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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

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

Display 100 coefficients 10 coefficients

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 available 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