Properties

Label 87.1
Level 87
Weight 1
Dimension 2
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 560
Trace bound 0

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Defining parameters

Level: \( N \) = \( 87 = 3 \cdot 29 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(560\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(87))\).

Total New Old
Modular forms 58 28 30
Cusp forms 2 2 0
Eisenstein series 56 26 30

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

\( 2q - 2q^{6} - 2q^{7} + 2q^{9} + O(q^{10}) \) \( 2q - 2q^{6} - 2q^{7} + 2q^{9} - 2q^{13} - 2q^{16} + 2q^{22} + 2q^{24} + 2q^{25} - 2q^{33} + 2q^{34} + 2q^{42} - 2q^{51} - 2q^{54} - 2q^{58} - 2q^{63} + 2q^{64} - 2q^{67} + 2q^{78} + 2q^{81} - 4q^{82} + 2q^{87} - 2q^{88} + 2q^{91} + 2q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(87))\)

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
87.1.b \(\chi_{87}(59, \cdot)\) None 0 1
87.1.d \(\chi_{87}(86, \cdot)\) 87.1.d.a 1 1
87.1.d.b 1
87.1.e \(\chi_{87}(46, \cdot)\) None 0 2
87.1.h \(\chi_{87}(5, \cdot)\) None 0 6
87.1.j \(\chi_{87}(20, \cdot)\) None 0 6
87.1.l \(\chi_{87}(10, \cdot)\) None 0 12

Hecke characteristic polynomials

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