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Properties

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

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
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

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

Display 100 coefficients 10 coefficients

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 available 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