Properties

Label 77.1
Level 77
Weight 1
Dimension 4
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 480
Trace bound 0

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Defining parameters

Level: \( N \) = \( 77 = 7 \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(480\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(77))\).

Total New Old
Modular forms 64 48 16
Cusp forms 4 4 0
Eisenstein series 60 44 16

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

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

Trace form

\( 4q - 2q^{2} - 3q^{4} - q^{7} + q^{8} - q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - 3q^{4} - q^{7} + q^{8} - q^{9} - q^{11} + 3q^{14} + 3q^{18} - 2q^{22} - 2q^{23} - q^{25} + 2q^{28} - 2q^{29} + 4q^{32} - 3q^{36} + 3q^{37} - 2q^{43} + 2q^{44} + q^{46} - q^{49} - 2q^{50} + 3q^{53} - 4q^{56} + q^{58} - q^{63} - 2q^{64} - 2q^{67} + 3q^{71} + q^{72} - 4q^{74} - q^{77} + 3q^{79} - q^{81} + q^{86} + q^{88} + 4q^{92} - 2q^{98} + 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(77))\)

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
77.1.c \(\chi_{77}(43, \cdot)\) None 0 1
77.1.d \(\chi_{77}(34, \cdot)\) None 0 1
77.1.g \(\chi_{77}(12, \cdot)\) None 0 2
77.1.h \(\chi_{77}(32, \cdot)\) None 0 2
77.1.j \(\chi_{77}(20, \cdot)\) 77.1.j.a 4 4
77.1.k \(\chi_{77}(8, \cdot)\) None 0 4
77.1.o \(\chi_{77}(2, \cdot)\) None 0 8
77.1.p \(\chi_{77}(3, \cdot)\) None 0 8