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Properties

Label 100.3
Level 100
Weight 3
Dimension 302
Nonzero newspaces 6
Newform subspaces 14
Sturm bound 1800
Trace bound 2

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Defining parameters

Level: \( N \) = \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 14 \)
Sturm bound: \(1800\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(100))\).

Total New Old
Modular forms 670 344 326
Cusp forms 530 302 228
Eisenstein series 140 42 98

Trace form

\( 302 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 10 q^{5} + 14 q^{6} + 28 q^{7} + 6 q^{8} - 4 q^{9} + O(q^{10}) \) \( 302 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 10 q^{5} + 14 q^{6} + 28 q^{7} + 6 q^{8} - 4 q^{9} - 16 q^{10} - 40 q^{11} - 90 q^{12} - 24 q^{13} - 122 q^{14} - 2 q^{15} - 114 q^{16} + 94 q^{17} - 54 q^{18} + 100 q^{19} + 34 q^{20} + 64 q^{21} + 150 q^{22} + 112 q^{23} + 268 q^{24} - 92 q^{25} + 188 q^{26} - 154 q^{27} + 70 q^{28} - 184 q^{29} - 50 q^{30} - 84 q^{31} - 266 q^{32} - 400 q^{33} - 322 q^{34} - 208 q^{35} - 330 q^{36} - 244 q^{37} - 500 q^{38} - 400 q^{39} - 436 q^{40} - 92 q^{41} - 470 q^{42} - 180 q^{43} - 200 q^{44} - 120 q^{45} + 74 q^{46} + 76 q^{47} - 140 q^{48} + 296 q^{49} - 6 q^{50} + 112 q^{51} + 148 q^{52} + 540 q^{53} + 416 q^{54} + 300 q^{55} + 114 q^{56} + 652 q^{57} + 692 q^{58} + 550 q^{59} + 1050 q^{60} + 184 q^{61} + 800 q^{62} + 914 q^{63} + 568 q^{64} + 260 q^{65} + 110 q^{66} + 308 q^{67} + 262 q^{68} - 614 q^{69} + 70 q^{70} - 272 q^{71} + 224 q^{72} - 704 q^{73} + 388 q^{74} - 18 q^{75} + 100 q^{76} - 460 q^{77} + 240 q^{78} - 200 q^{79} + 134 q^{80} - 232 q^{81} + 438 q^{82} - 698 q^{83} + 1126 q^{84} - 1208 q^{85} + 314 q^{86} - 1098 q^{87} + 990 q^{88} - 1064 q^{89} + 1454 q^{90} - 156 q^{91} + 930 q^{92} - 74 q^{93} + 998 q^{94} - 224 q^{95} + 794 q^{96} - 64 q^{97} - 114 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(100))\)

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
100.3.b \(\chi_{100}(51, \cdot)\) 100.3.b.a 1 1
100.3.b.b 1
100.3.b.c 2
100.3.b.d 4
100.3.b.e 4
100.3.b.f 4
100.3.d \(\chi_{100}(99, \cdot)\) 100.3.d.a 8 1
100.3.d.b 8
100.3.f \(\chi_{100}(57, \cdot)\) 100.3.f.a 2 2
100.3.f.b 4
100.3.h \(\chi_{100}(19, \cdot)\) 100.3.h.a 8 4
100.3.h.b 104
100.3.j \(\chi_{100}(11, \cdot)\) 100.3.j.a 112 4
100.3.k \(\chi_{100}(13, \cdot)\) 100.3.k.a 40 8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(100))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(100)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)