Properties

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

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Defining parameters

Level: \( N \) = \( 47\( 47 \) \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
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

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$3$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$5$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$7$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$11$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$13$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$17$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$19$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$23$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$29$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$31$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$37$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$41$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$43$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$47$ \( ( 1 - T )^{2} \)
$53$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$59$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$61$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$67$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$71$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$73$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$79$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$83$ \( ( 1 - T )^{4} \)
$89$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$97$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
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