Properties

Label 10.9
Level 10
Weight 9
Dimension 8
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 54
Trace bound 0

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(54\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(10))\).

Total New Old
Modular forms 28 8 20
Cusp forms 20 8 12
Eisenstein series 8 0 8

Trace form

\( 8 q + 140 q^{3} - 780 q^{5} + 512 q^{6} + 4540 q^{7} + O(q^{10}) \) \( 8 q + 140 q^{3} - 780 q^{5} + 512 q^{6} + 4540 q^{7} - 6400 q^{10} - 34584 q^{11} + 17920 q^{12} + 119280 q^{13} - 252580 q^{15} - 131072 q^{16} + 202560 q^{17} + 158720 q^{18} + 53760 q^{20} + 110696 q^{21} + 40960 q^{22} + 174540 q^{23} - 368000 q^{25} - 450048 q^{26} - 704560 q^{27} - 581120 q^{28} + 1697280 q^{30} + 2342456 q^{31} - 3190840 q^{33} + 4359900 q^{35} - 618496 q^{36} - 6531240 q^{37} - 5076480 q^{38} + 1146880 q^{40} + 6454056 q^{41} + 13150720 q^{42} + 12059820 q^{43} - 14797820 q^{45} - 17410048 q^{46} - 8748660 q^{47} - 2293760 q^{48} + 5414400 q^{50} + 4713976 q^{51} + 15267840 q^{52} + 30279480 q^{53} - 31155960 q^{55} - 14155776 q^{56} - 21729760 q^{57} - 24194560 q^{58} + 18675200 q^{60} + 41805096 q^{61} + 56017920 q^{62} + 21701900 q^{63} - 18428280 q^{65} - 94667776 q^{66} - 47676980 q^{67} - 25927680 q^{68} + 105582080 q^{70} + 133410936 q^{71} + 20316160 q^{72} - 72484120 q^{73} + 1104700 q^{75} - 44615680 q^{76} - 200406840 q^{77} - 100792320 q^{78} + 12779520 q^{80} + 131272288 q^{81} + 120186880 q^{82} + 135315900 q^{83} - 3822800 q^{85} - 35731968 q^{86} + 66654080 q^{87} - 5242880 q^{88} - 21256960 q^{90} - 291657384 q^{91} + 22341120 q^{92} + 115691240 q^{93} - 242319600 q^{95} - 8388608 q^{96} + 173745000 q^{97} + 115169280 q^{98} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.9.c \(\chi_{10}(3, \cdot)\) 10.9.c.a 4 2
10.9.c.b 4

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 1}\)