# Properties

 Label 504.2.ch Level 504 Weight 2 Character orbit ch Rep. character $$\chi_{504}(269,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 64 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.ch (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$168$$ 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 208 64 144
Cusp forms 176 64 112
Eisenstein series 32 0 32

## Trace form

 $$64q + O(q^{10})$$ $$64q + 4q^{16} - 16q^{22} + 32q^{25} + 44q^{28} + 60q^{40} - 16q^{46} + 16q^{49} + 36q^{52} - 44q^{58} - 24q^{64} - 60q^{70} + 48q^{73} + 16q^{79} - 132q^{82} + 4q^{88} - 108q^{94} + O(q^{100})$$

## 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.ch.a $$8$$ $$4.024$$ 8.0.4857532416.2 None $$0$$ $$0$$ $$0$$ $$20$$ $$q+\beta _{2}q^{2}+(2-2\beta _{3})q^{4}-\beta _{5}q^{5}+(3+\cdots)q^{7}+\cdots$$
504.2.ch.b $$56$$ $$4.024$$ None $$0$$ $$0$$ $$0$$ $$-20$$

## Decomposition of $$S_{2}^{\mathrm{old}}(504, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(504, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$( 1 - 2 T^{2} + 4 T^{4} )^{2}$$)
$3$ 1
$5$ ($$( 1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4} )^{2}( 1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4} )^{2}$$)
$7$ ($$( 1 - 5 T + 7 T^{2} )^{4}$$)
$11$ ($$( 1 + 11 T^{2} )^{4}( 1 - 11 T^{2} + 121 T^{4} )^{2}$$)
$13$ ($$( 1 + 4 T^{2} + 169 T^{4} )^{4}$$)
$17$ ($$( 1 - 28 T^{2} + 495 T^{4} - 8092 T^{6} + 83521 T^{8} )^{2}$$)
$19$ ($$( 1 - 16 T^{2} - 105 T^{4} - 5776 T^{6} + 130321 T^{8} )^{2}$$)
$23$ ($$( 1 + 44 T^{2} + 1407 T^{4} + 23276 T^{6} + 279841 T^{8} )^{2}$$)
$29$ ($$( 1 + 25 T^{2} + 841 T^{4} )^{4}$$)
$31$ ($$( 1 - 9 T + 58 T^{2} - 279 T^{3} + 961 T^{4} )^{4}$$)
$37$ ($$( 1 + 8 T^{2} - 1305 T^{4} + 10952 T^{6} + 1874161 T^{8} )^{2}$$)
$41$ ($$( 1 - 14 T^{2} + 1681 T^{4} )^{4}$$)
$43$ ($$( 1 - 20 T^{2} + 1849 T^{4} )^{4}$$)
$47$ ($$( 1 - 40 T^{2} - 609 T^{4} - 88360 T^{6} + 4879681 T^{8} )^{2}$$)
$53$ ($$( 1 - 73 T^{2} + 2520 T^{4} - 205057 T^{6} + 7890481 T^{8} )^{2}$$)
$59$ ($$( 1 - 15 T + 166 T^{2} - 885 T^{3} + 3481 T^{4} )^{2}( 1 + 15 T + 166 T^{2} + 885 T^{3} + 3481 T^{4} )^{2}$$)
$61$ ($$( 1 - 100 T^{2} + 6279 T^{4} - 372100 T^{6} + 13845841 T^{8} )^{2}$$)
$67$ ($$( 1 + 67 T^{2} + 4489 T^{4} )^{4}$$)
$71$ ($$( 1 - 140 T^{2} + 5041 T^{4} )^{4}$$)
$73$ ($$( 1 + 6 T + 85 T^{2} + 438 T^{3} + 5329 T^{4} )^{4}$$)
$79$ ($$( 1 - 7 T - 30 T^{2} - 553 T^{3} + 6241 T^{4} )^{4}$$)
$83$ ($$( 1 - 155 T^{2} + 6889 T^{4} )^{4}$$)
$89$ ($$( 1 - 82 T^{2} - 1197 T^{4} - 649522 T^{6} + 62742241 T^{8} )^{2}$$)
$97$ ($$( 1 - 191 T^{2} + 9409 T^{4} )^{4}$$)