Properties

Label 100.2
Level 100
Weight 2
Dimension 141
Nonzero newspaces 6
Newforms 10
Sturm bound 1200
Trace bound 1

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Defining parameters

Level: \( N \) = \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newforms: \( 10 \)
Sturm bound: \(1200\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(100))\).

Total New Old
Modular forms 370 181 189
Cusp forms 231 141 90
Eisenstein series 139 40 99

Trace form

\(141q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 18q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut -\mathstrut 22q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(141q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 18q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut -\mathstrut 22q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 20q^{13} \) \(\mathstrut -\mathstrut 10q^{14} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut -\mathstrut 48q^{21} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut -\mathstrut 57q^{25} \) \(\mathstrut -\mathstrut 36q^{26} \) \(\mathstrut -\mathstrut 38q^{27} \) \(\mathstrut -\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 52q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut -\mathstrut 26q^{32} \) \(\mathstrut -\mathstrut 40q^{33} \) \(\mathstrut -\mathstrut 10q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{36} \) \(\mathstrut +\mathstrut 9q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut +\mathstrut 48q^{39} \) \(\mathstrut +\mathstrut 44q^{40} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut 90q^{42} \) \(\mathstrut +\mathstrut 60q^{43} \) \(\mathstrut +\mathstrut 60q^{44} \) \(\mathstrut +\mathstrut 55q^{45} \) \(\mathstrut +\mathstrut 42q^{46} \) \(\mathstrut +\mathstrut 52q^{47} \) \(\mathstrut +\mathstrut 120q^{48} \) \(\mathstrut +\mathstrut 51q^{49} \) \(\mathstrut +\mathstrut 94q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 88q^{52} \) \(\mathstrut +\mathstrut q^{53} \) \(\mathstrut +\mathstrut 120q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 42q^{56} \) \(\mathstrut +\mathstrut 44q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut +\mathstrut 6q^{59} \) \(\mathstrut +\mathstrut 90q^{60} \) \(\mathstrut -\mathstrut 88q^{61} \) \(\mathstrut +\mathstrut 40q^{62} \) \(\mathstrut -\mathstrut 14q^{63} \) \(\mathstrut +\mathstrut 20q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut +\mathstrut 30q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut +\mathstrut 14q^{68} \) \(\mathstrut -\mathstrut 66q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 20q^{73} \) \(\mathstrut -\mathstrut 78q^{75} \) \(\mathstrut -\mathstrut 60q^{76} \) \(\mathstrut -\mathstrut 100q^{77} \) \(\mathstrut +\mathstrut 20q^{78} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut -\mathstrut 26q^{80} \) \(\mathstrut +\mathstrut 54q^{81} \) \(\mathstrut -\mathstrut 82q^{82} \) \(\mathstrut -\mathstrut 62q^{83} \) \(\mathstrut -\mathstrut 90q^{84} \) \(\mathstrut +\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 78q^{86} \) \(\mathstrut +\mathstrut 14q^{87} \) \(\mathstrut -\mathstrut 130q^{88} \) \(\mathstrut +\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 166q^{90} \) \(\mathstrut +\mathstrut 12q^{91} \) \(\mathstrut -\mathstrut 110q^{92} \) \(\mathstrut +\mathstrut 74q^{93} \) \(\mathstrut -\mathstrut 170q^{94} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 118q^{96} \) \(\mathstrut +\mathstrut 144q^{97} \) \(\mathstrut -\mathstrut 158q^{98} \) \(\mathstrut +\mathstrut 60q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)

We only show spaces with even 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
100.2.a \(\chi_{100}(1, \cdot)\) 100.2.a.a 1 1
100.2.c \(\chi_{100}(49, \cdot)\) 100.2.c.a 2 1
100.2.e \(\chi_{100}(7, \cdot)\) 100.2.e.a 2 2
100.2.e.b 2
100.2.e.c 2
100.2.e.d 8
100.2.g \(\chi_{100}(21, \cdot)\) 100.2.g.a 12 4
100.2.i \(\chi_{100}(9, \cdot)\) 100.2.i.a 8 4
100.2.l \(\chi_{100}(3, \cdot)\) 100.2.l.a 8 8
100.2.l.b 96

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(100))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(100)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)