# Properties

 Label 504.2.cc Level 504 Weight 2 Character orbit cc Rep. character $$\chi_{504}(293,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 184 Newform subspaces 2 Sturm bound 192 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$504 = 2^{3} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 504.cc (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$504$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$192$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(504, [\chi])$$.

Total New Old
Modular forms 200 200 0
Cusp forms 184 184 0
Eisenstein series 16 16 0

## Trace form

 $$184q - 6q^{2} - 2q^{4} - 2q^{7} - 8q^{9} + O(q^{10})$$ $$184q - 6q^{2} - 2q^{4} - 2q^{7} - 8q^{9} + 12q^{14} - 20q^{15} - 2q^{16} - 18q^{18} + 6q^{22} - 12q^{23} + 72q^{25} + 4q^{28} - 20q^{30} + 24q^{32} - 26q^{36} + 4q^{39} - 16q^{46} - 2q^{49} - 36q^{50} - 24q^{56} - 32q^{57} + 6q^{58} - 20q^{60} - 30q^{63} - 8q^{64} - 12q^{65} - 6q^{70} - 12q^{72} + 48q^{74} - 56q^{78} - 4q^{79} - 24q^{81} - 72q^{84} - 144q^{86} - 18q^{88} + 54q^{92} - 72q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(504, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
504.2.cc.a $$16$$ $$4.024$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ $$\Q(\sqrt{-14})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{11}q^{2}-\beta _{14}q^{3}+(2-2\beta _{4})q^{4}+\cdots$$
504.2.cc.b $$168$$ $$4.024$$ None $$-6$$ $$0$$ $$0$$ $$-2$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$( 1 - 2 T^{2} + 4 T^{4} )^{4}$$)
$3$ ($$( 1 - 10 T^{4} + 81 T^{8} )^{2}$$)
$5$ ($$( 1 + 22 T^{4} + 625 T^{8} )^{2}( 1 - 22 T^{4} - 141 T^{8} - 13750 T^{12} + 390625 T^{16} )$$)
$7$ ($$( 1 + 7 T^{2} + 49 T^{4} )^{4}$$)
$11$ ($$( 1 - 11 T^{2} + 121 T^{4} )^{8}$$)
$13$ ($$( 1 - 310 T^{4} + 67539 T^{8} - 8853910 T^{12} + 815730721 T^{16} )^{2}$$)
$17$ ($$( 1 + 17 T^{2} )^{16}$$)
$19$ ($$( 1 + 650 T^{4} + 292179 T^{8} + 84708650 T^{12} + 16983563041 T^{16} )^{2}$$)
$23$ ($$( 1 - 6 T + 23 T^{2} )^{8}( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} )^{4}$$)
$29$ ($$( 1 - 29 T^{2} + 841 T^{4} )^{8}$$)
$31$ ($$( 1 + 31 T^{2} + 961 T^{4} )^{8}$$)
$37$ ($$( 1 - 37 T^{2} )^{16}$$)
$41$ ($$( 1 - 41 T^{2} + 1681 T^{4} )^{8}$$)
$43$ ($$( 1 + 43 T^{2} + 1849 T^{4} )^{8}$$)
$47$ ($$( 1 - 47 T^{2} + 2209 T^{4} )^{8}$$)
$53$ ($$( 1 + 53 T^{2} )^{16}$$)
$59$ ($$( 1 + 1130 T^{4} - 10840461 T^{8} + 13692617930 T^{12} + 146830437604321 T^{16} )^{2}$$)
$61$ ($$( 1 - 7370 T^{4} + 13845841 T^{8} )^{2}( 1 + 7370 T^{4} + 40471059 T^{8} + 102043848170 T^{12} + 191707312997281 T^{16} )$$)
$67$ ($$( 1 + 67 T^{2} + 4489 T^{4} )^{8}$$)
$71$ ($$( 1 + 110 T^{2} + 7059 T^{4} + 554510 T^{6} + 25411681 T^{8} )^{4}$$)
$73$ ($$( 1 - 73 T^{2} )^{16}$$)
$79$ ($$( 1 + 130 T^{2} + 6241 T^{4} )^{4}( 1 - 130 T^{2} + 10659 T^{4} - 811330 T^{6} + 38950081 T^{8} )^{2}$$)
$83$ ($$( 1 + 13130 T^{4} + 124938579 T^{8} + 623127754730 T^{12} + 2252292232139041 T^{16} )^{2}$$)
$89$ ($$( 1 + 89 T^{2} )^{16}$$)
$97$ ($$( 1 + 97 T^{2} + 9409 T^{4} )^{8}$$)