Properties

Label 6009.2.a
Level 6009
Weight 2
Character orbit a
Rep. character \(\chi_{6009}(1,\cdot)\)
Character field \(\Q\)
Dimension 333
Newforms 4
Sturm bound 1336
Trace bound 2

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Defining parameters

Level: \( N \) = \( 6009 = 3 \cdot 2003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6009.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(1336\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6009))\).

Total New Old
Modular forms 670 333 337
Cusp forms 667 333 334
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.

\(3\)\(2003\)FrickeDim.
\(+\)\(+\)\(+\)\(74\)
\(+\)\(-\)\(-\)\(93\)
\(-\)\(+\)\(-\)\(92\)
\(-\)\(-\)\(+\)\(74\)
Plus space\(+\)\(148\)
Minus space\(-\)\(185\)

Trace form

\(333q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 335q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 333q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(333q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 335q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 333q^{9} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 327q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 30q^{20} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 335q^{25} \) \(\mathstrut -\mathstrut 22q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut +\mathstrut 28q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut +\mathstrut 29q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut +\mathstrut 10q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 335q^{36} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut +\mathstrut 28q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 2q^{40} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut +\mathstrut 28q^{44} \) \(\mathstrut -\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut +\mathstrut 12q^{47} \) \(\mathstrut +\mathstrut q^{48} \) \(\mathstrut +\mathstrut 305q^{49} \) \(\mathstrut +\mathstrut 11q^{50} \) \(\mathstrut +\mathstrut 10q^{51} \) \(\mathstrut +\mathstrut 18q^{52} \) \(\mathstrut -\mathstrut 14q^{53} \) \(\mathstrut +\mathstrut 3q^{54} \) \(\mathstrut -\mathstrut 24q^{55} \) \(\mathstrut -\mathstrut 4q^{56} \) \(\mathstrut -\mathstrut 12q^{57} \) \(\mathstrut -\mathstrut 10q^{58} \) \(\mathstrut -\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 10q^{61} \) \(\mathstrut -\mathstrut 8q^{62} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut -\mathstrut 32q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut -\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 20q^{71} \) \(\mathstrut +\mathstrut 9q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 30q^{74} \) \(\mathstrut -\mathstrut 23q^{75} \) \(\mathstrut -\mathstrut 24q^{76} \) \(\mathstrut -\mathstrut 44q^{77} \) \(\mathstrut -\mathstrut 10q^{78} \) \(\mathstrut +\mathstrut 12q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 333q^{81} \) \(\mathstrut -\mathstrut 54q^{82} \) \(\mathstrut -\mathstrut 48q^{83} \) \(\mathstrut -\mathstrut 4q^{84} \) \(\mathstrut -\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 14q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut -\mathstrut 66q^{89} \) \(\mathstrut +\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 16q^{92} \) \(\mathstrut +\mathstrut 4q^{93} \) \(\mathstrut +\mathstrut 28q^{94} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut +\mathstrut 23q^{96} \) \(\mathstrut -\mathstrut 14q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6009))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 2003
6009.2.a.a \(74\) \(47.982\) None \(-15\) \(74\) \(-34\) \(-24\) \(-\) \(-\)
6009.2.a.b \(74\) \(47.982\) None \(-3\) \(-74\) \(14\) \(-26\) \(+\) \(+\)
6009.2.a.c \(92\) \(47.982\) None \(17\) \(92\) \(34\) \(22\) \(-\) \(+\)
6009.2.a.d \(93\) \(47.982\) None \(2\) \(-93\) \(-20\) \(28\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6009))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6009)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(2003))\)\(^{\oplus 2}\)