# Properties

 Label 6017.2.a Level 6017 Weight 2 Character orbit a Rep. character $$\chi_{6017}(1,\cdot)$$ Character field $$\Q$$ Dimension 455 Newform subspaces 6 Sturm bound 1096 Trace bound 3

# Related objects

## Defining parameters

 Level: $$N$$ = $$6017 = 11 \cdot 547$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 6017.a (trivial) Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$1096$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(6017))$$.

Total New Old
Modular forms 550 455 95
Cusp forms 547 455 92
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$11$$$$547$$FrickeDim.
$$+$$$$+$$$$+$$$$107$$
$$+$$$$-$$$$-$$$$122$$
$$-$$$$+$$$$-$$$$120$$
$$-$$$$-$$$$+$$$$106$$
Plus space$$+$$$$213$$
Minus space$$-$$$$242$$

## Trace form

 $$455q + q^{2} + 2q^{3} + 451q^{4} - 4q^{5} + 4q^{6} + 8q^{7} + 9q^{8} + 461q^{9} + O(q^{10})$$ $$455q + q^{2} + 2q^{3} + 451q^{4} - 4q^{5} + 4q^{6} + 8q^{7} + 9q^{8} + 461q^{9} - 2q^{10} - 3q^{11} - 2q^{13} - 4q^{14} - 10q^{15} + 455q^{16} - 2q^{17} - 7q^{18} + 14q^{20} + 32q^{21} + 3q^{22} + 2q^{23} + 16q^{24} + 451q^{25} + 30q^{26} + 26q^{27} + 24q^{28} + 2q^{29} - 16q^{30} + 2q^{31} - 11q^{32} + 2q^{33} - 46q^{34} + 24q^{35} + 431q^{36} - 4q^{37} + 24q^{38} + 24q^{39} - 26q^{40} - 6q^{41} + 16q^{42} + 28q^{43} - 3q^{44} - 26q^{45} + 32q^{46} - 4q^{47} - 40q^{48} + 495q^{49} - 97q^{50} - 20q^{51} + 18q^{52} - 2q^{53} - 8q^{54} - 12q^{57} + 6q^{58} + 14q^{59} - 48q^{60} - 10q^{61} + 12q^{62} + 48q^{63} + 439q^{64} - 48q^{65} - 16q^{66} + 30q^{67} - 22q^{68} - 30q^{69} - 12q^{70} + 38q^{71} - 19q^{72} - 10q^{73} - 26q^{74} + 68q^{75} + 20q^{76} + 8q^{77} - 140q^{78} + 40q^{79} - 42q^{80} + 479q^{81} + 6q^{82} - 4q^{83} + 40q^{84} - 52q^{85} + 4q^{86} + 36q^{87} - 9q^{88} - 4q^{89} - 10q^{90} + 64q^{91} - 96q^{92} + 98q^{93} - 44q^{94} + 20q^{95} + 48q^{96} - 75q^{98} - 9q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(6017))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 11 547
6017.2.a.a $$1$$ $$48.046$$ $$\Q$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$+$$ $$-$$ $$q-2q^{4}-2q^{7}-3q^{9}-q^{11}-5q^{13}+\cdots$$
6017.2.a.b $$1$$ $$48.046$$ $$\Q$$ None $$0$$ $$2$$ $$4$$ $$2$$ $$-$$ $$+$$ $$q+2q^{3}-2q^{4}+4q^{5}+2q^{7}+q^{9}+\cdots$$
6017.2.a.c $$106$$ $$48.046$$ None $$-13$$ $$-15$$ $$-12$$ $$-66$$ $$-$$ $$-$$
6017.2.a.d $$107$$ $$48.046$$ None $$-3$$ $$-18$$ $$-15$$ $$-54$$ $$+$$ $$+$$
6017.2.a.e $$119$$ $$48.046$$ None $$15$$ $$15$$ $$6$$ $$72$$ $$-$$ $$+$$
6017.2.a.f $$121$$ $$48.046$$ None $$2$$ $$18$$ $$13$$ $$56$$ $$+$$ $$-$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(6017))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(6017)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(11))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(547))$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$1 + 2 T^{2}$$)($$1 + 2 T^{2}$$)
$3$ ($$1 + 3 T^{2}$$)($$1 - 2 T + 3 T^{2}$$)
$5$ ($$1 + 5 T^{2}$$)($$1 - 4 T + 5 T^{2}$$)
$7$ ($$1 + 2 T + 7 T^{2}$$)($$1 - 2 T + 7 T^{2}$$)
$11$ ($$1 + T$$)($$1 - T$$)
$13$ ($$1 + 5 T + 13 T^{2}$$)($$1 - T + 13 T^{2}$$)
$17$ ($$1 + 4 T + 17 T^{2}$$)($$1 - 8 T + 17 T^{2}$$)
$19$ ($$1 + 7 T + 19 T^{2}$$)($$1 + 5 T + 19 T^{2}$$)
$23$ ($$1 - 2 T + 23 T^{2}$$)($$1 - 6 T + 23 T^{2}$$)
$29$ ($$1 + T + 29 T^{2}$$)($$1 - 5 T + 29 T^{2}$$)
$31$ ($$1 - 4 T + 31 T^{2}$$)($$1 - 10 T + 31 T^{2}$$)
$37$ ($$1 + 6 T + 37 T^{2}$$)($$1 + 37 T^{2}$$)
$41$ ($$1 - 2 T + 41 T^{2}$$)($$1 + 41 T^{2}$$)
$43$ ($$1 + 8 T + 43 T^{2}$$)($$1 + 10 T + 43 T^{2}$$)
$47$ ($$1 + 9 T + 47 T^{2}$$)($$1 + 9 T + 47 T^{2}$$)
$53$ ($$1 - 2 T + 53 T^{2}$$)($$1 + 10 T + 53 T^{2}$$)
$59$ ($$1 + 6 T + 59 T^{2}$$)($$1 + 14 T + 59 T^{2}$$)
$61$ ($$1 + 14 T + 61 T^{2}$$)($$1 + 14 T + 61 T^{2}$$)
$67$ ($$1 + 5 T + 67 T^{2}$$)($$1 + T + 67 T^{2}$$)
$71$ ($$1 - 10 T + 71 T^{2}$$)($$1 - 12 T + 71 T^{2}$$)
$73$ ($$1 + 6 T + 73 T^{2}$$)($$1 + 2 T + 73 T^{2}$$)
$79$ ($$1 + 6 T + 79 T^{2}$$)($$1 - 4 T + 79 T^{2}$$)
$83$ ($$1 - 4 T + 83 T^{2}$$)($$1 - 6 T + 83 T^{2}$$)
$89$ ($$1 - 8 T + 89 T^{2}$$)($$1 + 6 T + 89 T^{2}$$)
$97$ ($$1 - 15 T + 97 T^{2}$$)($$1 + 13 T + 97 T^{2}$$)