Properties

Label 124.3.o.a
Level $124$
Weight $3$
Character orbit 124.o
Analytic conductor $3.379$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 124.o (of order \(30\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.37875527807\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(5\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9} + 2 q^{11} - 18 q^{13} + 35 q^{15} + 25 q^{17} - 11 q^{19} + 54 q^{21} + 25 q^{23} - 75 q^{25} + 225 q^{27} + 20 q^{29} + 59 q^{31} - 303 q^{33} - 66 q^{35} - 222 q^{37} - 169 q^{39} + q^{41} + 122 q^{43} + 54 q^{45} - 120 q^{47} - 118 q^{49} - 515 q^{51} + 61 q^{53} - 121 q^{55} - 201 q^{57} - 257 q^{59} - 158 q^{63} + 182 q^{65} - q^{67} + 510 q^{69} + 459 q^{71} + 253 q^{73} + 651 q^{75} + 670 q^{77} + 385 q^{79} + 974 q^{81} + 375 q^{83} - 370 q^{85} - 344 q^{87} + 245 q^{89} + 960 q^{91} - 212 q^{93} - 851 q^{95} - 797 q^{97} - 21 q^{99}+O(q^{100}) \) 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 −2.39545 5.38028i 0 −3.34056 5.78602i 0 5.42242 + 6.02221i 0 −17.1870 + 19.0881i 0
13.2 0 −1.21706 2.73355i 0 4.66965 + 8.08807i 0 2.28779 + 2.54085i 0 0.0310810 0.0345190i 0
13.3 0 −0.282508 0.634523i 0 −1.46593 2.53906i 0 −4.75907 5.28548i 0 5.69937 6.32979i 0
13.4 0 0.684837 + 1.53817i 0 −1.53767 2.66333i 0 8.16234 + 9.06519i 0 4.12521 4.58151i 0
13.5 0 1.73203 + 3.89021i 0 1.98810 + 3.44350i 0 −1.12705 1.25172i 0 −6.11161 + 6.78763i 0
17.1 0 −3.24569 2.92243i 0 −2.16722 + 3.75373i 0 −0.282561 + 2.68839i 0 1.05314 + 10.0199i 0
17.2 0 −1.31136 1.18075i 0 2.72362 4.71744i 0 −0.568373 + 5.40771i 0 −0.615273 5.85393i 0
17.3 0 −0.812474 0.731555i 0 0.0996144 0.172537i 0 0.900672 8.56932i 0 −0.815815 7.76196i 0
17.4 0 2.63052 + 2.36853i 0 −1.84144 + 3.18946i 0 −0.655396 + 6.23568i 0 0.368941 + 3.51024i 0
17.5 0 3.15255 + 2.83857i 0 4.11986 7.13581i 0 1.01453 9.65264i 0 0.940339 + 8.94673i 0
21.1 0 −4.90821 + 0.515874i 0 −1.45470 2.51962i 0 7.26879 + 1.54503i 0 15.0211 3.19283i 0
21.2 0 −2.43523 + 0.255953i 0 1.56711 + 2.71432i 0 −7.68423 1.63333i 0 −2.93848 + 0.624593i 0
21.3 0 −0.0268627 + 0.00282338i 0 −4.16141 7.20777i 0 0.359013 + 0.0763106i 0 −8.80261 + 1.87105i 0
21.4 0 2.04697 0.215145i 0 2.65148 + 4.59249i 0 3.34611 + 0.711237i 0 −4.65955 + 0.990417i 0
21.5 0 5.49247 0.577282i 0 −1.34312 2.32635i 0 0.977169 + 0.207704i 0 21.0307 4.47021i 0
53.1 0 −1.10618 + 5.20417i 0 1.56007 + 2.70213i 0 −1.90607 + 0.848638i 0 −17.6379 7.85289i 0
53.2 0 −0.357501 + 1.68191i 0 −4.52206 7.83243i 0 −12.1470 + 5.40819i 0 5.52090 + 2.45806i 0
53.3 0 −0.257314 + 1.21057i 0 −1.69238 2.93128i 0 9.33225 4.15499i 0 6.82265 + 3.03764i 0
53.4 0 0.177793 0.836450i 0 3.54343 + 6.13740i 0 −3.95326 + 1.76010i 0 7.55387 + 3.36320i 0
53.5 0 0.938675 4.41612i 0 −0.896461 1.55272i 0 3.51190 1.56360i 0 −10.3991 4.62997i 0
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 117.5
Significant digits:
Format:

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 124.3.o.a 40
31.h odd 30 1 inner 124.3.o.a 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
124.3.o.a 40 1.a even 1 1 trivial
124.3.o.a 40 31.h odd 30 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(124, [\chi])\).