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Properties

Label 11.11
Level 11
Weight 11
Dimension 45
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 110
Trace bound 1

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(110\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 55 55 0
Cusp forms 45 45 0
Eisenstein series 10 10 0

Trace form

\( 45 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} - 3525 q^{6} - 9740 q^{7} - 56325 q^{8} + 198545 q^{9} + O(q^{10}) \) \( 45 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} - 3525 q^{6} - 9740 q^{7} - 56325 q^{8} + 198545 q^{9} - 245200 q^{11} - 317450 q^{12} + 516610 q^{13} + 96410 q^{14} - 61495 q^{15} - 179745 q^{16} - 1563930 q^{17} - 3716190 q^{18} + 6441265 q^{19} + 16211140 q^{20} - 29049275 q^{22} - 19203795 q^{23} - 6935455 q^{24} + 62455685 q^{25} + 61650650 q^{26} - 38545490 q^{27} - 158441860 q^{28} - 30773770 q^{29} + 164452420 q^{30} + 155856685 q^{31} - 318996030 q^{33} - 16160070 q^{34} + 93755030 q^{35} + 67473990 q^{36} - 125448075 q^{37} + 109342140 q^{38} + 13696700 q^{39} + 66388740 q^{40} + 168755230 q^{41} + 54207230 q^{42} + 822430600 q^{44} - 1232915140 q^{45} - 843022850 q^{46} - 592219270 q^{47} - 458884920 q^{48} + 758776970 q^{49} + 1888812255 q^{50} + 2730932925 q^{51} - 1016067090 q^{52} - 1495992580 q^{53} + 801748135 q^{55} + 526524340 q^{56} - 1846600035 q^{57} - 7980213620 q^{58} - 2451810080 q^{59} + 2412560860 q^{60} + 4185015940 q^{61} + 8028589520 q^{62} + 5208740790 q^{63} + 4907781175 q^{64} - 7249567290 q^{66} - 8139514625 q^{67} - 12578329400 q^{68} - 5687707475 q^{69} - 4341760940 q^{70} + 4604271975 q^{71} + 14192383525 q^{72} + 6815310530 q^{73} + 27099775830 q^{74} + 22395754365 q^{75} - 20989098770 q^{77} - 52369004240 q^{78} - 28511789960 q^{79} - 12669286300 q^{80} + 4593744095 q^{81} + 5066108185 q^{82} + 6078874665 q^{83} + 75048937530 q^{84} + 52883120010 q^{85} + 36398318275 q^{86} - 56740848725 q^{88} - 39773682245 q^{89} - 98405028320 q^{90} - 57076722290 q^{91} - 41759733300 q^{92} + 19079675445 q^{93} + 94886813720 q^{94} + 79444332050 q^{95} + 162737230420 q^{96} + 56595302880 q^{97} - 76782985105 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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
11.11.b \(\chi_{11}(10, \cdot)\) 11.11.b.a 1 1
11.11.b.b 8
11.11.d \(\chi_{11}(2, \cdot)\) 11.11.d.a 36 4