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Properties

Label 124.2
Level 124
Weight 2
Dimension 250
Nonzero newspaces 8
Newform subspaces 13
Sturm bound 1920
Trace bound 1

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Defining parameters

Level: \( N \) = \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 13 \)
Sturm bound: \(1920\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(124))\).

Total New Old
Modular forms 555 310 245
Cusp forms 406 250 156
Eisenstein series 149 60 89

Trace form

\( 250 q - 15 q^{2} - 15 q^{4} - 30 q^{5} - 15 q^{6} - 15 q^{8} - 30 q^{9} + O(q^{10}) \) \( 250 q - 15 q^{2} - 15 q^{4} - 30 q^{5} - 15 q^{6} - 15 q^{8} - 30 q^{9} - 15 q^{10} - 15 q^{12} - 30 q^{13} - 15 q^{14} - 15 q^{16} - 30 q^{17} - 15 q^{18} - 15 q^{20} - 35 q^{21} - 15 q^{22} - 15 q^{23} - 15 q^{24} - 65 q^{25} - 15 q^{26} - 45 q^{27} - 15 q^{28} - 60 q^{29} - 30 q^{31} - 30 q^{32} - 60 q^{33} - 15 q^{34} - 30 q^{35} - 15 q^{36} - 75 q^{37} - 15 q^{38} - 35 q^{39} - 15 q^{40} - 45 q^{41} - 15 q^{42} - 5 q^{43} - 15 q^{44} - 30 q^{45} - 15 q^{46} + 30 q^{48} + 60 q^{50} + 90 q^{51} + 60 q^{52} + 150 q^{54} + 60 q^{55} + 120 q^{56} + 60 q^{57} + 90 q^{58} + 30 q^{59} + 210 q^{60} + 90 q^{61} + 75 q^{62} + 120 q^{63} + 75 q^{64} + 60 q^{65} + 210 q^{66} + 30 q^{67} + 90 q^{68} + 60 q^{69} + 120 q^{70} + 60 q^{71} + 150 q^{72} + 60 q^{74} + 75 q^{75} + 60 q^{76} - 45 q^{77} + 30 q^{78} - 35 q^{79} - 15 q^{80} - 90 q^{81} - 15 q^{82} - 105 q^{83} - 15 q^{84} - 90 q^{85} - 15 q^{86} - 60 q^{87} - 15 q^{88} - 105 q^{89} - 60 q^{90} - 65 q^{91} - 150 q^{93} - 30 q^{94} - 120 q^{95} + 30 q^{96} - 95 q^{97} - 15 q^{98} - 75 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
124.2.a \(\chi_{124}(1, \cdot)\) 124.2.a.a 1 1
124.2.a.b 1
124.2.d \(\chi_{124}(123, \cdot)\) 124.2.d.a 4 1
124.2.d.b 4
124.2.d.c 6
124.2.e \(\chi_{124}(5, \cdot)\) 124.2.e.a 6 2
124.2.f \(\chi_{124}(33, \cdot)\) 124.2.f.a 4 4
124.2.f.b 4
124.2.g \(\chi_{124}(99, \cdot)\) 124.2.g.a 28 2
124.2.j \(\chi_{124}(15, \cdot)\) 124.2.j.a 8 4
124.2.j.b 48
124.2.m \(\chi_{124}(9, \cdot)\) 124.2.m.a 24 8
124.2.p \(\chi_{124}(3, \cdot)\) 124.2.p.a 112 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(124))\) into lower level spaces

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