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Properties

Label 124.5
Level 124
Weight 5
Dimension 1088
Nonzero newspaces 8
Newform subspaces 8
Sturm bound 4800
Trace bound 1

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Defining parameters

Level: \( N \) = \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 8 \)
Sturm bound: \(4800\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(124))\).

Total New Old
Modular forms 1995 1144 851
Cusp forms 1845 1088 757
Eisenstein series 150 56 94

Trace form

\( 1088 q - 7 q^{2} - 47 q^{4} - 2 q^{5} - 15 q^{6} + 113 q^{8} - 192 q^{9} + O(q^{10}) \) \( 1088 q - 7 q^{2} - 47 q^{4} - 2 q^{5} - 15 q^{6} + 113 q^{8} - 192 q^{9} - 127 q^{10} - 15 q^{12} + 446 q^{13} - 15 q^{14} - 527 q^{16} - 674 q^{17} + 633 q^{18} + 433 q^{20} + 1725 q^{21} - 15 q^{22} + 315 q^{23} - 15 q^{24} - 3547 q^{25} - 1919 q^{26} - 6075 q^{27} - 15 q^{28} - 1904 q^{29} - 30 q^{30} + 1830 q^{31} + 2018 q^{32} + 5100 q^{33} + 2561 q^{34} + 6750 q^{35} - 2607 q^{36} + 3521 q^{37} - 15 q^{38} - 945 q^{39} - 1807 q^{40} - 389 q^{41} - 15 q^{42} - 5395 q^{43} - 15 q^{44} + 2238 q^{45} - 15 q^{46} - 42720 q^{48} - 21392 q^{49} - 20772 q^{50} + 1800 q^{51} + 23126 q^{52} + 5086 q^{53} + 68130 q^{54} + 26640 q^{55} + 58710 q^{56} + 35250 q^{57} + 34346 q^{58} + 6840 q^{59} + 26760 q^{60} + 13856 q^{61} - 11085 q^{62} - 29280 q^{63} - 40337 q^{64} - 47734 q^{65} - 120390 q^{66} - 17640 q^{67} - 74264 q^{68} - 53310 q^{69} - 71700 q^{70} - 25200 q^{71} - 31392 q^{72} - 3634 q^{73} + 37756 q^{74} + 93405 q^{75} + 82110 q^{76} + 96855 q^{77} + 101730 q^{78} + 5005 q^{79} + 7153 q^{80} - 40212 q^{81} - 24319 q^{82} - 80325 q^{83} - 15 q^{84} - 41834 q^{85} - 15 q^{86} - 44700 q^{87} - 15 q^{88} - 18539 q^{89} - 7872 q^{90} - 11765 q^{91} - 30 q^{92} + 22170 q^{93} - 30 q^{94} + 65160 q^{95} + 1200 q^{96} + 58731 q^{97} + 19193 q^{98} + 78225 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(124))\)

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
124.5.b \(\chi_{124}(63, \cdot)\) 124.5.b.a 60 1
124.5.c \(\chi_{124}(61, \cdot)\) 124.5.c.a 10 1
124.5.h \(\chi_{124}(37, \cdot)\) 124.5.h.a 22 2
124.5.i \(\chi_{124}(67, \cdot)\) 124.5.i.a 124 2
124.5.k \(\chi_{124}(29, \cdot)\) 124.5.k.a 40 4
124.5.l \(\chi_{124}(35, \cdot)\) 124.5.l.a 248 4
124.5.n \(\chi_{124}(7, \cdot)\) 124.5.n.a 496 8
124.5.o \(\chi_{124}(13, \cdot)\) 124.5.o.a 88 8

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(124))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(124)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 2}\)