Properties

Label 11.3
Level 11
Weight 3
Dimension 5
Nonzero newspaces 2
Newforms 2
Sturm bound 30
Trace bound 1

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 2 \)
Sturm bound: \(30\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(11))\).

Total New Old
Modular forms 15 15 0
Cusp forms 5 5 0
Eisenstein series 10 10 0

Trace form

\( 5q - 5q^{2} - 5q^{3} - 5q^{4} - 5q^{5} + 15q^{6} + 10q^{7} + 15q^{8} + 5q^{9} + O(q^{10}) \) \( 5q - 5q^{2} - 5q^{3} - 5q^{4} - 5q^{5} + 15q^{6} + 10q^{7} + 15q^{8} + 5q^{9} - 10q^{11} - 50q^{12} - 20q^{13} - 10q^{14} + 5q^{15} + 35q^{16} + 30q^{18} + 25q^{19} + 40q^{20} - 35q^{22} + 15q^{23} + 5q^{24} - 15q^{25} - 10q^{26} - 20q^{27} - 60q^{28} - 40q^{29} - 80q^{30} - 95q^{31} + 120q^{33} + 130q^{34} + 80q^{35} + 90q^{36} + 65q^{37} - 60q^{38} + 50q^{39} - 60q^{40} - 80q^{41} - 10q^{42} - 20q^{44} - 40q^{45} + 30q^{46} + 20q^{47} - 120q^{48} - 60q^{49} - 45q^{50} - 195q^{51} + 110q^{52} + 50q^{53} - 65q^{55} + 100q^{56} + 45q^{57} + 40q^{58} + 130q^{59} + 160q^{60} + 10q^{61} + 200q^{62} + 90q^{63} - 85q^{64} + 90q^{66} - 195q^{67} - 260q^{68} - 185q^{69} - 40q^{70} + 15q^{71} - 95q^{72} + 300q^{73} - 270q^{74} + 165q^{75} - 200q^{77} - 200q^{78} + 70q^{79} - 100q^{80} - 85q^{81} + 25q^{82} + 225q^{83} + 90q^{84} + 260q^{85} + 175q^{86} + 55q^{88} + 25q^{89} - 20q^{90} - 80q^{91} + 180q^{92} - 15q^{93} + 120q^{94} - 100q^{95} + 340q^{96} - 70q^{97} - 145q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(11))\)

We only show spaces with odd 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
11.3.b \(\chi_{11}(10, \cdot)\) 11.3.b.a 1 1
11.3.d \(\chi_{11}(2, \cdot)\) 11.3.d.a 4 4