Properties

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

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Defining parameters

Level: \( N \) = \( 77 = 7 \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
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

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

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