Properties

 Label 504.2.cz Level 504 Weight 2 Character orbit cz Rep. character $$\chi_{504}(187,\cdot)$$ 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.cz (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

 $$184q + q^{2} - 6q^{3} + q^{4} + 6q^{6} - 8q^{8} - 2q^{9} + O(q^{10})$$ $$184q + q^{2} - 6q^{3} + q^{4} + 6q^{6} - 8q^{8} - 2q^{9} - 6q^{10} - 4q^{11} - 3q^{12} + 5q^{14} + q^{16} - 12q^{17} - 7q^{18} - 12q^{19} - 24q^{20} - 6q^{22} - 12q^{24} + 148q^{25} + 4q^{30} + 21q^{32} - 6q^{33} + 6q^{34} - 18q^{35} + 2q^{36} + 25q^{42} - 4q^{43} - 21q^{44} + 2q^{46} + 9q^{48} - 2q^{49} + 19q^{50} - 54q^{51} - 30q^{54} - 20q^{56} - 20q^{57} - 10q^{58} - 6q^{59} - 50q^{60} - 8q^{64} - 18q^{65} - 21q^{66} + 2q^{67} - 24q^{70} - 7q^{72} - 12q^{73} - 94q^{74} - 36q^{75} + 12q^{76} - 39q^{78} - 63q^{80} - 10q^{81} - 12q^{82} - 60q^{83} - 41q^{84} + 62q^{86} - 18q^{88} - 36q^{89} + 33q^{90} + 20q^{91} - 32q^{92} - 3q^{94} - 54q^{96} + 27q^{98} - 26q^{99} + O(q^{100})$$

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.cz.a $$4$$ $$4.024$$ $$\Q(\zeta_{12})$$ None $$-2$$ $$-6$$ $$0$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-1+\cdots)q^{3}+\cdots$$
504.2.cz.b $$180$$ $$4.024$$ None $$3$$ $$0$$ $$0$$ $$0$$

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$1 + 2 T + 2 T^{2} + 4 T^{3} + 4 T^{4}$$)
$3$ ($$( 1 + 3 T + 3 T^{2} )^{2}$$)
$5$ ($$( 1 + 7 T^{2} + 25 T^{4} )^{2}$$)
$7$ ($$1 + 11 T^{2} + 49 T^{4}$$)
$11$ ($$( 1 + 5 T + 11 T^{2} )^{4}$$)
$13$ ($$( 1 - 22 T^{2} + 169 T^{4} )( 1 - T^{2} + 169 T^{4} )$$)
$17$ ($$( 1 - 3 T + 20 T^{2} - 51 T^{3} + 289 T^{4} )^{2}$$)
$19$ ($$( 1 + 3 T + 22 T^{2} + 57 T^{3} + 361 T^{4} )^{2}$$)
$23$ ($$( 1 + 3 T^{2} + 529 T^{4} )^{2}$$)
$29$ ($$1 + 9 T^{2} - 760 T^{4} + 7569 T^{6} + 707281 T^{8}$$)
$31$ ($$1 - 14 T^{2} - 765 T^{4} - 13454 T^{6} + 923521 T^{8}$$)
$37$ ($$( 1 + 26 T^{2} + 1369 T^{4} )( 1 + 47 T^{2} + 1369 T^{4} )$$)
$41$ ($$( 1 + 21 T + 188 T^{2} + 861 T^{3} + 1681 T^{4} )^{2}$$)
$43$ ($$( 1 + 9 T + 38 T^{2} + 387 T^{3} + 1849 T^{4} )^{2}$$)
$47$ ($$1 - 82 T^{2} + 4515 T^{4} - 181138 T^{6} + 4879681 T^{8}$$)
$53$ ($$1 - 15 T^{2} - 2584 T^{4} - 42135 T^{6} + 7890481 T^{8}$$)
$59$ ($$( 1 + 12 T + 107 T^{2} + 708 T^{3} + 3481 T^{4} )^{2}$$)
$61$ ($$1 - 110 T^{2} + 8379 T^{4} - 409310 T^{6} + 13845841 T^{8}$$)
$67$ ($$( 1 - 8 T - 3 T^{2} - 536 T^{3} + 4489 T^{4} )^{2}$$)
$71$ ($$( 1 - 42 T^{2} + 5041 T^{4} )^{2}$$)
$73$ ($$( 1 + 15 T + 148 T^{2} + 1095 T^{3} + 5329 T^{4} )^{2}$$)
$79$ ($$1 + 122 T^{2} + 8643 T^{4} + 761402 T^{6} + 38950081 T^{8}$$)
$83$ ($$( 1 + 27 T + 326 T^{2} + 2241 T^{3} + 6889 T^{4} )^{2}$$)
$89$ ($$( 1 - 15 T + 164 T^{2} - 1335 T^{3} + 7921 T^{4} )^{2}$$)
$97$ ($$( 1 + 3 T + 100 T^{2} + 291 T^{3} + 9409 T^{4} )^{2}$$)