Properties

Label 6015.2.a
Level 6015
Weight 2
Character orbit a
Rep. character \(\chi_{6015}(1,\cdot)\)
Character field \(\Q\)
Dimension 267
Newform subspaces 9
Sturm bound 1608
Trace bound 2

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 6015 = 3 \cdot 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6015.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(1608\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6015))\).

Total New Old
Modular forms 808 267 541
Cusp forms 801 267 534
Eisenstein series 7 0 7

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

\(3\)\(5\)\(401\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(36\)
\(+\)\(+\)\(-\)\(-\)\(31\)
\(+\)\(-\)\(+\)\(-\)\(36\)
\(+\)\(-\)\(-\)\(+\)\(29\)
\(-\)\(+\)\(+\)\(-\)\(39\)
\(-\)\(+\)\(-\)\(+\)\(28\)
\(-\)\(-\)\(+\)\(+\)\(23\)
\(-\)\(-\)\(-\)\(-\)\(45\)
Plus space\(+\)\(116\)
Minus space\(-\)\(151\)

Trace form

\( 267q - 3q^{2} + 3q^{3} + 269q^{4} - q^{5} + q^{6} - 15q^{8} + 267q^{9} + O(q^{10}) \) \( 267q - 3q^{2} + 3q^{3} + 269q^{4} - q^{5} + q^{6} - 15q^{8} + 267q^{9} + q^{10} - 12q^{11} + 5q^{12} + 10q^{13} - 8q^{14} + 3q^{15} + 261q^{16} + 6q^{17} - 3q^{18} + 4q^{19} - 7q^{20} + 8q^{21} + 4q^{22} - 16q^{23} + 21q^{24} + 267q^{25} - 42q^{26} + 3q^{27} - 8q^{28} + 2q^{29} + q^{30} + 8q^{31} - 23q^{32} + 4q^{33} + 42q^{34} + 269q^{36} + 26q^{37} + 12q^{38} + 10q^{39} - 3q^{40} - 10q^{41} + 24q^{42} + 4q^{43} - 44q^{44} - q^{45} - 24q^{46} - 16q^{47} - 3q^{48} + 307q^{49} - 3q^{50} + 14q^{51} + 30q^{52} + 34q^{53} + q^{54} - 4q^{55} - 72q^{56} + 20q^{57} - 58q^{58} - 28q^{59} + 5q^{60} + 34q^{61} - 24q^{62} + 221q^{64} - 14q^{65} - 28q^{66} + 4q^{67} - 46q^{68} + 16q^{69} - 24q^{70} - 15q^{72} + 22q^{73} - 42q^{74} + 3q^{75} - 28q^{76} + 8q^{77} - 2q^{78} - 40q^{79} + q^{80} + 267q^{81} - 62q^{82} - 20q^{83} + 32q^{84} + 14q^{85} - 68q^{86} + 10q^{87} + 4q^{88} - 34q^{89} + q^{90} + 24q^{91} - 64q^{92} + 8q^{93} + 80q^{94} - 4q^{95} + 13q^{96} - 2q^{97} - 67q^{98} - 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6015))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 401
6015.2.a.a \(2\) \(48.030\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(2\) \(4\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+(2-2\beta )q^{7}+\cdots\)
6015.2.a.b \(23\) \(48.030\) None \(-5\) \(23\) \(23\) \(-16\) \(-\) \(-\) \(+\)
6015.2.a.c \(28\) \(48.030\) None \(-1\) \(28\) \(-28\) \(-20\) \(-\) \(+\) \(-\)
6015.2.a.d \(29\) \(48.030\) None \(-1\) \(-29\) \(29\) \(2\) \(+\) \(-\) \(-\)
6015.2.a.e \(31\) \(48.030\) None \(6\) \(-31\) \(-31\) \(-4\) \(+\) \(+\) \(-\)
6015.2.a.f \(36\) \(48.030\) None \(-7\) \(-36\) \(-36\) \(2\) \(+\) \(+\) \(+\)
6015.2.a.g \(36\) \(48.030\) None \(0\) \(-36\) \(36\) \(-4\) \(+\) \(-\) \(+\)
6015.2.a.h \(39\) \(48.030\) None \(0\) \(39\) \(-39\) \(22\) \(-\) \(+\) \(+\)
6015.2.a.i \(43\) \(48.030\) None \(3\) \(43\) \(43\) \(14\) \(-\) \(-\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6015))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6015)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(401))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1203))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2005))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - T + 2 T^{2} )^{2} \))
$3$ (\( ( 1 - T )^{2} \))
$5$ (\( ( 1 - T )^{2} \))
$7$ (\( 1 - 4 T + 10 T^{2} - 28 T^{3} + 49 T^{4} \))
$11$ (\( ( 1 + 4 T + 11 T^{2} )^{2} \))
$13$ (\( 1 - 8 T + 40 T^{2} - 104 T^{3} + 169 T^{4} \))
$17$ (\( 1 + 32 T^{2} + 289 T^{4} \))
$19$ (\( 1 + 4 T + 24 T^{2} + 76 T^{3} + 361 T^{4} \))
$23$ (\( 1 - 8 T + 54 T^{2} - 184 T^{3} + 529 T^{4} \))
$29$ (\( 1 - 8 T + 42 T^{2} - 232 T^{3} + 841 T^{4} \))
$31$ (\( 1 + 4 T + 16 T^{2} + 124 T^{3} + 961 T^{4} \))
$37$ (\( 1 - 8 T + 72 T^{2} - 296 T^{3} + 1369 T^{4} \))
$41$ (\( 1 - 12 T + 86 T^{2} - 492 T^{3} + 1681 T^{4} \))
$43$ (\( 1 + 8 T + 70 T^{2} + 344 T^{3} + 1849 T^{4} \))
$47$ (\( 1 + 62 T^{2} + 2209 T^{4} \))
$53$ (\( 1 + 8 T^{2} + 2809 T^{4} \))
$59$ (\( 1 + 12 T + 152 T^{2} + 708 T^{3} + 3481 T^{4} \))
$61$ (\( 1 + 12 T + 126 T^{2} + 732 T^{3} + 3721 T^{4} \))
$67$ (\( 1 - 8 T + 78 T^{2} - 536 T^{3} + 4489 T^{4} \))
$71$ (\( 1 - 4 T + 48 T^{2} - 284 T^{3} + 5041 T^{4} \))
$73$ (\( ( 1 - 2 T + 73 T^{2} )^{2} \))
$79$ (\( 1 - 12 T + 192 T^{2} - 948 T^{3} + 6241 T^{4} \))
$83$ (\( 1 - 20 T + 258 T^{2} - 1660 T^{3} + 6889 T^{4} \))
$89$ (\( 1 + 8 T + 66 T^{2} + 712 T^{3} + 7921 T^{4} \))
$97$ (\( 1 - 32 T + 448 T^{2} - 3104 T^{3} + 9409 T^{4} \))
show more
show less