Properties

Label 6041.2.a
Level 6041
Weight 2
Character orbit a
Rep. character \(\chi_{6041}(1,\cdot)\)
Character field \(\Q\)
Dimension 431
Newforms 6
Sturm bound 1152
Trace bound 1

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Defining parameters

Level: \( N \) = \( 6041 = 7 \cdot 863 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6041.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(1152\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6041))\).

Total New Old
Modular forms 578 431 147
Cusp forms 575 431 144
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.

\(7\)\(863\)FrickeDim.
\(+\)\(+\)\(+\)\(103\)
\(+\)\(-\)\(-\)\(112\)
\(-\)\(+\)\(-\)\(133\)
\(-\)\(-\)\(+\)\(83\)
Plus space\(+\)\(186\)
Minus space\(-\)\(245\)

Trace form

\(431q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 435q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 423q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(431q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 435q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 423q^{9} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 16q^{12} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 455q^{16} \) \(\mathstrut -\mathstrut 14q^{17} \) \(\mathstrut -\mathstrut 9q^{18} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut +\mathstrut 24q^{22} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 20q^{24} \) \(\mathstrut +\mathstrut 421q^{25} \) \(\mathstrut +\mathstrut 30q^{26} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 18q^{29} \) \(\mathstrut +\mathstrut 20q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 15q^{32} \) \(\mathstrut -\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 463q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut -\mathstrut 52q^{38} \) \(\mathstrut +\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 26q^{40} \) \(\mathstrut -\mathstrut 26q^{41} \) \(\mathstrut +\mathstrut 12q^{42} \) \(\mathstrut -\mathstrut 8q^{44} \) \(\mathstrut +\mathstrut 14q^{45} \) \(\mathstrut +\mathstrut 32q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut -\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 431q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 46q^{52} \) \(\mathstrut +\mathstrut 14q^{53} \) \(\mathstrut -\mathstrut 20q^{54} \) \(\mathstrut +\mathstrut 32q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 26q^{58} \) \(\mathstrut -\mathstrut 44q^{60} \) \(\mathstrut -\mathstrut 14q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 13q^{63} \) \(\mathstrut +\mathstrut 519q^{64} \) \(\mathstrut -\mathstrut 20q^{65} \) \(\mathstrut -\mathstrut 28q^{66} \) \(\mathstrut +\mathstrut 12q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut +\mathstrut 20q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 19q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 14q^{74} \) \(\mathstrut +\mathstrut 40q^{76} \) \(\mathstrut +\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 32q^{79} \) \(\mathstrut -\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 391q^{81} \) \(\mathstrut +\mathstrut 62q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut +\mathstrut 12q^{84} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut +\mathstrut 68q^{88} \) \(\mathstrut -\mathstrut 6q^{89} \) \(\mathstrut -\mathstrut 138q^{90} \) \(\mathstrut -\mathstrut 6q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 48q^{93} \) \(\mathstrut +\mathstrut 92q^{94} \) \(\mathstrut +\mathstrut 40q^{95} \) \(\mathstrut +\mathstrut 92q^{96} \) \(\mathstrut -\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut +\mathstrut 8q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6041))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 863
6041.2.a.a \(1\) \(48.238\) \(\Q\) None \(1\) \(2\) \(-4\) \(1\) \(-\) \(+\) \(q+q^{2}+2q^{3}-q^{4}-4q^{5}+2q^{6}+q^{7}+\cdots\)
6041.2.a.b \(2\) \(48.238\) \(\Q(\sqrt{5}) \) None \(-2\) \(3\) \(1\) \(-2\) \(+\) \(+\) \(q-q^{2}+(1+\beta )q^{3}-q^{4}+(1-\beta )q^{5}+\cdots\)
6041.2.a.c \(83\) \(48.238\) None \(-8\) \(-12\) \(-11\) \(83\) \(-\) \(-\)
6041.2.a.d \(101\) \(48.238\) None \(3\) \(-17\) \(-12\) \(-101\) \(+\) \(+\)
6041.2.a.e \(112\) \(48.238\) None \(-3\) \(14\) \(13\) \(-112\) \(+\) \(-\)
6041.2.a.f \(132\) \(48.238\) None \(8\) \(10\) \(11\) \(132\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6041))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6041)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(863))\)\(^{\oplus 2}\)