# Properties

 Label 3600.1.cc Level $3600$ Weight $1$ Character orbit 3600.cc Rep. character $\chi_{3600}(751,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $4$ Newform subspaces $2$ Sturm bound $720$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3600 = 2^{4} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3600.cc (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$36$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$720$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(3600, [\chi])$$.

Total New Old
Modular forms 88 4 84
Cusp forms 16 4 12
Eisenstein series 72 0 72

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

## Trace form

 $$4q - 2q^{9} + O(q^{10})$$ $$4q - 2q^{9} - 2q^{29} - 2q^{41} + 4q^{49} - 2q^{61} + 6q^{69} - 2q^{81} + 4q^{89} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(3600, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
3600.1.cc.a $$2$$ $$1.797$$ $$\Q(\sqrt{-3})$$ $$D_{6}$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$-1$$ $$0$$ $$-3$$ $$q-\zeta_{6}q^{3}+(-1-\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+\cdots$$
3600.1.cc.b $$2$$ $$1.797$$ $$\Q(\sqrt{-3})$$ $$D_{6}$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$1$$ $$0$$ $$3$$ $$q+\zeta_{6}q^{3}+(1+\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\cdots)q^{21}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(3600, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(3600, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(900, [\chi])$$$$^{\oplus 3}$$

## Hecke characteristic polynomials

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