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Properties

Label 5.9
Level 5
Weight 9
Dimension 6
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 18
Trace bound 0

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(5))\).

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

Trace form

\( 6 q - 2 q^{2} - 72 q^{3} + 220 q^{5} + 1752 q^{6} - 2352 q^{7} - 8220 q^{8} + O(q^{10}) \) \( 6 q - 2 q^{2} - 72 q^{3} + 220 q^{5} + 1752 q^{6} - 2352 q^{7} - 8220 q^{8} + 30870 q^{10} + 23192 q^{11} - 45912 q^{12} - 119142 q^{13} + 241440 q^{15} + 218616 q^{16} - 265502 q^{17} - 454062 q^{18} + 412260 q^{20} + 231672 q^{21} - 35664 q^{22} + 28888 q^{23} - 340350 q^{25} - 801388 q^{26} + 392040 q^{27} + 1305192 q^{28} - 2549760 q^{30} - 747648 q^{31} + 3033928 q^{32} + 4269096 q^{33} - 4971680 q^{35} - 3972804 q^{36} - 454002 q^{37} + 1443720 q^{38} + 2683500 q^{40} + 2489432 q^{41} + 4223856 q^{42} + 792648 q^{43} + 210690 q^{45} - 3149928 q^{46} - 15313352 q^{47} - 21677712 q^{48} + 29537650 q^{50} + 35567712 q^{51} - 735732 q^{52} - 13509122 q^{53} + 4448040 q^{55} - 18454800 q^{56} - 34625520 q^{57} - 23903520 q^{58} + 13688520 q^{60} + 24111192 q^{61} + 53913416 q^{62} + 44837688 q^{63} - 30943610 q^{65} - 55047936 q^{66} - 32827752 q^{67} + 8118692 q^{68} - 44156280 q^{70} - 13992928 q^{71} + 82596420 q^{72} + 111859638 q^{73} - 126793200 q^{75} - 56470800 q^{76} + 26260136 q^{77} + 31125576 q^{78} + 23045920 q^{80} + 65834226 q^{81} + 38023056 q^{82} - 14768432 q^{83} - 19713030 q^{85} - 135560008 q^{86} - 133207680 q^{87} - 44555040 q^{88} + 135147990 q^{90} + 167542032 q^{91} + 69931048 q^{92} - 96798024 q^{93} + 239661000 q^{95} + 184867872 q^{96} - 186656202 q^{97} - 345959698 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(5))\)

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
5.9.c \(\chi_{5}(2, \cdot)\) 5.9.c.a 6 2