Properties

Label 47.1
Level 47
Weight 1
Dimension 2
Nonzero newspaces 1
Newforms 1
Sturm bound 184
Trace bound 0

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Defining parameters

Level: \( N \) = \( 47 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(184\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(47))\).

Total New Old
Modular forms 25 25 0
Cusp forms 2 2 0
Eisenstein series 23 23 0

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

\(2q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut q^{17} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 2q^{21} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut 2q^{27} \) \(\mathstrut -\mathstrut 3q^{28} \) \(\mathstrut +\mathstrut 2q^{32} \) \(\mathstrut -\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut +\mathstrut q^{42} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut -\mathstrut q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut +\mathstrut q^{56} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut q^{61} \) \(\mathstrut +\mathstrut 2q^{63} \) \(\mathstrut -\mathstrut q^{64} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut -\mathstrut q^{72} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut -\mathstrut q^{75} \) \(\mathstrut -\mathstrut q^{79} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut q^{84} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut q^{94} \) \(\mathstrut -\mathstrut q^{96} \) \(\mathstrut -\mathstrut q^{97} \) \(\mathstrut -\mathstrut 3q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(47))\)

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
47.1.b \(\chi_{47}(46, \cdot)\) 47.1.b.a 2 1
47.1.d \(\chi_{47}(5, \cdot)\) None 0 22