# Properties

 Label 87.1.d Level 87 Weight 1 Character orbit d Rep. character $$\chi_{87}(86,\cdot)$$ Character field $$\Q$$ Dimension 2 Newform subspaces 2 Sturm bound 10 Trace bound 2

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## Defining parameters

 Level: $$N$$ $$=$$ $$87 = 3 \cdot 29$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 87.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$87$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$10$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(87, [\chi])$$.

Total New Old
Modular forms 4 4 0
Cusp forms 2 2 0
Eisenstein series 2 2 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

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

## Decomposition of $$S_{1}^{\mathrm{new}}(87, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
87.1.d.a $$1$$ $$0.043$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-87})$$ None $$-1$$ $$1$$ $$0$$ $$-1$$ $$q-q^{2}+q^{3}-q^{6}-q^{7}+q^{8}+q^{9}+\cdots$$
87.1.d.b $$1$$ $$0.043$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-87})$$ None $$1$$ $$-1$$ $$0$$ $$-1$$ $$q+q^{2}-q^{3}-q^{6}-q^{7}-q^{8}+q^{9}+\cdots$$

## 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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