Properties

Label 61.2
Level 61
Weight 2
Dimension 126
Nonzero newspaces 8
Newforms 10
Sturm bound 620
Trace bound 3

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Defining parameters

Level: \( N \) = \( 61 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newforms: \( 10 \)
Sturm bound: \(620\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(61))\).

Total New Old
Modular forms 185 185 0
Cusp forms 126 126 0
Eisenstein series 59 59 0

Trace form

\(126q \) \(\mathstrut -\mathstrut 27q^{2} \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut -\mathstrut 23q^{4} \) \(\mathstrut -\mathstrut 24q^{5} \) \(\mathstrut -\mathstrut 18q^{6} \) \(\mathstrut -\mathstrut 22q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut -\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(126q \) \(\mathstrut -\mathstrut 27q^{2} \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut -\mathstrut 23q^{4} \) \(\mathstrut -\mathstrut 24q^{5} \) \(\mathstrut -\mathstrut 18q^{6} \) \(\mathstrut -\mathstrut 22q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut -\mathstrut 17q^{9} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut -\mathstrut 2q^{12} \) \(\mathstrut -\mathstrut 16q^{13} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut q^{16} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut +\mathstrut 9q^{18} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut +\mathstrut 12q^{20} \) \(\mathstrut +\mathstrut 2q^{21} \) \(\mathstrut +\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 12q^{26} \) \(\mathstrut +\mathstrut 10q^{27} \) \(\mathstrut +\mathstrut 26q^{28} \) \(\mathstrut +\mathstrut 42q^{30} \) \(\mathstrut +\mathstrut 2q^{31} \) \(\mathstrut +\mathstrut 33q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 24q^{34} \) \(\mathstrut +\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 61q^{36} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 30q^{38} \) \(\mathstrut +\mathstrut 26q^{39} \) \(\mathstrut +\mathstrut 60q^{40} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut +\mathstrut 66q^{42} \) \(\mathstrut +\mathstrut 14q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 48q^{45} \) \(\mathstrut +\mathstrut 42q^{46} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut -\mathstrut 6q^{48} \) \(\mathstrut -\mathstrut 43q^{49} \) \(\mathstrut -\mathstrut 12q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 157q^{52} \) \(\mathstrut -\mathstrut 6q^{53} \) \(\mathstrut -\mathstrut 90q^{54} \) \(\mathstrut -\mathstrut 78q^{55} \) \(\mathstrut -\mathstrut 90q^{56} \) \(\mathstrut -\mathstrut 70q^{57} \) \(\mathstrut -\mathstrut 60q^{58} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 132q^{60} \) \(\mathstrut -\mathstrut 99q^{61} \) \(\mathstrut -\mathstrut 144q^{62} \) \(\mathstrut -\mathstrut 56q^{63} \) \(\mathstrut -\mathstrut 143q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut -\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 82q^{67} \) \(\mathstrut -\mathstrut 84q^{68} \) \(\mathstrut -\mathstrut 54q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut +\mathstrut 12q^{71} \) \(\mathstrut -\mathstrut 60q^{72} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 10q^{76} \) \(\mathstrut +\mathstrut 36q^{77} \) \(\mathstrut +\mathstrut 138q^{78} \) \(\mathstrut +\mathstrut 50q^{79} \) \(\mathstrut +\mathstrut 156q^{80} \) \(\mathstrut +\mathstrut 91q^{81} \) \(\mathstrut +\mathstrut 96q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 194q^{84} \) \(\mathstrut +\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 102q^{86} \) \(\mathstrut +\mathstrut 90q^{87} \) \(\mathstrut +\mathstrut 150q^{88} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut +\mathstrut 204q^{90} \) \(\mathstrut +\mathstrut 82q^{91} \) \(\mathstrut +\mathstrut 138q^{92} \) \(\mathstrut +\mathstrut 98q^{93} \) \(\mathstrut +\mathstrut 114q^{94} \) \(\mathstrut +\mathstrut 90q^{95} \) \(\mathstrut +\mathstrut 222q^{96} \) \(\mathstrut +\mathstrut 68q^{97} \) \(\mathstrut +\mathstrut 141q^{98} \) \(\mathstrut +\mathstrut 126q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(61))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
61.2.a \(\chi_{61}(1, \cdot)\) 61.2.a.a 1 1
61.2.a.b 3
61.2.b \(\chi_{61}(60, \cdot)\) 61.2.b.a 4 1
61.2.c \(\chi_{61}(13, \cdot)\) 61.2.c.a 8 2
61.2.e \(\chi_{61}(9, \cdot)\) 61.2.e.a 12 4
61.2.f \(\chi_{61}(14, \cdot)\) 61.2.f.a 2 2
61.2.f.b 8
61.2.g \(\chi_{61}(3, \cdot)\) 61.2.g.a 16 4
61.2.i \(\chi_{61}(12, \cdot)\) 61.2.i.a 32 8
61.2.k \(\chi_{61}(4, \cdot)\) 61.2.k.a 40 8