Properties

Label 900.3.y.a
Level $900$
Weight $3$
Character orbit 900.y
Analytic conductor $24.523$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.y (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.5232237924\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 80q + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 80q + 60q^{19} + 56q^{25} - 120q^{31} + 20q^{37} - 680q^{49} - 56q^{55} - 80q^{61} - 280q^{67} - 360q^{73} + 40q^{79} + 192q^{85} + 140q^{91} - 40q^{97} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
89.1 0 0 0 −4.98948 + 0.324198i 0 11.3476i 0 0 0
89.2 0 0 0 −4.98426 0.396382i 0 2.05133i 0 0 0
89.3 0 0 0 −4.98271 0.415486i 0 3.91927i 0 0 0
89.4 0 0 0 −4.08889 2.87767i 0 4.24698i 0 0 0
89.5 0 0 0 −3.94179 + 3.07609i 0 7.41454i 0 0 0
89.6 0 0 0 −2.56782 4.29026i 0 2.96738i 0 0 0
89.7 0 0 0 −2.55393 + 4.29854i 0 5.96546i 0 0 0
89.8 0 0 0 −1.41055 + 4.79691i 0 7.51506i 0 0 0
89.9 0 0 0 −0.741250 4.94475i 0 10.0354i 0 0 0
89.10 0 0 0 −0.657760 + 4.95655i 0 12.7771i 0 0 0
89.11 0 0 0 0.657760 4.95655i 0 12.7771i 0 0 0
89.12 0 0 0 0.741250 + 4.94475i 0 10.0354i 0 0 0
89.13 0 0 0 1.41055 4.79691i 0 7.51506i 0 0 0
89.14 0 0 0 2.55393 4.29854i 0 5.96546i 0 0 0
89.15 0 0 0 2.56782 + 4.29026i 0 2.96738i 0 0 0
89.16 0 0 0 3.94179 3.07609i 0 7.41454i 0 0 0
89.17 0 0 0 4.08889 + 2.87767i 0 4.24698i 0 0 0
89.18 0 0 0 4.98271 + 0.415486i 0 3.91927i 0 0 0
89.19 0 0 0 4.98426 + 0.396382i 0 2.05133i 0 0 0
89.20 0 0 0 4.98948 0.324198i 0 11.3476i 0 0 0
See all 80 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 809.20
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
25.e even 10 1 inner
75.h odd 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 900.3.y.a 80
3.b odd 2 1 inner 900.3.y.a 80
25.e even 10 1 inner 900.3.y.a 80
75.h odd 10 1 inner 900.3.y.a 80
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
900.3.y.a 80 1.a even 1 1 trivial
900.3.y.a 80 3.b odd 2 1 inner
900.3.y.a 80 25.e even 10 1 inner
900.3.y.a 80 75.h odd 10 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(900, [\chi])\).