Properties

Label 112.1
Level 112
Weight 1
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 768
Trace bound 0

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Defining parameters

Level: \( N \) = \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(768\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(112))\).

Total New Old
Modular forms 88 25 63
Cusp forms 4 2 2
Eisenstein series 84 23 61

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q - 2q^{4} + O(q^{10}) \) \( 2q - 2q^{4} - 2q^{11} - 2q^{14} + 2q^{16} + 2q^{18} + 2q^{22} - 2q^{29} - 2q^{37} + 2q^{43} + 2q^{44} - 2q^{49} - 2q^{50} + 2q^{53} + 2q^{56} - 2q^{58} + 2q^{63} - 2q^{64} + 2q^{67} - 2q^{72} + 2q^{74} + 2q^{77} - 2q^{81} - 2q^{86} - 2q^{88} - 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)

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
112.1.c \(\chi_{112}(97, \cdot)\) None 0 1
112.1.d \(\chi_{112}(15, \cdot)\) None 0 1
112.1.g \(\chi_{112}(71, \cdot)\) None 0 1
112.1.h \(\chi_{112}(41, \cdot)\) None 0 1
112.1.k \(\chi_{112}(43, \cdot)\) None 0 2
112.1.l \(\chi_{112}(13, \cdot)\) 112.1.l.a 2 2
112.1.n \(\chi_{112}(73, \cdot)\) None 0 2
112.1.o \(\chi_{112}(23, \cdot)\) None 0 2
112.1.r \(\chi_{112}(79, \cdot)\) None 0 2
112.1.s \(\chi_{112}(17, \cdot)\) None 0 2
112.1.u \(\chi_{112}(11, \cdot)\) None 0 4
112.1.x \(\chi_{112}(5, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(112))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(112)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)