# Properties

 Label 6034.2.a.p Level 6034 Weight 2 Character orbit 6034.a Self dual Yes Analytic conductor 48.182 Analytic rank 0 Dimension 27 CM No

# Related objects

## 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: $$27$$ 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.

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

## 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 −3.22794 1.00000 1.50843 3.22794 1.00000 −1.00000 7.41957 −1.50843
1.2 −1.00000 −3.20972 1.00000 −3.26323 3.20972 1.00000 −1.00000 7.30232 3.26323
1.3 −1.00000 −3.03412 1.00000 1.18387 3.03412 1.00000 −1.00000 6.20591 −1.18387
1.4 −1.00000 −2.59011 1.00000 1.58456 2.59011 1.00000 −1.00000 3.70867 −1.58456
1.5 −1.00000 −2.42517 1.00000 2.60497 2.42517 1.00000 −1.00000 2.88143 −2.60497
1.6 −1.00000 −1.90367 1.00000 −3.72741 1.90367 1.00000 −1.00000 0.623956 3.72741
1.7 −1.00000 −1.81149 1.00000 −1.26479 1.81149 1.00000 −1.00000 0.281479 1.26479
1.8 −1.00000 −1.32317 1.00000 −0.695345 1.32317 1.00000 −1.00000 −1.24923 0.695345
1.9 −1.00000 −0.743500 1.00000 −1.77052 0.743500 1.00000 −1.00000 −2.44721 1.77052
1.10 −1.00000 −0.679472 1.00000 −2.19065 0.679472 1.00000 −1.00000 −2.53832 2.19065
1.11 −1.00000 −0.394534 1.00000 4.36123 0.394534 1.00000 −1.00000 −2.84434 −4.36123
1.12 −1.00000 −0.302933 1.00000 3.48262 0.302933 1.00000 −1.00000 −2.90823 −3.48262
1.13 −1.00000 −0.252343 1.00000 2.45924 0.252343 1.00000 −1.00000 −2.93632 −2.45924
1.14 −1.00000 −0.222181 1.00000 0.181430 0.222181 1.00000 −1.00000 −2.95064 −0.181430
1.15 −1.00000 0.396413 1.00000 −1.85319 −0.396413 1.00000 −1.00000 −2.84286 1.85319
1.16 −1.00000 0.482352 1.00000 2.96654 −0.482352 1.00000 −1.00000 −2.76734 −2.96654
1.17 −1.00000 0.975695 1.00000 −1.65902 −0.975695 1.00000 −1.00000 −2.04802 1.65902
1.18 −1.00000 1.58330 1.00000 −2.70248 −1.58330 1.00000 −1.00000 −0.493160 2.70248
1.19 −1.00000 1.64919 1.00000 0.930561 −1.64919 1.00000 −1.00000 −0.280182 −0.930561
1.20 −1.00000 1.94651 1.00000 3.30450 −1.94651 1.00000 −1.00000 0.788913 −3.30450
See all 27 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1.27 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## 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 $$S_{2}^{\mathrm{new}}(\Gamma_0(6034))$$:

 $$T_{3}^{27} - \cdots$$ $$T_{5}^{27} - \cdots$$ $$T_{11}^{27} - \cdots$$