Properties

Label 6013.2.a
Level 6013
Weight 2
Character orbit a
Rep. character \(\chi_{6013}(1,\cdot)\)
Character field \(\Q\)
Dimension 429
Newforms 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: \(\Q\)
Newforms: \( 6 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6013))\) into irreducible Hecke orbits

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

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