# Properties

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

## 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

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