Properties

Label 5.27.c.a
Level $5$
Weight $27$
Character orbit 5.c
Analytic conductor $21.415$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 27 \)
Character orbit: \([\chi]\) \(=\) 5.c (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.4146460365\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8190 q^{2} + 1867680 q^{3} - 140947920 q^{5} - 3382472712 q^{6} - 99234643200 q^{7} - 2004366809340 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8190 q^{2} + 1867680 q^{3} - 140947920 q^{5} - 3382472712 q^{6} - 99234643200 q^{7} - 2004366809340 q^{8} - 1486502924970 q^{10} - 60046450487712 q^{11} + 474303804173880 q^{12} - 175933888149240 q^{13} + 81\!\cdots\!60 q^{15}+ \cdots + 37\!\cdots\!90 q^{98}+O(q^{100}) \) 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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2.1 −9199.72 9199.72i 1.92148e6 1.92148e6i 1.02161e8i 1.20945e9 + 1.65366e8i −3.53542e10 2.78396e10 + 2.78396e10i 3.22468e11 3.22468e11i 4.84231e12i −9.60528e12 1.26479e13i
2.2 −8967.06 8967.06i −1.25875e6 + 1.25875e6i 9.37076e7i 2.09822e8 + 1.20254e9i 2.25746e10 5.31741e10 + 5.31741e10i 2.38512e11 2.38512e11i 6.27038e11i 8.90172e12 1.26647e13i
2.3 −8964.00 8964.00i −84346.8 + 84346.8i 9.35978e7i −6.90551e8 1.00661e9i 1.51217e9 −8.97185e10 8.97185e10i 2.37446e11 2.37446e11i 2.52764e12i −2.83311e12 + 1.52133e13i
2.4 −3781.13 3781.13i 1.14164e6 1.14164e6i 3.85150e7i −1.21579e9 + 1.09366e8i −8.63336e9 1.09895e11 + 1.09895e11i −3.99377e11 + 3.99377e11i 6.48110e10i 5.01060e12 + 4.18355e12i
2.5 −2621.08 2621.08i −823115. + 823115.i 5.33688e7i 9.07026e8 8.16957e8i 4.31489e9 3.09387e10 + 3.09387e10i −3.15781e11 + 3.15781e11i 1.18683e12i −4.51869e12 2.36078e11i
2.6 −1256.27 1256.27i 745542. 745542.i 6.39524e7i 1.73270e8 + 1.20834e9i −1.87321e9 −1.19717e11 1.19717e11i −1.64649e11 + 1.64649e11i 1.43020e12i 1.30034e12 1.73568e12i
2.7 584.877 + 584.877i −2.17135e6 + 2.17135e6i 6.64247e7i −1.21727e9 + 9.14507e7i −2.53995e9 −4.74948e10 4.74948e10i 7.81007e10 7.81007e10i 6.88765e12i −7.65443e11 6.58468e11i
2.8 4190.94 + 4190.94i 1.61385e6 1.61385e6i 3.19809e7i 6.93244e8 1.00475e9i 1.35270e10 −1.14147e10 1.14147e10i 4.15279e11 4.15279e11i 2.66713e12i 7.11620e12 1.30552e12i
2.9 6254.19 + 6254.19i −748889. + 748889.i 1.11210e7i 7.43869e8 + 9.67872e8i −9.36739e9 5.67260e10 + 5.67260e10i 3.50159e11 3.50159e11i 1.42020e12i −1.40096e12 + 1.07056e13i
2.10 6346.94 + 6346.94i 105171. 105171.i 1.34583e7i −1.17280e9 3.38608e8i 1.33503e9 1.02411e10 + 1.02411e10i 3.40516e11 3.40516e11i 2.51974e12i −5.29457e12 9.59281e12i
2.11 10388.0 + 10388.0i −1.27015e6 + 1.27015e6i 1.48710e8i 4.12302e8 1.14897e9i −2.63886e10 −8.34659e10 8.34659e10i −8.47671e11 + 8.47671e11i 6.84708e11i 1.62184e13 7.65243e12i
2.12 11119.4 + 11119.4i 1.76277e6 1.76277e6i 1.80172e8i −1.23038e8 + 1.21449e9i 3.92017e10 1.33787e10 + 1.33787e10i −1.25719e12 + 1.25719e12i 3.67282e12i −1.48724e13 + 1.21362e13i
3.1 −9199.72 + 9199.72i 1.92148e6 + 1.92148e6i 1.02161e8i 1.20945e9 1.65366e8i −3.53542e10 2.78396e10 2.78396e10i 3.22468e11 + 3.22468e11i 4.84231e12i −9.60528e12 + 1.26479e13i
3.2 −8967.06 + 8967.06i −1.25875e6 1.25875e6i 9.37076e7i 2.09822e8 1.20254e9i 2.25746e10 5.31741e10 5.31741e10i 2.38512e11 + 2.38512e11i 6.27038e11i 8.90172e12 + 1.26647e13i
3.3 −8964.00 + 8964.00i −84346.8 84346.8i 9.35978e7i −6.90551e8 + 1.00661e9i 1.51217e9 −8.97185e10 + 8.97185e10i 2.37446e11 + 2.37446e11i 2.52764e12i −2.83311e12 1.52133e13i
3.4 −3781.13 + 3781.13i 1.14164e6 + 1.14164e6i 3.85150e7i −1.21579e9 1.09366e8i −8.63336e9 1.09895e11 1.09895e11i −3.99377e11 3.99377e11i 6.48110e10i 5.01060e12 4.18355e12i
3.5 −2621.08 + 2621.08i −823115. 823115.i 5.33688e7i 9.07026e8 + 8.16957e8i 4.31489e9 3.09387e10 3.09387e10i −3.15781e11 3.15781e11i 1.18683e12i −4.51869e12 + 2.36078e11i
3.6 −1256.27 + 1256.27i 745542. + 745542.i 6.39524e7i 1.73270e8 1.20834e9i −1.87321e9 −1.19717e11 + 1.19717e11i −1.64649e11 1.64649e11i 1.43020e12i 1.30034e12 + 1.73568e12i
3.7 584.877 584.877i −2.17135e6 2.17135e6i 6.64247e7i −1.21727e9 9.14507e7i −2.53995e9 −4.74948e10 + 4.74948e10i 7.81007e10 + 7.81007e10i 6.88765e12i −7.65443e11 + 6.58468e11i
3.8 4190.94 4190.94i 1.61385e6 + 1.61385e6i 3.19809e7i 6.93244e8 + 1.00475e9i 1.35270e10 −1.14147e10 + 1.14147e10i 4.15279e11 + 4.15279e11i 2.66713e12i 7.11620e12 + 1.30552e12i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 3.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5.27.c.a 24
5.b even 2 1 25.27.c.b 24
5.c odd 4 1 inner 5.27.c.a 24
5.c odd 4 1 25.27.c.b 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5.27.c.a 24 1.a even 1 1 trivial
5.27.c.a 24 5.c odd 4 1 inner
25.27.c.b 24 5.b even 2 1
25.27.c.b 24 5.c odd 4 1

Hecke kernels

This newform subspace is the entire newspace \(S_{27}^{\mathrm{new}}(5, [\chi])\).