Properties

Label 83.1
Level 83
Weight 1
Dimension 1
Nonzero newspaces 1
Newforms 1
Sturm bound 574
Trace bound 0

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Defining parameters

Level: \( N \) = \( 83 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(574\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(83))\).

Total New Old
Modular forms 42 42 0
Cusp forms 1 1 0
Eisenstein series 41 41 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\(q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut +\mathstrut q^{16} \) \(\mathstrut -\mathstrut q^{17} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut q^{27} \) \(\mathstrut -\mathstrut q^{28} \) \(\mathstrut -\mathstrut q^{29} \) \(\mathstrut -\mathstrut q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut -\mathstrut q^{44} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut q^{51} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut q^{61} \) \(\mathstrut +\mathstrut q^{64} \) \(\mathstrut -\mathstrut q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut q^{75} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut +\mathstrut q^{83} \) \(\mathstrut +\mathstrut q^{84} \) \(\mathstrut +\mathstrut q^{87} \) \(\mathstrut +\mathstrut 2q^{92} \) \(\mathstrut +\mathstrut q^{93} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(83))\)

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
83.1.b \(\chi_{83}(82, \cdot)\) 83.1.b.a 1 1
83.1.d \(\chi_{83}(2, \cdot)\) None 0 40