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Properties

Label 5.11
Level 5
Weight 11
Dimension 8
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 22
Trace bound 0

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(22\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 12 12 0
Cusp forms 8 8 0
Eisenstein series 4 4 0

Trace form

\( 8 q + 30 q^{2} + 60 q^{3} - 5340 q^{5} + 17016 q^{6} - 14500 q^{7} + 22020 q^{8} + O(q^{10}) \) \( 8 q + 30 q^{2} + 60 q^{3} - 5340 q^{5} + 17016 q^{6} - 14500 q^{7} + 22020 q^{8} - 161290 q^{10} - 233784 q^{11} + 863160 q^{12} + 433520 q^{13} - 3188580 q^{15} - 1193992 q^{16} + 1045440 q^{17} + 12804210 q^{18} - 16739820 q^{20} - 20777784 q^{21} + 25939360 q^{22} + 24737580 q^{23} - 35382400 q^{25} - 34440684 q^{26} + 27386640 q^{27} + 89876920 q^{28} - 115784880 q^{30} + 258616 q^{31} - 11664120 q^{32} + 11269320 q^{33} + 113638860 q^{35} + 66085308 q^{36} + 92216120 q^{37} - 435848520 q^{38} + 432590700 q^{40} + 115357416 q^{41} - 609152160 q^{42} - 262653700 q^{43} + 593742420 q^{45} + 1023085816 q^{46} - 669481140 q^{47} - 618046320 q^{48} + 944762850 q^{50} - 768258984 q^{51} - 70856500 q^{52} - 1321976040 q^{53} + 2597320 q^{55} + 852915600 q^{56} + 2367269280 q^{57} + 2687784720 q^{58} - 4237774440 q^{60} - 3143200184 q^{61} - 1373690040 q^{62} + 2578662540 q^{63} - 1924527480 q^{65} + 766734432 q^{66} + 4912566140 q^{67} + 6614874660 q^{68} - 8299690440 q^{70} - 4375053384 q^{71} + 808889220 q^{72} - 786968920 q^{73} + 5379002700 q^{75} - 5577898800 q^{76} + 7522045800 q^{77} + 4109901000 q^{78} + 47717760 q^{80} - 2499208992 q^{81} - 19442731040 q^{82} - 11064240660 q^{83} + 15814282160 q^{85} + 36286046616 q^{86} + 2020273920 q^{87} - 13252572960 q^{88} + 9489047670 q^{90} - 12917794184 q^{91} - 25757138760 q^{92} - 40141724280 q^{93} + 14671558800 q^{95} + 38082222816 q^{96} + 24688294760 q^{97} + 13744332030 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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
5.11.c \(\chi_{5}(2, \cdot)\) 5.11.c.a 8 2