytic conductor $50.136$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1840.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(50.1363686423\)
Analytic rank: \(0\)
Dimension: \(56\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 56q - 120q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 56q - 120q^{9} - 56q^{13} - 96q^{17} + 104q^{21} + 280q^{25} - 76q^{29} + 240q^{33} - 88q^{37} - 76q^{41} - 356q^{49} - 88q^{53} - 256q^{57} + 376q^{61} + 120q^{65} + 192q^{73} - 168q^{77} - 392q^{81} - 60q^{85} + 368q^{89} + 216q^{93} + 264q^{97} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1151.1 0 5.32909i 0 −2.23607 0 11.3168i 0 −19.3992 0
1151.2 0 5.24733i 0 2.23607 0 2.50180i 0 −18.5344 0
1151.3 0 5.22053i 0 −2.23607 0 0.326739i 0 −18.2539 0
1151.4 0 5.16732i 0 2.23607 0 5.17862i 0 −17.7012 0
1151.5 0 4.56892i 0 2.23607 0 2.46851i 0 −11.8750 0
1151.6 0 4.48524i 0 −2.23607 0 1.27380i 0 −11.1174 0
1151.7 0 4.41875i 0 2.23607 0 4.25333i 0 −10.5254 0
1151.8 0 4.39101i 0 −2.23607 0 9.33722i 0 −10.2810 0
1151.9 0 4.12760i 0 2.23607 0 9.93424i 0 −8.03709 0
1151.10 0 3.65039i 0 −2.23607 0 6.59183i 0 −4.32537 0
1151.11 0 3.56153i 0 −2.23607 0 11.6857i 0 −3.68450 0
1151.12 0 3.51586i 0 2.23607 0 8.23373i 0 −3.36124 0
1151.13 0 3.44787i 0 −2.23607 0 10.1149i 0 −2.88780 0
1151.14 0 3.31883i 0 −2.23607 0 7.99843i 0 −2.01461 0
1151.15 0 3.27428i 0 2.23607 0 5.54665i 0 −1.72088 0
1151.16 0 2.96566i 0 2.23607 0 5.20785i 0 0.204832 0
1151.17 0 2.55509i 0 2.23607 0 8.88631i 0 2.47152 0
1151.18 0 2.47004i 0 −2.23607 0 4.00490i 0 2.89892 0
1151.19 0 1.90665i 0 −2.23607 0 1.76313i 0 5.36467 0
1151.20 0 1.78315i 0 2.23607 0 11.2760i 0 5.82039 0
See all 56 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1151.56
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
4.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1840.3.c.b 56
4.b odd 2 1 inner 1840.3.c.b 56
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1840.3.c.b 56 1.a even 1 1 trivial
1840.3.c.b 56 4.b odd 2 1 inner