Properties

Label 6010.2.a
Level 6010
Weight 2
Character orbit a
Rep. character \(\chi_{6010}(1,\cdot)\)
Character field \(\Q\)
Dimension 199
Newforms 10
Sturm bound 1806
Trace bound 3

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Defining parameters

Level: \( N \) = \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6010.a (trivial)
Character field: \(\Q\)
Newforms: \( 10 \)
Sturm bound: \(1806\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6010))\).

Total New Old
Modular forms 906 199 707
Cusp forms 899 199 700
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.

\(2\)\(5\)\(601\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(29\)
\(+\)\(+\)\(-\)\(-\)\(21\)
\(+\)\(-\)\(+\)\(-\)\(27\)
\(+\)\(-\)\(-\)\(+\)\(23\)
\(-\)\(+\)\(+\)\(-\)\(28\)
\(-\)\(+\)\(-\)\(+\)\(22\)
\(-\)\(-\)\(+\)\(+\)\(16\)
\(-\)\(-\)\(-\)\(-\)\(33\)
Plus space\(+\)\(90\)
Minus space\(-\)\(109\)

Trace form

\( 199q - q^{2} - 4q^{3} + 199q^{4} - q^{5} - 4q^{6} - 8q^{7} - q^{8} + 195q^{9} + O(q^{10}) \) \( 199q - q^{2} - 4q^{3} + 199q^{4} - q^{5} - 4q^{6} - 8q^{7} - q^{8} + 195q^{9} - q^{10} + 4q^{11} - 4q^{12} - 6q^{13} - 8q^{14} + 4q^{15} + 199q^{16} - 2q^{17} + 3q^{18} - 20q^{19} - q^{20} + 16q^{21} - 8q^{22} + 16q^{23} - 4q^{24} + 199q^{25} + 10q^{26} + 8q^{27} - 8q^{28} + 2q^{29} - 4q^{30} - q^{32} + 40q^{33} - 2q^{34} - 4q^{35} + 195q^{36} - 6q^{37} + 24q^{39} - q^{40} + 14q^{41} + 32q^{42} + 4q^{44} + 3q^{45} - 8q^{46} + 24q^{47} - 4q^{48} + 159q^{49} - q^{50} + 16q^{51} - 6q^{52} - 10q^{53} + 8q^{54} - 12q^{55} - 8q^{56} - 24q^{57} + 30q^{58} - 28q^{59} + 4q^{60} - 22q^{61} + 16q^{62} - 24q^{63} + 199q^{64} - 6q^{65} + 16q^{66} - 36q^{67} - 2q^{68} - 4q^{70} + 16q^{71} + 3q^{72} - 10q^{73} + 18q^{74} - 4q^{75} - 20q^{76} - 16q^{77} + 16q^{78} - 40q^{79} - q^{80} + 143q^{81} + 14q^{82} + 16q^{83} + 16q^{84} + 10q^{85} - 4q^{86} + 16q^{87} - 8q^{88} + 22q^{89} - 13q^{90} - 16q^{91} + 16q^{92} - 24q^{93} - 16q^{94} + 20q^{95} - 4q^{96} - 2q^{97} + 39q^{98} + 44q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6010))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 601
6010.2.a.a \(1\) \(47.990\) \(\Q\) None \(-1\) \(-3\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-3q^{3}+q^{4}+q^{5}+3q^{6}-q^{8}+\cdots\)
6010.2.a.b \(1\) \(47.990\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-3q^{9}-q^{10}+\cdots\)
6010.2.a.c \(16\) \(47.990\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(-8\) \(16\) \(-10\) \(-\) \(-\) \(+\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
6010.2.a.d \(21\) \(47.990\) None \(-21\) \(-1\) \(21\) \(0\) \(+\) \(-\) \(-\)
6010.2.a.e \(21\) \(47.990\) None \(-21\) \(8\) \(-21\) \(0\) \(+\) \(+\) \(-\)
6010.2.a.f \(22\) \(47.990\) None \(22\) \(-6\) \(-22\) \(-12\) \(-\) \(+\) \(-\)
6010.2.a.g \(27\) \(47.990\) None \(-27\) \(6\) \(27\) \(0\) \(+\) \(-\) \(+\)
6010.2.a.h \(28\) \(47.990\) None \(28\) \(4\) \(-28\) \(10\) \(-\) \(+\) \(+\)
6010.2.a.i \(29\) \(47.990\) None \(-29\) \(-10\) \(-29\) \(0\) \(+\) \(+\) \(+\)
6010.2.a.j \(33\) \(47.990\) None \(33\) \(6\) \(33\) \(4\) \(-\) \(-\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6010))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6010)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(601))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1202))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3005))\)\(^{\oplus 2}\)