# Properties

 Label 4017.2.a.g Level 4017 Weight 2 Character orbit 4017.a Self dual yes Analytic conductor 32.076 Analytic rank 0 Dimension 24 CM no Inner twists 1

# Related objects

## Newspace parameters

 Level: $$N$$ = $$4017 = 3 \cdot 13 \cdot 103$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 4017.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$32.0759064919$$ 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.

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

## 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 −2.64656 −1.00000 5.00429 2.13528 2.64656 3.46294 −7.95105 1.00000 −5.65115
1.2 −2.42509 −1.00000 3.88107 −0.736887 2.42509 −2.40625 −4.56178 1.00000 1.78702
1.3 −2.29414 −1.00000 3.26307 −3.12687 2.29414 −2.80124 −2.89765 1.00000 7.17346
1.4 −2.16909 −1.00000 2.70494 0.657691 2.16909 −0.817989 −1.52908 1.00000 −1.42659
1.5 −1.94312 −1.00000 1.77572 −0.275874 1.94312 3.15290 0.435811 1.00000 0.536057
1.6 −1.52294 −1.00000 0.319360 3.31668 1.52294 −2.60872 2.55952 1.00000 −5.05112
1.7 −1.32626 −1.00000 −0.241032 −0.192408 1.32626 3.16535 2.97219 1.00000 0.255184
1.8 −1.17908 −1.00000 −0.609765 4.22706 1.17908 3.50133 3.07713 1.00000 −4.98405
1.9 −0.607674 −1.00000 −1.63073 −3.70104 0.607674 0.175250 2.20630 1.00000 2.24902
1.10 −0.574597 −1.00000 −1.66984 −2.72483 0.574597 0.829930 2.10868 1.00000 1.56568
1.11 −0.389331 −1.00000 −1.84842 0.642702 0.389331 −1.35418 1.49831 1.00000 −0.250224
1.12 0.0298243 −1.00000 −1.99911 3.06004 −0.0298243 −1.69214 −0.119271 1.00000 0.0912635
1.13 0.543206 −1.00000 −1.70493 2.45290 −0.543206 0.874109 −2.01254 1.00000 1.33243
1.14 0.671722 −1.00000 −1.54879 −1.67775 −0.671722 5.02977 −2.38380 1.00000 −1.12698
1.15 0.794802 −1.00000 −1.36829 −2.06654 −0.794802 −0.419104 −2.67712 1.00000 −1.64249
1.16 1.05828 −1.00000 −0.880046 −0.912505 −1.05828 −3.63309 −3.04789 1.00000 −0.965685
1.17 1.57828 −1.00000 0.490964 −1.83430 −1.57828 4.32058 −2.38168 1.00000 −2.89504
1.18 1.68466 −1.00000 0.838074 0.142092 −1.68466 −0.0282508 −1.95745 1.00000 0.239376
1.19 1.73242 −1.00000 1.00128 0.756937 −1.73242 −4.14115 −1.73020 1.00000 1.31133
1.20 1.86289 −1.00000 1.47035 4.02931 −1.86289 3.22519 −0.986675 1.00000 7.50616
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 4017.2.a.g 24

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4017.2.a.g 24 1.a even 1 1 trivial

## Atkin-Lehner signs

$$p$$ Sign
$$3$$ $$1$$
$$13$$ $$1$$
$$103$$ $$-1$$

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(4017))$$:

 $$T_{2}^{24} - \cdots$$ $$T_{23}^{24} - \cdots$$