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Properties

Label 11.13
Level 11
Weight 13
Dimension 55
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 130
Trace bound 1

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 13 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(130\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(\Gamma_1(11))\).

Total New Old
Modular forms 65 65 0
Cusp forms 55 55 0
Eisenstein series 10 10 0

Trace form

\( 55 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} + 147195 q^{6} - 219605 q^{7} + 921595 q^{8} - 1626565 q^{9} + O(q^{10}) \) \( 55 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} + 147195 q^{6} - 219605 q^{7} + 921595 q^{8} - 1626565 q^{9} + 2620795 q^{11} - 6553610 q^{12} - 6670805 q^{13} - 15388790 q^{14} + 75977555 q^{15} - 147498305 q^{16} - 7887605 q^{17} + 296147970 q^{18} - 59195705 q^{19} - 350824500 q^{20} + 699057445 q^{22} - 213204610 q^{23} + 217767665 q^{24} - 1120322405 q^{25} - 1661299430 q^{26} + 1550199895 q^{27} + 5018997220 q^{28} - 541321205 q^{29} - 7192403540 q^{30} + 1230283795 q^{31} + 4160639295 q^{33} + 12345883610 q^{34} - 3628416965 q^{35} - 27442421730 q^{36} - 3402704405 q^{37} + 9699057220 q^{38} + 24275524235 q^{39} + 17352998460 q^{40} - 20307362045 q^{41} - 84031400650 q^{42} + 86885769280 q^{44} + 43266433790 q^{45} - 10698599530 q^{46} - 17130718805 q^{47} - 38260116960 q^{48} - 4023400925 q^{49} + 8631835695 q^{50} + 103295029335 q^{51} - 124762325930 q^{52} + 81233222395 q^{53} - 119103875285 q^{55} - 79751896300 q^{56} + 156654446895 q^{57} - 16078640780 q^{58} + 143017587535 q^{59} + 68984365060 q^{60} - 130004870645 q^{61} - 478111392680 q^{62} + 56162082000 q^{63} + 251966159415 q^{64} - 224168624370 q^{66} + 84990880790 q^{67} + 550428178040 q^{68} + 677904575350 q^{69} + 273257770020 q^{70} - 776125893605 q^{71} - 1923582671435 q^{72} + 401204208595 q^{73} + 668106311350 q^{74} - 11084424945 q^{75} - 5458797005 q^{77} - 134364155360 q^{78} + 454959862075 q^{79} + 1448142212340 q^{80} + 908812980815 q^{81} + 1080751288345 q^{82} - 1768304661305 q^{83} - 2152859747190 q^{84} - 2586009108005 q^{85} - 1905733708605 q^{86} + 2782018753195 q^{88} + 2203429332590 q^{89} + 6704158241200 q^{90} + 1111122406435 q^{91} - 730816348060 q^{92} + 871645993995 q^{93} - 1053727188680 q^{94} - 7101305012165 q^{95} - 13699998107060 q^{96} - 3941371271105 q^{97} + 7867493365235 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{13}^{\mathrm{new}}(\Gamma_1(11))\)

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
11.13.b \(\chi_{11}(10, \cdot)\) 11.13.b.a 1 1
11.13.b.b 10
11.13.d \(\chi_{11}(2, \cdot)\) 11.13.d.a 44 4