Properties

Label 33.2
Level 33
Weight 2
Dimension 19
Nonzero newspaces 4
Newforms 5
Sturm bound 160
Trace bound 2

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Defining parameters

Level: \( N \) = \( 33 = 3 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newforms: \( 5 \)
Sturm bound: \(160\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(33))\).

Total New Old
Modular forms 60 39 21
Cusp forms 21 19 2
Eisenstein series 39 20 19

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)

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
33.2.a \(\chi_{33}(1, \cdot)\) 33.2.a.a 1 1
33.2.d \(\chi_{33}(32, \cdot)\) 33.2.d.a 2 1
33.2.e \(\chi_{33}(4, \cdot)\) 33.2.e.a 4 4
33.2.e.b 4
33.2.f \(\chi_{33}(2, \cdot)\) 33.2.f.a 8 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(33))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(33)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)