Properties

Label 124.5.o.a
Level $124$
Weight $5$
Character orbit 124.o
Analytic conductor $12.818$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 124.o (of order \(30\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.8178754224\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(11\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9} - 42 q^{11} + 6 q^{13} + 665 q^{15} - 585 q^{17} - 153 q^{19} - 402 q^{21} - 1365 q^{23} - 5933 q^{25} - 9225 q^{27} - 1140 q^{29} + 117 q^{31} + 5151 q^{33} + 2898 q^{35} + 6594 q^{37} + 3173 q^{39} - 9393 q^{41} - 5322 q^{43} + 2010 q^{45} - 5112 q^{47} - 5210 q^{49} - 1829 q^{51} + 7395 q^{53} + 10585 q^{55} + 40485 q^{57} + 5625 q^{59} - 14954 q^{63} - 17094 q^{65} + 8909 q^{67} - 35370 q^{69} - 11811 q^{71} - 22105 q^{73} + 79377 q^{75} + 71490 q^{77} + 219 q^{79} - 5422 q^{81} + 10545 q^{83} - 53630 q^{85} + 13732 q^{87} - 40305 q^{89} + 42760 q^{91} - 1028 q^{93} + 62319 q^{95} + 35201 q^{97} + 16197 q^{99}+O(q^{100}) \) 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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
13.1 0 −7.03588 15.8028i 0 11.6814 + 20.2328i 0 −44.3877 49.2975i 0 −146.027 + 162.179i 0
13.2 0 −4.27952 9.61195i 0 3.43229 + 5.94490i 0 43.1077 + 47.8760i 0 −19.8758 + 22.0743i 0
13.3 0 −3.80107 8.53733i 0 −24.2686 42.0344i 0 −45.8945 50.9710i 0 −4.23837 + 4.70719i 0
13.4 0 −3.55268 7.97945i 0 −12.5017 21.6535i 0 17.4290 + 19.3568i 0 3.14955 3.49793i 0
13.5 0 −2.05606 4.61799i 0 6.14252 + 10.6392i 0 −13.6062 15.1112i 0 37.1012 41.2050i 0
13.6 0 1.38100 + 3.10178i 0 21.1680 + 36.6640i 0 12.2350 + 13.5884i 0 46.4857 51.6276i 0
13.7 0 1.72821 + 3.88162i 0 7.33763 + 12.7091i 0 −56.6769 62.9461i 0 42.1193 46.7783i 0
13.8 0 2.78469 + 6.25452i 0 −8.17325 14.1565i 0 16.4871 + 18.3107i 0 22.8350 25.3609i 0
13.9 0 3.39298 + 7.62076i 0 −15.4750 26.8035i 0 11.7917 + 13.0960i 0 7.63586 8.48048i 0
13.10 0 6.41385 + 14.4058i 0 12.5721 + 21.7754i 0 47.7518 + 53.0337i 0 −112.189 + 124.598i 0
13.11 0 6.77929 + 15.2265i 0 −2.22895 3.86066i 0 −53.4498 59.3620i 0 −131.689 + 146.256i 0
17.1 0 −11.7991 10.6240i 0 −0.510945 + 0.884982i 0 −6.63263 + 63.1052i 0 17.8835 + 170.150i 0
17.2 0 −8.97256 8.07893i 0 −1.91809 + 3.32223i 0 7.45792 70.9574i 0 6.77094 + 64.4212i 0
17.3 0 −5.42475 4.88447i 0 22.7477 39.4001i 0 0.180678 1.71904i 0 −2.89691 27.5623i 0
17.4 0 −3.98717 3.59007i 0 −24.6255 + 42.6526i 0 3.33835 31.7622i 0 −5.45784 51.9279i 0
17.5 0 −3.07010 2.76433i 0 −0.342480 + 0.593193i 0 −3.29625 + 31.3617i 0 −6.68282 63.5828i 0
17.6 0 1.30013 + 1.17065i 0 −13.3049 + 23.0447i 0 −8.54338 + 81.2848i 0 −8.14687 77.5123i 0
17.7 0 3.32625 + 2.99497i 0 10.0265 17.3665i 0 0.840912 8.00074i 0 −6.37270 60.6322i 0
17.8 0 6.29564 + 5.66862i 0 −3.44300 + 5.96345i 0 −1.27725 + 12.1523i 0 −0.964961 9.18099i 0
17.9 0 6.45809 + 5.81489i 0 4.44246 7.69456i 0 6.90219 65.6700i 0 −0.572828 5.45009i 0
See all 88 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 117.11
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
31.h odd 30 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 124.5.o.a 88
31.h odd 30 1 inner 124.5.o.a 88
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
124.5.o.a 88 1.a even 1 1 trivial
124.5.o.a 88 31.h odd 30 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(124, [\chi])\).