Properties

Label 125.4
Level 125
Weight 4
Dimension 1664
Nonzero newspaces 6
Newform subspaces 13
Sturm bound 5000
Trace bound 4

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Defining parameters

Level: \( N \) = \( 125 = 5^{3} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 13 \)
Sturm bound: \(5000\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(125))\).

Total New Old
Modular forms 1965 1792 173
Cusp forms 1785 1664 121
Eisenstein series 180 128 52

Trace form

\( 1664 q - 34 q^{2} - 28 q^{3} - 22 q^{4} - 40 q^{5} - 62 q^{6} - 24 q^{7} - 30 q^{8} - 53 q^{9} + O(q^{10}) \) \( 1664 q - 34 q^{2} - 28 q^{3} - 22 q^{4} - 40 q^{5} - 62 q^{6} - 24 q^{7} - 30 q^{8} - 53 q^{9} - 40 q^{10} - 22 q^{11} - 14 q^{12} - 68 q^{13} - 54 q^{14} - 40 q^{15} + 394 q^{16} + 636 q^{17} + 962 q^{18} + 310 q^{19} - 180 q^{20} - 522 q^{21} - 1598 q^{22} - 988 q^{23} - 2890 q^{24} - 760 q^{25} - 802 q^{26} - 1210 q^{27} - 1422 q^{28} - 240 q^{29} + 200 q^{30} + 558 q^{31} + 2466 q^{32} + 1954 q^{33} + 3166 q^{34} + 820 q^{35} + 2514 q^{36} + 1306 q^{37} + 4550 q^{38} + 4774 q^{39} + 2010 q^{40} + 888 q^{41} + 1322 q^{42} - 148 q^{43} - 2434 q^{44} - 2360 q^{45} - 4182 q^{46} - 3984 q^{47} - 12218 q^{48} - 4727 q^{49} - 4450 q^{50} - 5662 q^{51} - 7914 q^{52} - 3358 q^{53} - 7170 q^{54} - 800 q^{55} + 130 q^{56} + 1290 q^{57} + 3390 q^{58} + 7070 q^{59} + 11500 q^{60} + 7068 q^{61} + 20942 q^{62} + 16272 q^{63} + 14878 q^{64} + 1715 q^{65} + 2906 q^{66} - 1344 q^{67} - 7502 q^{68} - 6346 q^{69} - 4360 q^{70} - 4602 q^{71} - 18530 q^{72} - 6668 q^{73} - 15874 q^{74} - 5960 q^{75} - 9770 q^{76} - 10718 q^{77} - 11586 q^{78} - 3750 q^{79} - 6200 q^{80} + 3639 q^{81} + 13562 q^{82} + 13812 q^{83} + 26466 q^{84} + 9725 q^{85} + 15098 q^{86} + 17190 q^{87} + 25170 q^{88} + 15070 q^{89} + 8570 q^{90} + 3318 q^{91} + 9306 q^{92} - 8566 q^{93} - 20054 q^{94} - 6360 q^{95} - 13742 q^{96} - 25684 q^{97} - 25802 q^{98} - 24506 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(125))\)

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
125.4.a \(\chi_{125}(1, \cdot)\) 125.4.a.a 4 1
125.4.a.b 6
125.4.a.c 6
125.4.a.d 8
125.4.b \(\chi_{125}(124, \cdot)\) 125.4.b.a 4 1
125.4.b.b 8
125.4.b.c 12
125.4.d \(\chi_{125}(26, \cdot)\) 125.4.d.a 28 4
125.4.d.b 48
125.4.e \(\chi_{125}(24, \cdot)\) 125.4.e.a 24 4
125.4.e.b 56
125.4.g \(\chi_{125}(6, \cdot)\) 125.4.g.a 740 20
125.4.h \(\chi_{125}(4, \cdot)\) 125.4.h.a 720 20

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(125))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(125)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)