Properties

Label 11.6
Level 11
Weight 6
Dimension 20
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 60
Trace bound 1

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(60\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(11))\).

Total New Old
Modular forms 30 28 2
Cusp forms 20 20 0
Eisenstein series 10 8 2

Trace form

\( 20q - 5q^{2} - 5q^{3} - 5q^{4} - 5q^{5} - 25q^{6} + 290q^{7} + 155q^{8} - 555q^{9} + O(q^{10}) \) \( 20q - 5q^{2} - 5q^{3} - 5q^{4} - 5q^{5} - 25q^{6} + 290q^{7} + 155q^{8} - 555q^{9} - 1010q^{10} - 450q^{11} - 330q^{12} + 500q^{13} - 500q^{14} + 3735q^{15} + 8135q^{16} + 1750q^{17} - 2800q^{18} - 2240q^{19} - 8690q^{20} - 8830q^{21} - 12575q^{22} - 10205q^{23} - 1395q^{24} + 12865q^{25} + 32940q^{26} + 23425q^{27} + 32390q^{28} + 4220q^{29} - 21320q^{30} - 25305q^{31} - 76340q^{32} - 42615q^{33} - 4390q^{34} + 18950q^{35} + 68740q^{36} + 34425q^{37} + 60440q^{38} + 30960q^{39} + 33360q^{40} - 10340q^{41} - 117150q^{42} - 54610q^{43} - 92860q^{44} - 78680q^{45} + 18810q^{46} + 30300q^{47} + 95140q^{48} + 64070q^{49} + 62965q^{50} + 42550q^{51} - 97590q^{52} + 9070q^{53} + 46950q^{54} + 12255q^{55} + 30240q^{56} - 14100q^{57} + 2800q^{58} + 60605q^{59} + 28100q^{60} - 29940q^{61} - 147590q^{62} - 19740q^{63} + 26015q^{64} - 27140q^{65} + 15820q^{66} - 81955q^{67} - 117690q^{68} - 83005q^{69} - 226380q^{70} - 114075q^{71} - 113225q^{72} + 15600q^{73} + 411090q^{74} + 266140q^{75} + 284870q^{76} + 393600q^{77} + 417020q^{78} + 214610q^{79} - 262900q^{80} - 400680q^{81} - 565515q^{82} - 292670q^{83} + 74060q^{84} - 53160q^{85} + 282095q^{86} + 14400q^{87} + 120395q^{88} + 58955q^{89} - 245130q^{90} - 379560q^{91} - 454530q^{92} - 307455q^{93} - 158970q^{94} - 19620q^{95} + 328740q^{96} + 560885q^{97} + 814000q^{98} + 726295q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)

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
11.6.a \(\chi_{11}(1, \cdot)\) 11.6.a.a 1 1
11.6.a.b 3
11.6.c \(\chi_{11}(3, \cdot)\) 11.6.c.a 16 4