Properties

Label 36.2
Level 36
Weight 2
Dimension 13
Nonzero newspaces 4
Newforms 4
Sturm bound 144
Trace bound 4

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Defining parameters

Level: \( N \) = \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newforms: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(36))\).

Total New Old
Modular forms 56 21 35
Cusp forms 17 13 4
Eisenstein series 39 8 31

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)

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
36.2.a \(\chi_{36}(1, \cdot)\) 36.2.a.a 1 1
36.2.b \(\chi_{36}(35, \cdot)\) 36.2.b.a 2 1
36.2.e \(\chi_{36}(13, \cdot)\) 36.2.e.a 2 2
36.2.h \(\chi_{36}(11, \cdot)\) 36.2.h.a 8 2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(36))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(36)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)