# Properties

 Label 95.1.d Level 95 Weight 1 Character orbit d Rep. character $$\chi_{95}(94,\cdot)$$ Character field $$\Q$$ Dimension 3 Newform subspaces 2 Sturm bound 10 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$95 = 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 95.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$10$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(95, [\chi])$$.

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 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 3 0 0 0

## Trace form

 $$3q + q^{4} - q^{5} - 4q^{6} + q^{9} + O(q^{10})$$ $$3q + q^{4} - q^{5} - 4q^{6} + q^{9} - 2q^{11} - q^{16} - q^{19} - 3q^{20} + 3q^{25} + 4q^{26} + 4q^{30} + 3q^{36} - 4q^{39} + 2q^{44} - 3q^{45} + 3q^{49} - 2q^{55} - 2q^{61} - 3q^{64} - 4q^{74} - 3q^{76} + 3q^{80} - q^{81} + 3q^{95} + 4q^{96} + 2q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(95, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
95.1.d.a $$1$$ $$0.047$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-19})$$, $$\Q(\sqrt{-95})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$1$$ $$0$$ $$q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\cdots$$
95.1.d.b $$2$$ $$0.047$$ $$\Q(\sqrt{2})$$ $$D_{4}$$ $$\Q(\sqrt{-95})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots$$

## Hecke characteristic polynomials

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