# Properties

 Label 276.1.h Level 276 Weight 1 Character orbit h Rep. character $$\chi_{276}(275,\cdot)$$ Character field $$\Q$$ Dimension 6 Newform subspaces 4 Sturm bound 48 Trace bound 2

# Related objects

## Defining parameters

 Level: $$N$$ = $$276 = 2^{2} \cdot 3 \cdot 23$$ Weight: $$k$$ = $$1$$ Character orbit: $$[\chi]$$ = 276.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$276$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$48$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(276, [\chi])$$.

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 6 0 0 0

## Trace form

 $$6q - 3q^{6} + O(q^{10})$$ $$6q - 3q^{6} - 3q^{12} + 3q^{18} - 6q^{25} + 3q^{36} + 3q^{48} - 6q^{49} - 6q^{52} - 6q^{58} + 6q^{64} + 3q^{78} + 6q^{82} + 6q^{93} + 6q^{94} - 3q^{96} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(276, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
276.1.h.a $$1$$ $$0.138$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-23})$$, $$\Q(\sqrt{-69})$$ $$\Q(\sqrt{3})$$ $$-1$$ $$1$$ $$0$$ $$0$$ $$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$$
276.1.h.b $$1$$ $$0.138$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-23})$$, $$\Q(\sqrt{-69})$$ $$\Q(\sqrt{3})$$ $$1$$ $$-1$$ $$0$$ $$0$$ $$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$$
276.1.h.c $$2$$ $$0.138$$ $$\Q(\sqrt{-3})$$ $$D_{6}$$ $$\Q(\sqrt{-23})$$ None $$-1$$ $$1$$ $$0$$ $$0$$ $$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots$$
276.1.h.d $$2$$ $$0.138$$ $$\Q(\sqrt{-3})$$ $$D_{6}$$ $$\Q(\sqrt{-23})$$ None $$1$$ $$-1$$ $$0$$ $$0$$ $$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}-q^{8}+\cdots$$

## Hecke Characteristic Polynomials

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