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Properties

Label 11.5
Level 11
Weight 5
Dimension 15
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 50
Trace bound 1

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(50\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(11))\).

Total New Old
Modular forms 25 25 0
Cusp forms 15 15 0
Eisenstein series 10 10 0

Trace form

\( 15 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} + 75 q^{6} - 80 q^{7} - 245 q^{8} - 175 q^{9} + O(q^{10}) \) \( 15 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} + 75 q^{6} - 80 q^{7} - 245 q^{8} - 175 q^{9} + 100 q^{11} + 790 q^{12} + 250 q^{13} + 1210 q^{14} + 605 q^{15} - 945 q^{16} - 1250 q^{17} - 3150 q^{18} - 1025 q^{19} - 900 q^{20} + 1285 q^{22} + 2405 q^{23} + 5345 q^{24} + 2645 q^{25} + 1450 q^{26} - 560 q^{27} - 3580 q^{28} - 2690 q^{29} - 6740 q^{30} - 4415 q^{31} + 6720 q^{33} + 4890 q^{34} + 3610 q^{35} + 990 q^{36} - 2115 q^{37} + 820 q^{38} - 6880 q^{39} - 2340 q^{40} - 4550 q^{41} - 490 q^{42} - 4640 q^{44} + 2240 q^{45} + 4150 q^{46} + 1510 q^{47} + 3840 q^{48} + 2030 q^{49} + 8895 q^{50} + 13155 q^{51} + 14070 q^{52} + 8740 q^{53} - 7985 q^{55} - 20140 q^{56} - 26925 q^{57} - 10940 q^{58} - 10250 q^{59} - 9740 q^{60} + 9460 q^{61} - 6200 q^{62} + 9150 q^{63} + 7495 q^{64} - 7170 q^{66} - 1205 q^{67} - 9400 q^{68} - 9515 q^{69} + 9220 q^{70} + 31975 q^{71} + 43045 q^{72} + 27950 q^{73} + 43270 q^{74} + 8655 q^{75} - 9110 q^{77} - 36800 q^{78} - 41540 q^{79} - 32460 q^{80} - 15115 q^{81} - 39815 q^{82} - 18665 q^{83} + 26250 q^{84} - 4230 q^{85} + 3075 q^{86} - 12485 q^{88} - 10225 q^{89} + 18400 q^{90} + 27790 q^{91} - 1180 q^{92} + 41205 q^{93} + 18920 q^{94} + 14110 q^{95} - 21140 q^{96} + 19470 q^{97} - 8725 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(11))\)

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
11.5.b \(\chi_{11}(10, \cdot)\) 11.5.b.a 1 1
11.5.b.b 2
11.5.d \(\chi_{11}(2, \cdot)\) 11.5.d.a 12 4