Properties

Label 6005.2.a
Level 6005
Weight 2
Character orbit a
Rep. character \(\chi_{6005}(1,\cdot)\)
Character field \(\Q\)
Dimension 401
Newforms 7
Sturm bound 1202
Trace bound 2

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Defining parameters

Level: \( N \) = \( 6005 = 5 \cdot 1201 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6005.a (trivial)
Character field: \(\Q\)
Newforms: \( 7 \)
Sturm bound: \(1202\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6005))\).

Total New Old
Modular forms 602 401 201
Cusp forms 599 401 198
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.

\(5\)\(1201\)FrickeDim.
\(+\)\(+\)\(+\)\(87\)
\(+\)\(-\)\(-\)\(113\)
\(-\)\(+\)\(-\)\(113\)
\(-\)\(-\)\(+\)\(88\)
Plus space\(+\)\(175\)
Minus space\(-\)\(226\)

Trace form

\(401q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 407q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 413q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(401q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 407q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 413q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut +\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut +\mathstrut 10q^{13} \) \(\mathstrut -\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 423q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 9q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 401q^{25} \) \(\mathstrut -\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 8q^{27} \) \(\mathstrut +\mathstrut 32q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 12q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 479q^{36} \) \(\mathstrut +\mathstrut 10q^{37} \) \(\mathstrut +\mathstrut 16q^{38} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 20q^{42} \) \(\mathstrut +\mathstrut 36q^{43} \) \(\mathstrut +\mathstrut 56q^{44} \) \(\mathstrut +\mathstrut 5q^{45} \) \(\mathstrut +\mathstrut 64q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 48q^{48} \) \(\mathstrut +\mathstrut 421q^{49} \) \(\mathstrut +\mathstrut 3q^{50} \) \(\mathstrut -\mathstrut 20q^{51} \) \(\mathstrut +\mathstrut 6q^{52} \) \(\mathstrut -\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut -\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut +\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 26q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 28q^{60} \) \(\mathstrut +\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut -\mathstrut 16q^{63} \) \(\mathstrut +\mathstrut 403q^{64} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut 56q^{66} \) \(\mathstrut +\mathstrut 60q^{67} \) \(\mathstrut +\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 56q^{69} \) \(\mathstrut -\mathstrut 8q^{70} \) \(\mathstrut -\mathstrut 20q^{71} \) \(\mathstrut -\mathstrut 9q^{72} \) \(\mathstrut +\mathstrut 38q^{73} \) \(\mathstrut -\mathstrut 26q^{74} \) \(\mathstrut +\mathstrut 4q^{75} \) \(\mathstrut +\mathstrut 76q^{76} \) \(\mathstrut -\mathstrut 60q^{77} \) \(\mathstrut -\mathstrut 60q^{78} \) \(\mathstrut +\mathstrut 52q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 417q^{81} \) \(\mathstrut -\mathstrut 78q^{82} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut -\mathstrut 20q^{84} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut +\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 68q^{87} \) \(\mathstrut -\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 6q^{89} \) \(\mathstrut +\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 4q^{91} \) \(\mathstrut -\mathstrut 8q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 44q^{94} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut -\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 7q^{98} \) \(\mathstrut +\mathstrut 76q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6005))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 1201
6005.2.a.a \(1\) \(47.950\) \(\Q\) None \(-2\) \(-2\) \(1\) \(-2\) \(-\) \(+\) \(q-2q^{2}-2q^{3}+2q^{4}+q^{5}+4q^{6}+\cdots\)
6005.2.a.b \(1\) \(47.950\) \(\Q\) None \(-1\) \(0\) \(1\) \(4\) \(-\) \(+\) \(q-q^{2}-q^{4}+q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots\)
6005.2.a.c \(4\) \(47.950\) 4.4.2777.1 None \(2\) \(-2\) \(-4\) \(-7\) \(+\) \(+\) \(q+(1-\beta _{3})q^{2}+(-1-\beta _{2}+\beta _{3})q^{3}+\cdots\)
6005.2.a.d \(83\) \(47.950\) None \(1\) \(-4\) \(-83\) \(2\) \(+\) \(+\)
6005.2.a.e \(88\) \(47.950\) None \(-14\) \(-34\) \(88\) \(-35\) \(-\) \(-\)
6005.2.a.f \(111\) \(47.950\) None \(20\) \(40\) \(111\) \(39\) \(-\) \(+\)
6005.2.a.g \(113\) \(47.950\) None \(-3\) \(6\) \(-113\) \(7\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6005))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6005)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1201))\)\(^{\oplus 2}\)