Properties

 Label 6011.2.a Level 6011 Weight 2 Character orbit a Rep. character $$\chi_{6011}(1,\cdot)$$ Character field $$\Q$$ Dimension 501 Newform subspaces 6 Sturm bound 1002 Trace bound 2

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$6011$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 6011.a (trivial) Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$1002$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(6011))$$.

Total New Old
Modular forms 502 502 0
Cusp forms 501 501 0
Eisenstein series 1 1 0

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

$$6011$$Dim.
$$+$$$$224$$
$$-$$$$277$$

Trace form

 $$501q - 2q^{3} + 504q^{4} - 4q^{6} - 6q^{8} + 501q^{9} + O(q^{10})$$ $$501q - 2q^{3} + 504q^{4} - 4q^{6} - 6q^{8} + 501q^{9} - 8q^{10} - 2q^{11} - 22q^{12} + 6q^{13} - 18q^{14} - 10q^{15} + 506q^{16} - 10q^{18} - 2q^{20} + 16q^{21} - 4q^{22} - 6q^{23} - 22q^{24} + 497q^{25} - 6q^{26} - 8q^{27} - 12q^{28} + 4q^{29} - 34q^{30} + 2q^{31} - 22q^{32} - 28q^{33} - 20q^{34} - 4q^{35} + 502q^{36} + 14q^{37} + 16q^{38} - 2q^{39} - 24q^{40} - 10q^{41} - 14q^{42} - 8q^{43} + 2q^{45} + 6q^{46} - 54q^{48} + 491q^{49} + 10q^{50} - 12q^{51} - 22q^{52} - 18q^{53} - 26q^{54} - 56q^{55} - 14q^{56} - 12q^{57} - 44q^{58} - 22q^{59} - 74q^{60} + 18q^{61} - 2q^{62} + 10q^{63} + 490q^{64} - 24q^{65} - 56q^{66} + 6q^{67} - 32q^{68} - 50q^{69} - 82q^{70} + 10q^{71} - 72q^{72} - 6q^{73} + 48q^{74} + 56q^{75} - 14q^{76} - 26q^{77} - 22q^{78} + 26q^{79} + 4q^{80} + 477q^{81} + 18q^{82} + 24q^{83} + 104q^{84} + 24q^{85} - 22q^{86} + 34q^{87} - 36q^{88} + 18q^{89} - 22q^{90} - 6q^{91} + 74q^{92} - 38q^{93} - 12q^{94} - 28q^{95} - 26q^{96} + 4q^{97} + 26q^{98} - 24q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(6011))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 6011
6011.2.a.a $$1$$ $$47.998$$ $$\Q$$ None $$-2$$ $$0$$ $$-2$$ $$1$$ $$-$$ $$q-2q^{2}+2q^{4}-2q^{5}+q^{7}-3q^{9}+\cdots$$
6011.2.a.b $$1$$ $$47.998$$ $$\Q$$ None $$0$$ $$3$$ $$1$$ $$-1$$ $$-$$ $$q+3q^{3}-2q^{4}+q^{5}-q^{7}+6q^{9}+6q^{11}+\cdots$$
6011.2.a.c $$1$$ $$47.998$$ $$\Q$$ None $$1$$ $$-1$$ $$-3$$ $$1$$ $$+$$ $$q+q^{2}-q^{3}-q^{4}-3q^{5}-q^{6}+q^{7}+\cdots$$
6011.2.a.d $$2$$ $$47.998$$ $$\Q(\sqrt{2})$$ None $$0$$ $$4$$ $$0$$ $$-2$$ $$+$$ $$q+\beta q^{2}+2q^{3}+2\beta q^{5}+2\beta q^{6}-q^{7}+\cdots$$
6011.2.a.e $$221$$ $$47.998$$ None $$-15$$ $$-17$$ $$-32$$ $$-40$$ $$+$$
6011.2.a.f $$275$$ $$47.998$$ None $$16$$ $$9$$ $$36$$ $$41$$ $$-$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 + 2 T + 2 T^{2}$$)($$1 + 2 T^{2}$$)($$1 - T + 2 T^{2}$$)($$1 + 2 T^{2} + 4 T^{4}$$)
$3$ ($$1 + 3 T^{2}$$)($$1 - 3 T + 3 T^{2}$$)($$1 + T + 3 T^{2}$$)($$( 1 - 2 T + 3 T^{2} )^{2}$$)
$5$ ($$1 + 2 T + 5 T^{2}$$)($$1 - T + 5 T^{2}$$)($$1 + 3 T + 5 T^{2}$$)($$1 + 2 T^{2} + 25 T^{4}$$)
$7$ ($$1 - T + 7 T^{2}$$)($$1 + T + 7 T^{2}$$)($$1 - T + 7 T^{2}$$)($$( 1 + T + 7 T^{2} )^{2}$$)
$11$ ($$1 + 2 T + 11 T^{2}$$)($$1 - 6 T + 11 T^{2}$$)($$1 - 2 T + 11 T^{2}$$)($$1 + 4 T^{2} + 121 T^{4}$$)
$13$ ($$1 + 13 T^{2}$$)($$1 + 13 T^{2}$$)($$1 + 13 T^{2}$$)($$1 + 4 T + 28 T^{2} + 52 T^{3} + 169 T^{4}$$)
$17$ ($$1 + 6 T + 17 T^{2}$$)($$1 + 17 T^{2}$$)($$1 + 17 T^{2}$$)($$1 + 32 T^{2} + 289 T^{4}$$)
$19$ ($$1 + 2 T + 19 T^{2}$$)($$1 - 2 T + 19 T^{2}$$)($$1 - 2 T + 19 T^{2}$$)($$( 1 - 2 T + 19 T^{2} )^{2}$$)
$23$ ($$1 + 6 T + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 + 4 T + 42 T^{2} + 92 T^{3} + 529 T^{4}$$)
$29$ ($$1 + 8 T + 29 T^{2}$$)($$1 - 2 T + 29 T^{2}$$)($$1 + 29 T^{2}$$)($$1 - 14 T^{2} + 841 T^{4}$$)
$31$ ($$1 - 2 T + 31 T^{2}$$)($$1 - 8 T + 31 T^{2}$$)($$1 - 4 T + 31 T^{2}$$)($$1 + 8 T + 60 T^{2} + 248 T^{3} + 961 T^{4}$$)
$37$ ($$1 + 10 T + 37 T^{2}$$)($$1 - 2 T + 37 T^{2}$$)($$1 - 4 T + 37 T^{2}$$)($$1 + 8 T + 72 T^{2} + 296 T^{3} + 1369 T^{4}$$)
$41$ ($$1 - 3 T + 41 T^{2}$$)($$1 - 6 T + 41 T^{2}$$)($$1 + 9 T + 41 T^{2}$$)($$( 1 + 3 T + 41 T^{2} )^{2}$$)
$43$ ($$1 - T + 43 T^{2}$$)($$1 + 5 T + 43 T^{2}$$)($$1 - 5 T + 43 T^{2}$$)($$( 1 - 5 T + 43 T^{2} )^{2}$$)
$47$ ($$1 + 6 T + 47 T^{2}$$)($$1 + 8 T + 47 T^{2}$$)($$1 - 2 T + 47 T^{2}$$)($$1 + 8 T + 108 T^{2} + 376 T^{3} + 2209 T^{4}$$)
$53$ ($$1 + 12 T + 53 T^{2}$$)($$1 + 6 T + 53 T^{2}$$)($$1 - 6 T + 53 T^{2}$$)($$( 1 + 53 T^{2} )^{2}$$)
$59$ ($$1 - T + 59 T^{2}$$)($$1 - 5 T + 59 T^{2}$$)($$1 + 59 T^{2}$$)($$1 - 18 T + 167 T^{2} - 1062 T^{3} + 3481 T^{4}$$)
$61$ ($$1 - 6 T + 61 T^{2}$$)($$1 + 61 T^{2}$$)($$1 - 6 T + 61 T^{2}$$)($$1 - 4 T + 118 T^{2} - 244 T^{3} + 3721 T^{4}$$)
$67$ ($$1 - 5 T + 67 T^{2}$$)($$1 - T + 67 T^{2}$$)($$1 + 8 T + 67 T^{2}$$)($$1 - 14 T + 151 T^{2} - 938 T^{3} + 4489 T^{4}$$)
$71$ ($$1 - 5 T + 71 T^{2}$$)($$1 - 3 T + 71 T^{2}$$)($$1 - 5 T + 71 T^{2}$$)($$1 + 22 T + 255 T^{2} + 1562 T^{3} + 5041 T^{4}$$)
$73$ ($$1 - 2 T + 73 T^{2}$$)($$1 + 11 T + 73 T^{2}$$)($$1 - 5 T + 73 T^{2}$$)($$1 - 16 T + 202 T^{2} - 1168 T^{3} + 5329 T^{4}$$)
$79$ ($$1 + 11 T + 79 T^{2}$$)($$1 - 17 T + 79 T^{2}$$)($$1 + 4 T + 79 T^{2}$$)($$1 - 14 T + 135 T^{2} - 1106 T^{3} + 6241 T^{4}$$)
$83$ ($$1 + T + 83 T^{2}$$)($$1 + 3 T + 83 T^{2}$$)($$1 - 7 T + 83 T^{2}$$)($$( 1 - 9 T + 83 T^{2} )^{2}$$)
$89$ ($$1 + 8 T + 89 T^{2}$$)($$1 - 12 T + 89 T^{2}$$)($$1 - 8 T + 89 T^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)
$97$ ($$1 + 7 T + 97 T^{2}$$)($$1 - 5 T + 97 T^{2}$$)($$1 + 14 T + 97 T^{2}$$)($$1 + 14 T + 171 T^{2} + 1358 T^{3} + 9409 T^{4}$$)