Properties

Label 6013.2.a
Level $6013$
Weight $2$
Character orbit 6013.a
Rep. character $\chi_{6013}(1,\cdot)$
Character field $\Q$
Dimension $429$
Newform subspaces $6$
Sturm bound $1146$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 6013 = 7 \cdot 859 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6013.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(1146\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6013))\).

Total New Old
Modular forms 574 429 145
Cusp forms 571 429 142
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.

\(7\)\(859\)FrickeDim.
\(+\)\(+\)\(+\)\(104\)
\(+\)\(-\)\(-\)\(111\)
\(-\)\(+\)\(-\)\(110\)
\(-\)\(-\)\(+\)\(104\)
Plus space\(+\)\(208\)
Minus space\(-\)\(221\)

Trace form

\( 429q - q^{2} + 4q^{3} + 431q^{4} - 2q^{5} + 12q^{6} - q^{7} + 3q^{8} + 433q^{9} + O(q^{10}) \) \( 429q - q^{2} + 4q^{3} + 431q^{4} - 2q^{5} + 12q^{6} - q^{7} + 3q^{8} + 433q^{9} + 6q^{10} + 28q^{12} - 6q^{13} + q^{14} + 20q^{15} + 439q^{16} - 2q^{17} - 9q^{18} + 20q^{19} - 26q^{20} + 4q^{23} + 32q^{24} + 427q^{25} + 2q^{26} + 40q^{27} - 7q^{28} - 2q^{29} + 16q^{30} + 4q^{31} - 25q^{32} + 48q^{33} - 2q^{34} - 6q^{35} + 459q^{36} - 2q^{37} - 24q^{38} + 4q^{39} + 6q^{40} - 6q^{41} - 12q^{42} + 16q^{43} - 20q^{44} + 2q^{45} + 16q^{46} - 16q^{47} + 44q^{48} + 429q^{49} - 71q^{50} + 8q^{51} + 18q^{52} + 2q^{53} + 44q^{54} + 12q^{55} - 3q^{56} + 12q^{57} - 22q^{58} + 28q^{60} - 22q^{61} + 8q^{62} + 3q^{63} + 475q^{64} - 28q^{65} + 80q^{66} + 4q^{67} - 6q^{68} + 16q^{69} - 6q^{70} - 12q^{71} + 31q^{72} - 18q^{73} - 82q^{74} - 24q^{75} + 48q^{76} + 4q^{77} - 56q^{78} - 56q^{79} - 54q^{80} + 469q^{81} - 38q^{82} - 24q^{83} - 16q^{84} - 16q^{85} + 8q^{88} - 42q^{89} + 38q^{90} - 14q^{91} + 12q^{92} + 60q^{93} + 28q^{94} + 156q^{96} - 22q^{97} - q^{98} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6013))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 859
6013.2.a.a \(1\) \(48.014\) \(\Q\) None \(-2\) \(-2\) \(-1\) \(1\) \(-\) \(+\) \(q-2q^{2}-2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots\)
6013.2.a.b \(1\) \(48.014\) \(\Q\) None \(2\) \(-1\) \(0\) \(-1\) \(+\) \(-\) \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-q^{7}-2q^{9}+\cdots\)
6013.2.a.c \(104\) \(48.014\) None \(-19\) \(-26\) \(2\) \(-104\) \(+\) \(+\)
6013.2.a.d \(104\) \(48.014\) None \(-17\) \(-34\) \(-46\) \(104\) \(-\) \(-\)
6013.2.a.e \(109\) \(48.014\) None \(19\) \(38\) \(43\) \(109\) \(-\) \(+\)
6013.2.a.f \(110\) \(48.014\) None \(16\) \(29\) \(0\) \(-110\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6013))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6013)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(859))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

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