Properties

Label 124.4
Level 124
Weight 4
Dimension 810
Nonzero newspaces 8
Newform subspaces 13
Sturm bound 3840
Trace bound 1

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Defining parameters

Level: \( N \) = \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 13 \)
Sturm bound: \(3840\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(124))\).

Total New Old
Modular forms 1515 870 645
Cusp forms 1365 810 555
Eisenstein series 150 60 90

Trace form

\( 810 q - 15 q^{2} - 15 q^{4} - 30 q^{5} - 15 q^{6} - 15 q^{8} - 30 q^{9} + O(q^{10}) \) \( 810 q - 15 q^{2} - 15 q^{4} - 30 q^{5} - 15 q^{6} - 15 q^{8} - 30 q^{9} - 15 q^{10} - 15 q^{12} - 30 q^{13} - 15 q^{14} - 15 q^{16} - 30 q^{17} - 15 q^{18} - 15 q^{20} - 330 q^{21} - 15 q^{22} - 390 q^{23} - 15 q^{24} - 30 q^{25} - 15 q^{26} + 810 q^{27} - 15 q^{28} + 810 q^{29} + 900 q^{31} - 30 q^{32} + 690 q^{33} - 15 q^{34} + 300 q^{35} - 15 q^{36} - 570 q^{37} - 15 q^{38} - 1470 q^{39} - 15 q^{40} - 1230 q^{41} - 15 q^{42} - 630 q^{43} - 15 q^{44} - 30 q^{45} - 15 q^{46} + 5430 q^{48} + 2820 q^{49} + 5310 q^{50} + 4410 q^{51} + 2160 q^{52} + 300 q^{53} - 840 q^{54} - 1140 q^{55} - 4200 q^{56} - 3720 q^{57} - 5160 q^{58} - 1650 q^{59} - 13290 q^{60} - 5490 q^{61} - 5505 q^{62} - 7080 q^{63} - 4965 q^{64} - 4440 q^{65} - 9240 q^{66} - 930 q^{67} - 2010 q^{68} - 480 q^{69} + 1470 q^{70} + 1740 q^{71} + 8070 q^{72} + 2100 q^{73} + 7110 q^{74} + 7680 q^{75} + 11160 q^{76} - 1320 q^{77} + 9480 q^{78} - 3150 q^{79} - 15 q^{80} - 2430 q^{81} - 15 q^{82} + 210 q^{83} - 15 q^{84} + 2130 q^{85} - 15 q^{86} + 3720 q^{87} - 15 q^{88} + 5970 q^{89} - 420 q^{90} + 5850 q^{91} + 11010 q^{93} - 30 q^{94} + 10320 q^{95} + 390 q^{96} + 4650 q^{97} - 15 q^{98} + 3750 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(124))\)

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
124.4.a \(\chi_{124}(1, \cdot)\) 124.4.a.a 4 1
124.4.a.b 4
124.4.d \(\chi_{124}(123, \cdot)\) 124.4.d.a 2 1
124.4.d.b 4
124.4.d.c 40
124.4.e \(\chi_{124}(5, \cdot)\) 124.4.e.a 2 2
124.4.e.b 6
124.4.e.c 8
124.4.f \(\chi_{124}(33, \cdot)\) 124.4.f.a 32 4
124.4.g \(\chi_{124}(99, \cdot)\) 124.4.g.a 92 2
124.4.j \(\chi_{124}(15, \cdot)\) 124.4.j.a 184 4
124.4.m \(\chi_{124}(9, \cdot)\) 124.4.m.a 64 8
124.4.p \(\chi_{124}(3, \cdot)\) 124.4.p.a 368 8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(124))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(124)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 2}\)