# Properties

 Label 6034.2.a.n Level 6034 Weight 2 Character orbit 6034.a Self dual yes Analytic conductor 48.182 Analytic rank 0 Dimension 24 CM no Inner twists 1

# 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: $$24$$ Coefficient ring index: multiple of None Twist minimal: yes 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.

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

## 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 −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
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1.24 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

This newform does not admit any (nontrivial) inner twists.

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 6034.2.a.n 24

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6034.2.a.n 24 1.a even 1 1 trivial

## Atkin-Lehner signs

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

## Hecke kernels

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

 $$T_{3}^{24} - \cdots$$ $$T_{5}^{24} - \cdots$$ $$T_{11}^{24} - \cdots$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database