Properties

Label 41.2.a
Level 41
Weight 2
Character orbit a
Rep. character \(\chi_{41}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 1
Sturm bound 7
Trace bound 0

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Defining parameters

Level: \( N \) = \( 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 41.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(41))\).

Total New Old
Modular forms 4 4 0
Cusp forms 3 3 0
Eisenstein series 1 1 0

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

\(41\)Dim.
\(-\)\(3\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(41))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 41
41.2.a.a \(3\) \(0.327\) 3.3.148.1 None \(-1\) \(0\) \(-2\) \(6\) \(-\) \(q+(-\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)