# Properties

 Label 276.1 Level 276 Weight 1 Dimension 6 Nonzero newspaces 1 Newform subspaces 4 Sturm bound 4224 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$276 = 2^{2} \cdot 3 \cdot 23$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$4$$ Sturm bound: $$4224$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(276))$$.

Total New Old
Modular forms 232 50 182
Cusp forms 12 6 6
Eisenstein series 220 44 176

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 $$S_{1}^{\mathrm{new}}(\Gamma_1(276))$$

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
276.1.b $$\chi_{276}(229, \cdot)$$ None 0 1
276.1.d $$\chi_{276}(185, \cdot)$$ None 0 1
276.1.f $$\chi_{276}(139, \cdot)$$ None 0 1
276.1.h $$\chi_{276}(275, \cdot)$$ 276.1.h.a 1 1
276.1.h.b 1
276.1.h.c 2
276.1.h.d 2
276.1.j $$\chi_{276}(11, \cdot)$$ None 0 10
276.1.l $$\chi_{276}(31, \cdot)$$ None 0 10
276.1.n $$\chi_{276}(29, \cdot)$$ None 0 10
276.1.p $$\chi_{276}(37, \cdot)$$ None 0 10

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(276))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(276)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 6}$$

## Hecke Characteristic Polynomials

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