Properties

Label 10.5
Level 10
Weight 5
Dimension 4
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 30
Trace bound 0

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(30\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(10))\).

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\( 4 q + 20 q^{3} - 60 q^{5} - 64 q^{6} + 20 q^{7} + O(q^{10}) \) \( 4 q + 20 q^{3} - 60 q^{5} - 64 q^{6} + 20 q^{7} + 160 q^{10} + 168 q^{11} + 160 q^{12} - 60 q^{13} + 20 q^{15} - 256 q^{16} - 1020 q^{17} - 640 q^{18} + 968 q^{21} + 1280 q^{22} + 1620 q^{23} - 700 q^{25} - 1344 q^{26} + 320 q^{27} - 160 q^{28} + 960 q^{30} - 1112 q^{31} - 1720 q^{33} - 2220 q^{35} + 32 q^{36} - 1020 q^{37} + 960 q^{38} + 1280 q^{40} + 5448 q^{41} - 2240 q^{42} + 660 q^{43} + 6400 q^{45} + 2176 q^{46} + 1620 q^{47} - 1280 q^{48} - 4800 q^{50} - 10712 q^{51} - 480 q^{52} - 4860 q^{53} - 2520 q^{55} + 3072 q^{56} + 5120 q^{57} + 3520 q^{58} - 4960 q^{60} - 7032 q^{61} - 3840 q^{62} + 7700 q^{63} + 7620 q^{65} + 10112 q^{66} + 8660 q^{67} + 8160 q^{68} + 1600 q^{70} + 5928 q^{71} - 5120 q^{72} - 12860 q^{73} - 13100 q^{75} - 5120 q^{76} - 14520 q^{77} - 5760 q^{78} + 3840 q^{80} + 964 q^{81} - 2560 q^{82} - 300 q^{83} + 16580 q^{85} - 14784 q^{86} + 11840 q^{87} - 10240 q^{88} + 9440 q^{90} + 15528 q^{91} + 12960 q^{92} + 2120 q^{93} - 9600 q^{95} + 4096 q^{96} - 13500 q^{97} + 3840 q^{98} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(10))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
10.5.c \(\chi_{10}(3, \cdot)\) 10.5.c.a 2 2
10.5.c.b 2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

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