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

Downloads

Learn more about

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

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