Properties

 Label 111.1.d Level 111 Weight 1 Character orbit d Rep. character $$\chi_{111}(110,\cdot)$$ Character field $$\Q$$ Dimension 3 Newform subspaces 2 Sturm bound 12 Trace bound 1

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$111 = 3 \cdot 37$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 111.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$111$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$12$$ Trace bound: $$1$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(111, [\chi])$$.

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

 $$3q - q^{3} + q^{4} - 2q^{7} + 3q^{9} + O(q^{10})$$ $$3q - q^{3} + q^{4} - 2q^{7} + 3q^{9} - 4q^{10} - 3q^{12} - q^{16} - 2q^{21} + q^{25} - q^{27} + 2q^{28} + 4q^{30} + 4q^{34} + q^{36} - q^{37} - 4q^{46} + 3q^{48} + q^{49} + 4q^{58} - 2q^{63} - 3q^{64} - 2q^{67} - 2q^{73} - 3q^{75} + 3q^{81} + 2q^{84} - 4q^{85} - 4q^{90} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(111, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
111.1.d.a $$1$$ $$0.055$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-111})$$ $$\Q(\sqrt{37})$$ $$0$$ $$1$$ $$0$$ $$-2$$ $$q+q^{3}-q^{4}-2q^{7}+q^{9}-q^{12}+q^{16}+\cdots$$
111.1.d.b $$2$$ $$0.055$$ $$\Q(\sqrt{2})$$ $$D_{4}$$ $$\Q(\sqrt{-111})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-\beta q^{2}-q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{9}+\cdots$$

Hecke characteristic polynomials

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