Properties

Label 5625.2.a.bf
Level $5625$
Weight $2$
Character orbit 5625.a
Self dual yes
Analytic conductor $44.916$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 5625 = 3^{2} \cdot 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5625.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.9158511370\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 225)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 32 q^{4}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 32 q^{4} + 56 q^{16} + 36 q^{19} + 52 q^{31} + 60 q^{34} + 60 q^{46} + 72 q^{49} + 68 q^{61} + 108 q^{64} + 88 q^{76} + 84 q^{79} + 80 q^{91} + 100 q^{94}+O(q^{100}) \) 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.

Label \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.64061 0 4.97280 0 0 −4.34551 −7.84999 0 0
1.2 −2.64061 0 4.97280 0 0 4.34551 −7.84999 0 0
1.3 −2.61097 0 4.81718 0 0 −1.21018 −7.35558 0 0
1.4 −2.61097 0 4.81718 0 0 1.21018 −7.35558 0 0
1.5 −1.71285 0 0.933844 0 0 −3.13880 1.82616 0 0
1.6 −1.71285 0 0.933844 0 0 3.13880 1.82616 0 0
1.7 −1.54077 0 0.373979 0 0 −3.37636 2.50533 0 0
1.8 −1.54077 0 0.373979 0 0 3.37636 2.50533 0 0
1.9 −0.899356 0 −1.19116 0 0 −3.86000 2.86999 0 0
1.10 −0.899356 0 −1.19116 0 0 3.86000 2.86999 0 0
1.11 −0.305545 0 −1.90664 0 0 −1.87098 1.19366 0 0
1.12 −0.305545 0 −1.90664 0 0 1.87098 1.19366 0 0
1.13 0.305545 0 −1.90664 0 0 −1.87098 −1.19366 0 0
1.14 0.305545 0 −1.90664 0 0 1.87098 −1.19366 0 0
1.15 0.899356 0 −1.19116 0 0 −3.86000 −2.86999 0 0
1.16 0.899356 0 −1.19116 0 0 3.86000 −2.86999 0 0
1.17 1.54077 0 0.373979 0 0 −3.37636 −2.50533 0 0
1.18 1.54077 0 0.373979 0 0 3.37636 −2.50533 0 0
1.19 1.71285 0 0.933844 0 0 −3.13880 −1.82616 0 0
1.20 1.71285 0 0.933844 0 0 3.13880 −1.82616 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
Significant digits:
Format:

Atkin-Lehner signs

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

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5625.2.a.bf 24
3.b odd 2 1 inner 5625.2.a.bf 24
5.b even 2 1 inner 5625.2.a.bf 24
15.d odd 2 1 inner 5625.2.a.bf 24
25.f odd 20 2 225.2.m.c 24
75.l even 20 2 225.2.m.c 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
225.2.m.c 24 25.f odd 20 2
225.2.m.c 24 75.l even 20 2
5625.2.a.bf 24 1.a even 1 1 trivial
5625.2.a.bf 24 3.b odd 2 1 inner
5625.2.a.bf 24 5.b even 2 1 inner
5625.2.a.bf 24 15.d odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5625))\):

\( T_{2}^{12} - 20T_{2}^{10} + 145T_{2}^{8} - 465T_{2}^{6} + 655T_{2}^{4} - 325T_{2}^{2} + 25 \) Copy content Toggle raw display
\( T_{7}^{12} - 60T_{7}^{10} + 1390T_{7}^{8} - 15575T_{7}^{6} + 85825T_{7}^{4} - 207000T_{7}^{2} + 162000 \) Copy content Toggle raw display