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Properties

Label 100.7
Level 100
Weight 7
Dimension 948
Nonzero newspaces 6
Newform subspaces 18
Sturm bound 4200
Trace bound 2

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Defining parameters

Level: \( N \) = \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 18 \)
Sturm bound: \(4200\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(100))\).

Total New Old
Modular forms 1870 990 880
Cusp forms 1730 948 782
Eisenstein series 140 42 98

Trace form

\( 948 q - 2 q^{2} - 64 q^{3} - 114 q^{4} + 140 q^{5} - 178 q^{6} + 528 q^{7} + 1222 q^{8} - 466 q^{9} + O(q^{10}) \) \( 948 q - 2 q^{2} - 64 q^{3} - 114 q^{4} + 140 q^{5} - 178 q^{6} + 528 q^{7} + 1222 q^{8} - 466 q^{9} - 2096 q^{10} - 4400 q^{11} - 4890 q^{12} - 452 q^{13} + 17638 q^{14} + 7768 q^{15} - 10610 q^{16} + 16972 q^{17} - 28818 q^{18} - 19200 q^{19} + 19394 q^{20} - 40388 q^{21} + 7670 q^{22} - 10048 q^{23} - 36212 q^{24} - 3382 q^{25} + 43748 q^{26} + 114416 q^{27} + 18950 q^{28} - 47648 q^{29} + 12670 q^{30} - 99072 q^{31} - 65802 q^{32} - 246340 q^{33} - 240826 q^{34} - 35288 q^{35} - 58938 q^{36} + 133984 q^{37} + 8580 q^{38} + 414800 q^{39} + 661324 q^{40} - 286752 q^{41} + 538810 q^{42} - 277680 q^{43} - 115560 q^{44} - 700530 q^{45} - 465958 q^{46} + 239216 q^{47} - 823820 q^{48} - 723766 q^{49} + 684194 q^{50} - 443384 q^{51} + 1102676 q^{52} + 772112 q^{53} + 1128776 q^{54} + 898440 q^{55} - 931598 q^{56} + 773452 q^{57} - 2354956 q^{58} - 67600 q^{59} - 3232710 q^{60} - 1512064 q^{61} + 778760 q^{62} - 1652416 q^{63} + 3575736 q^{64} - 344650 q^{65} + 3667790 q^{66} + 1226688 q^{67} + 1755174 q^{68} + 5338156 q^{69} - 1170090 q^{70} + 1169504 q^{71} - 5115712 q^{72} + 391108 q^{73} - 3858836 q^{74} - 3181128 q^{75} - 4014620 q^{76} - 8797380 q^{77} - 3050160 q^{78} - 2289600 q^{79} + 1331974 q^{80} + 1832066 q^{81} + 12039326 q^{82} + 3782672 q^{83} + 8222566 q^{84} + 9792332 q^{85} + 3343082 q^{86} + 2876112 q^{87} - 3528610 q^{88} + 5474942 q^{89} + 372614 q^{90} + 1491072 q^{91} - 3305630 q^{92} - 15127844 q^{93} - 3317882 q^{94} - 6884344 q^{95} - 10392358 q^{96} - 14367716 q^{97} + 1617962 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(100))\)

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
100.7.b \(\chi_{100}(51, \cdot)\) 100.7.b.a 1 1
100.7.b.b 1
100.7.b.c 2
100.7.b.d 2
100.7.b.e 12
100.7.b.f 12
100.7.b.g 12
100.7.b.h 12
100.7.d \(\chi_{100}(99, \cdot)\) 100.7.d.a 4 1
100.7.d.b 24
100.7.d.c 24
100.7.f \(\chi_{100}(57, \cdot)\) 100.7.f.a 4 2
100.7.f.b 6
100.7.f.c 8
100.7.h \(\chi_{100}(19, \cdot)\) 100.7.h.a 8 4
100.7.h.b 344
100.7.j \(\chi_{100}(11, \cdot)\) 100.7.j.a 352 4
100.7.k \(\chi_{100}(13, \cdot)\) 100.7.k.a 120 8

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(100))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(100)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 1}\)