LMFDB - Newform 6034.2.a.n

Newspace parameters

Level:	$ N $	=	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	6034.a (trivial)

Newform invariants

Self dual:	Yes
Analytic conductor:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$24$
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) = $ $24q $ $\mathstrut -\mathstrut 24q^{2} $ $\mathstrut +\mathstrut 7q^{3} $ $\mathstrut +\mathstrut 24q^{4} $ $\mathstrut +\mathstrut 8q^{5} $ $\mathstrut -\mathstrut 7q^{6} $ $\mathstrut -\mathstrut 24q^{7} $ $\mathstrut -\mathstrut 24q^{8} $ $\mathstrut +\mathstrut 19q^{9} $ $\mathstrut -\mathstrut 8q^{10} $ $\mathstrut +\mathstrut 15q^{11} $ $\mathstrut +\mathstrut 7q^{12} $ $\mathstrut -\mathstrut 7q^{13} $ $\mathstrut +\mathstrut 24q^{14} $ $\mathstrut +\mathstrut 13q^{15} $ $\mathstrut +\mathstrut 24q^{16} $ $\mathstrut -\mathstrut 5q^{17} $ $\mathstrut -\mathstrut 19q^{18} $ $\mathstrut +\mathstrut 6q^{19} $ $\mathstrut +\mathstrut 8q^{20} $ $\mathstrut -\mathstrut 7q^{21} $ $\mathstrut -\mathstrut 15q^{22} $ $\mathstrut +\mathstrut 3q^{23} $ $\mathstrut -\mathstrut 7q^{24} $ $\mathstrut +\mathstrut 12q^{25} $ $\mathstrut +\mathstrut 7q^{26} $ $\mathstrut +\mathstrut 22q^{27} $ $\mathstrut -\mathstrut 24q^{28} $ $\mathstrut +\mathstrut 5q^{29} $ $\mathstrut -\mathstrut 13q^{30} $ $\mathstrut +\mathstrut 13q^{31} $ $\mathstrut -\mathstrut 24q^{32} $ $\mathstrut -\mathstrut 8q^{33} $ $\mathstrut +\mathstrut 5q^{34} $ $\mathstrut -\mathstrut 8q^{35} $ $\mathstrut +\mathstrut 19q^{36} $ $\mathstrut +\mathstrut 2q^{37} $ $\mathstrut -\mathstrut 6q^{38} $ $\mathstrut +\mathstrut 7q^{39} $ $\mathstrut -\mathstrut 8q^{40} $ $\mathstrut +\mathstrut 25q^{41} $ $\mathstrut +\mathstrut 7q^{42} $ $\mathstrut -\mathstrut 15q^{43} $ $\mathstrut +\mathstrut 15q^{44} $ $\mathstrut +\mathstrut 41q^{45} $ $\mathstrut -\mathstrut 3q^{46} $ $\mathstrut +\mathstrut 35q^{47} $ $\mathstrut +\mathstrut 7q^{48} $ $\mathstrut +\mathstrut 24q^{49} $ $\mathstrut -\mathstrut 12q^{50} $ $\mathstrut +\mathstrut 31q^{51} $ $\mathstrut -\mathstrut 7q^{52} $ $\mathstrut +\mathstrut 2q^{53} $ $\mathstrut -\mathstrut 22q^{54} $ $\mathstrut +\mathstrut 14q^{55} $ $\mathstrut +\mathstrut 24q^{56} $ $\mathstrut -\mathstrut 13q^{57} $ $\mathstrut -\mathstrut 5q^{58} $ $\mathstrut +\mathstrut 35q^{59} $ $\mathstrut +\mathstrut 13q^{60} $ $\mathstrut -\mathstrut 7q^{61} $ $\mathstrut -\mathstrut 13q^{62} $ $\mathstrut -\mathstrut 19q^{63} $ $\mathstrut +\mathstrut 24q^{64} $ $\mathstrut -\mathstrut 4q^{65} $ $\mathstrut +\mathstrut 8q^{66} $ $\mathstrut +\mathstrut 10q^{67} $ $\mathstrut -\mathstrut 5q^{68} $ $\mathstrut +\mathstrut 6q^{69} $ $\mathstrut +\mathstrut 8q^{70} $ $\mathstrut +\mathstrut 58q^{71} $ $\mathstrut -\mathstrut 19q^{72} $ $\mathstrut +\mathstrut 9q^{73} $ $\mathstrut -\mathstrut 2q^{74} $ $\mathstrut +\mathstrut 7q^{75} $ $\mathstrut +\mathstrut 6q^{76} $ $\mathstrut -\mathstrut 15q^{77} $ $\mathstrut -\mathstrut 7q^{78} $ $\mathstrut +\mathstrut 31q^{79} $ $\mathstrut +\mathstrut 8q^{80} $ $\mathstrut +\mathstrut 16q^{81} $ $\mathstrut -\mathstrut 25q^{82} $ $\mathstrut -\mathstrut q^{83} $ $\mathstrut -\mathstrut 7q^{84} $ $\mathstrut -\mathstrut 4q^{85} $ $\mathstrut +\mathstrut 15q^{86} $ $\mathstrut +\mathstrut 30q^{87} $ $\mathstrut -\mathstrut 15q^{88} $ $\mathstrut +\mathstrut 45q^{89} $ $\mathstrut -\mathstrut 41q^{90} $ $\mathstrut +\mathstrut 7q^{91} $ $\mathstrut +\mathstrut 3q^{92} $ $\mathstrut +\mathstrut 25q^{93} $ $\mathstrut -\mathstrut 35q^{94} $ $\mathstrut -\mathstrut 10q^{95} $ $\mathstrut -\mathstrut 7q^{96} $ $\mathstrut -\mathstrut 9q^{97} $ $\mathstrut -\mathstrut 24q^{98} $ $\mathstrut +\mathstrut 64q^{99} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

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	−1.00000	−2.83864	1.00000	0.330019	2.83864	−1.00000	−1.00000	5.05788	−0.330019
1.2	−1.00000	−2.67063	1.00000	3.15601	2.67063	−1.00000	−1.00000	4.13228	−3.15601
1.3	−1.00000	−2.58057	1.00000	−2.90281	2.58057	−1.00000	−1.00000	3.65935	2.90281
1.4	−1.00000	−1.92027	1.00000	−2.53143	1.92027	−1.00000	−1.00000	0.687441	2.53143
1.5	−1.00000	−1.91791	1.00000	0.374562	1.91791	−1.00000	−1.00000	0.678384	−0.374562
1.6	−1.00000	−1.69422	1.00000	3.76480	1.69422	−1.00000	−1.00000	−0.129635	−3.76480
1.7	−1.00000	−1.44122	1.00000	−2.06061	1.44122	−1.00000	−1.00000	−0.922894	2.06061
1.8	−1.00000	−0.920246	1.00000	2.96551	0.920246	−1.00000	−1.00000	−2.15315	−2.96551
1.9	−1.00000	−0.797155	1.00000	1.40867	0.797155	−1.00000	−1.00000	−2.36454	−1.40867
1.10	−1.00000	−0.0752307	1.00000	−2.78876	0.0752307	−1.00000	−1.00000	−2.99434	2.78876
1.11	−1.00000	0.0287183	1.00000	1.06252	−0.0287183	−1.00000	−1.00000	−2.99918	−1.06252
1.12	−1.00000	0.430787	1.00000	1.34011	−0.430787	−1.00000	−1.00000	−2.81442	−1.34011
1.13	−1.00000	0.632516	1.00000	−0.321740	−0.632516	−1.00000	−1.00000	−2.59992	0.321740
1.14	−1.00000	0.685916	1.00000	1.44966	−0.685916	−1.00000	−1.00000	−2.52952	−1.44966
1.15	−1.00000	1.20386	1.00000	−2.97794	−1.20386	−1.00000	−1.00000	−1.55072	2.97794
1.16	−1.00000	1.44853	1.00000	−1.26403	−1.44853	−1.00000	−1.00000	−0.901751	1.26403
1.17	−1.00000	1.52105	1.00000	−3.19164	−1.52105	−1.00000	−1.00000	−0.686407	3.19164
1.18	−1.00000	1.56085	1.00000	−1.28710	−1.56085	−1.00000	−1.00000	−0.563752	1.28710
1.19	−1.00000	2.10114	1.00000	4.16694	−2.10114	−1.00000	−1.00000	1.41477	−4.16694
1.20	−1.00000	2.39691	1.00000	1.79254	−2.39691	−1.00000	−1.00000	2.74520	−1.79254
See all 24 embeddings

Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

$ p $	Sign
$2$	$1$
$7$	$1$
$431$	$-1$

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(6034))$:

$T_{3}^{24} - \cdots$

$T_{5}^{24} - \cdots$

$T_{11}^{24} - \cdots$

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	6034.a (trivial)

\(n\):		e.g. 2-40 or 990-1000
Embeddings:		e.g. 1-3 or 1.24
Significant digits:
Format:

\( p \)	Sign
\(2\)	\(1\)
\(7\)	\(1\)
\(431\)	\(-1\)

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