# Properties

 Label 2880.1.bh Level 2880 Weight 1 Character orbit bh Rep. character $$\chi_{2880}(577,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 6 Newform subspaces 3 Sturm bound 576 Trace bound 5

# Related objects

## Defining parameters

 Level: $$N$$ = $$2880 = 2^{6} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ = $$1$$ Character orbit: $$[\chi]$$ = 2880.bh (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$5$$ Character field: $$\Q(i)$$ Newform subspaces: $$3$$ Sturm bound: $$576$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2880, [\chi])$$.

Total New Old
Modular forms 132 10 122
Cusp forms 36 6 30
Eisenstein series 96 4 92

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

 $$6q + O(q^{10})$$ $$6q - 2q^{13} + 2q^{17} + 2q^{25} - 6q^{37} + 2q^{53} - 2q^{65} - 2q^{73} + 6q^{85} - 2q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(2880, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2880.1.bh.a $$2$$ $$1.437$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-q^{5}+(-1-i)q^{13}+(-1+i)q^{17}+\cdots$$
2880.1.bh.b $$2$$ $$1.437$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{5}+(1+i)q^{13}+(1-i)q^{17}-q^{25}+\cdots$$
2880.1.bh.c $$2$$ $$1.437$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+q^{5}+(-1-i)q^{13}+(1-i)q^{17}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(2880, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(2880, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(320, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(1440, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

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