Properties

Label 124.1
Level 124
Weight 1
Dimension 4
Nonzero newspaces 1
Newforms 1
Sturm bound 960
Trace bound 0

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Defining parameters

Level: \( N \) = \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(960\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(124))\).

Total New Old
Modular forms 82 32 50
Cusp forms 7 4 3
Eisenstein series 75 28 47

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 4 0 0

Trace form

\( 4q - 4q^{4} - 2q^{5} - 2q^{6} + O(q^{10}) \) \( 4q - 4q^{4} - 2q^{5} - 2q^{6} + 2q^{13} + 2q^{14} + 4q^{16} - 2q^{17} + 2q^{20} - 2q^{21} - 2q^{22} + 2q^{24} + 4q^{30} - 4q^{33} - 2q^{37} - 2q^{38} - 2q^{41} - 2q^{52} + 2q^{53} + 4q^{54} - 2q^{56} + 2q^{57} + 4q^{62} - 4q^{64} + 2q^{65} + 2q^{68} - 4q^{70} - 2q^{73} + 4q^{77} - 4q^{78} - 2q^{80} + 2q^{81} + 2q^{84} + 4q^{85} - 2q^{86} + 2q^{88} + 2q^{93} - 2q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(124))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
124.1.b \(\chi_{124}(63, \cdot)\) None 0 1
124.1.c \(\chi_{124}(61, \cdot)\) None 0 1
124.1.h \(\chi_{124}(37, \cdot)\) None 0 2
124.1.i \(\chi_{124}(67, \cdot)\) 124.1.i.a 4 2
124.1.k \(\chi_{124}(29, \cdot)\) None 0 4
124.1.l \(\chi_{124}(35, \cdot)\) None 0 4
124.1.n \(\chi_{124}(7, \cdot)\) None 0 8
124.1.o \(\chi_{124}(13, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(124))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(124)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 3}\)