# Properties

 Label 6026.2.a.j Level 6026 Weight 2 Character orbit 6026.a Self dual yes Analytic conductor 48.118 Analytic rank 0 Dimension 33 CM no Inner twists 1

# Related objects

## Newspace parameters

 Level: $$N$$ = $$6026 = 2 \cdot 23 \cdot 131$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 6026.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$48.1178522580$$ Analytic rank: $$0$$ Dimension: $$33$$ 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.

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

## 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 −3.30495 1.00000 3.30220 3.30495 3.90022 −1.00000 7.92270 −3.30220
1.2 −1.00000 −2.92506 1.00000 0.618794 2.92506 −2.50272 −1.00000 5.55600 −0.618794
1.3 −1.00000 −2.90304 1.00000 −1.99628 2.90304 −0.299170 −1.00000 5.42764 1.99628
1.4 −1.00000 −2.82338 1.00000 −3.52183 2.82338 3.82891 −1.00000 4.97150 3.52183
1.5 −1.00000 −2.71066 1.00000 −2.38566 2.71066 −4.13924 −1.00000 4.34767 2.38566
1.6 −1.00000 −2.31184 1.00000 −1.83764 2.31184 0.291912 −1.00000 2.34459 1.83764
1.7 −1.00000 −1.90551 1.00000 3.90912 1.90551 1.35086 −1.00000 0.630974 −3.90912
1.8 −1.00000 −1.82570 1.00000 −3.75704 1.82570 0.299528 −1.00000 0.333191 3.75704
1.9 −1.00000 −1.80561 1.00000 −1.32735 1.80561 −4.32567 −1.00000 0.260232 1.32735
1.10 −1.00000 −1.47729 1.00000 2.55278 1.47729 −3.54262 −1.00000 −0.817604 −2.55278
1.11 −1.00000 −1.46112 1.00000 2.24970 1.46112 −0.440676 −1.00000 −0.865116 −2.24970
1.12 −1.00000 −0.987482 1.00000 −4.26130 0.987482 0.584751 −1.00000 −2.02488 4.26130
1.13 −1.00000 −0.968563 1.00000 −0.0731928 0.968563 −0.501115 −1.00000 −2.06189 0.0731928
1.14 −1.00000 −0.909549 1.00000 0.734986 0.909549 5.27401 −1.00000 −2.17272 −0.734986
1.15 −1.00000 −0.471999 1.00000 1.82038 0.471999 −1.64482 −1.00000 −2.77722 −1.82038
1.16 −1.00000 −0.0820624 1.00000 −3.26458 0.0820624 −0.430136 −1.00000 −2.99327 3.26458
1.17 −1.00000 0.189963 1.00000 2.89176 −0.189963 3.54124 −1.00000 −2.96391 −2.89176
1.18 −1.00000 0.214096 1.00000 2.53148 −0.214096 4.82861 −1.00000 −2.95416 −2.53148
1.19 −1.00000 0.539204 1.00000 −2.22740 −0.539204 4.94386 −1.00000 −2.70926 2.22740
1.20 −1.00000 0.581698 1.00000 −2.21086 −0.581698 1.23881 −1.00000 −2.66163 2.21086
See all 33 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1.33 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 6026.2.a.j 33

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6026.2.a.j 33 1.a even 1 1 trivial

## Atkin-Lehner signs

$$p$$ Sign
$$2$$ $$1$$
$$23$$ $$-1$$
$$131$$ $$1$$

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(6026))$$:

 $$T_{3}^{33} - \cdots$$ $$T_{5}^{33} + \cdots$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database