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Properties

Label 100.10
Level 100
Weight 10
Dimension 1430
Nonzero newspaces 6
Newform subspaces 20
Sturm bound 6000
Trace bound 3

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Defining parameters

Level: \( N \) = \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 20 \)
Sturm bound: \(6000\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(100))\).

Total New Old
Modular forms 2770 1470 1300
Cusp forms 2630 1430 1200
Eisenstein series 140 40 100

Trace form

\( 1430 q - 6 q^{2} - 68 q^{3} - 10 q^{4} + 615 q^{5} - 12322 q^{6} + 20808 q^{7} + 1422 q^{8} - 113841 q^{9} + O(q^{10}) \) \( 1430 q - 6 q^{2} - 68 q^{3} - 10 q^{4} + 615 q^{5} - 12322 q^{6} + 20808 q^{7} + 1422 q^{8} - 113841 q^{9} - 11456 q^{10} + 21780 q^{11} + 310710 q^{12} + 110402 q^{13} - 10 q^{14} + 119108 q^{15} - 6018 q^{16} + 1011294 q^{17} + 1358162 q^{18} - 1457676 q^{19} + 334314 q^{20} + 4515484 q^{21} - 6353850 q^{22} - 4847696 q^{23} - 9118987 q^{25} + 22445436 q^{26} + 22243876 q^{27} - 25463690 q^{28} - 9291106 q^{29} - 15498690 q^{30} - 17202152 q^{31} + 58185574 q^{32} + 56183580 q^{33} - 10 q^{34} + 14227852 q^{35} - 87449610 q^{36} + 12110231 q^{37} - 69637840 q^{38} - 107494896 q^{39} + 177357644 q^{40} + 14614102 q^{41} - 14157310 q^{42} + 1602460 q^{43} - 267384540 q^{44} - 238195375 q^{45} + 68667698 q^{46} + 40890376 q^{47} + 457877080 q^{48} - 173186172 q^{49} + 507772594 q^{50} - 51742444 q^{51} - 386340832 q^{52} + 450388015 q^{53} - 1175338980 q^{54} - 66220180 q^{55} + 137038218 q^{56} - 257853268 q^{57} + 648339664 q^{58} - 632888832 q^{59} + 1084802570 q^{60} - 434289790 q^{61} - 428135060 q^{62} - 117341732 q^{63} - 82684780 q^{64} + 530410705 q^{65} - 1148060850 q^{66} + 105624108 q^{67} + 579736814 q^{68} - 1221463628 q^{69} + 203227590 q^{70} - 681242296 q^{71} - 1860632176 q^{72} - 104948258 q^{73} - 252309748 q^{75} + 2121586020 q^{76} - 257180500 q^{77} - 98528380 q^{78} - 2780062368 q^{79} - 210150746 q^{80} + 5824753295 q^{81} + 1323703758 q^{82} + 2152826524 q^{83} + 4835499110 q^{84} - 745153113 q^{85} - 1749735702 q^{86} - 4357912628 q^{87} - 8831592450 q^{88} - 143907679 q^{89} + 1142112134 q^{90} - 1691761248 q^{91} + 9722149090 q^{92} - 314274308 q^{93} + 9059876630 q^{94} + 1327806516 q^{95} - 5343623542 q^{96} + 2507963906 q^{97} - 3844372778 q^{98} - 933319360 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(100))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
100.10.a \(\chi_{100}(1, \cdot)\) 100.10.a.a 1 1
100.10.a.b 1
100.10.a.c 2
100.10.a.d 3
100.10.a.e 3
100.10.a.f 4
100.10.c \(\chi_{100}(49, \cdot)\) 100.10.c.a 2 1
100.10.c.b 2
100.10.c.c 4
100.10.c.d 6
100.10.e \(\chi_{100}(7, \cdot)\) 100.10.e.a 2 2
100.10.e.b 2
100.10.e.c 2
100.10.e.d 32
100.10.e.e 48
100.10.e.f 72
100.10.g \(\chi_{100}(21, \cdot)\) 100.10.g.a 92 4
100.10.i \(\chi_{100}(9, \cdot)\) 100.10.i.a 88 4
100.10.l \(\chi_{100}(3, \cdot)\) 100.10.l.a 8 8
100.10.l.b 1056

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(100))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(100)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)