Properties

 Label 224.3.v Level 224 Weight 3 Character orbit v Rep. character $$\chi_{224}(13,\cdot)$$ Character field $$\Q(\zeta_{8})$$ Dimension 248 Newform subspaces 2 Sturm bound 96 Trace bound 1

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$224 = 2^{5} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 224.v (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$224$$ Character field: $$\Q(\zeta_{8})$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(224, [\chi])$$.

Total New Old
Modular forms 264 264 0
Cusp forms 248 248 0
Eisenstein series 16 16 0

Trace form

 $$248q - 8q^{2} - 8q^{4} - 4q^{7} - 8q^{8} - 8q^{9} + O(q^{10})$$ $$248q - 8q^{2} - 8q^{4} - 4q^{7} - 8q^{8} - 8q^{9} - 8q^{11} + 12q^{14} + 12q^{16} - 68q^{18} - 4q^{21} - 44q^{22} + 56q^{23} - 8q^{25} + 56q^{28} - 8q^{29} - 16q^{30} - 8q^{32} + 92q^{35} + 192q^{36} - 8q^{37} - 8q^{39} - 424q^{42} - 104q^{43} + 308q^{44} - 8q^{46} - 320q^{50} - 80q^{51} - 168q^{53} + 356q^{56} - 8q^{57} - 712q^{58} + 264q^{60} - 8q^{63} - 272q^{64} - 16q^{65} - 168q^{67} + 320q^{70} + 504q^{71} - 8q^{72} + 124q^{74} - 4q^{77} + 560q^{78} - 1000q^{84} - 208q^{85} - 8q^{86} - 800q^{88} + 188q^{91} + 852q^{92} + 64q^{93} - 16q^{95} - 376q^{98} + 64q^{99} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(224, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
224.3.v.a $$8$$ $$6.104$$ 8.0.157351936.1 $$\Q(\sqrt{-7})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(2\beta _{6}-\beta _{7})q^{2}+(-\beta _{3}+3\beta _{5})q^{4}+\cdots$$
224.3.v.b $$240$$ $$6.104$$ None $$-8$$ $$0$$ $$0$$ $$-4$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 - 31 T^{4} + 256 T^{8}$$)
$3$ ($$( 1 + 6561 T^{8} )^{2}$$)
$5$ ($$( 1 + 390625 T^{8} )^{2}$$)
$7$ ($$( 1 + 2401 T^{4} )^{2}$$)
$11$ ($$( 1 - 206 T^{2} + 14641 T^{4} )^{2}( 1 + 13154 T^{4} + 214358881 T^{8} )$$)
$13$ ($$( 1 + 815730721 T^{8} )^{2}$$)
$17$ ($$( 1 + 289 T^{2} )^{8}$$)
$19$ ($$( 1 + 16983563041 T^{8} )^{2}$$)
$23$ ($$( 1 + 18 T + 529 T^{2} )^{4}( 1 - 734 T^{2} + 279841 T^{4} )^{2}$$)
$29$ ($$( 1 + 1234 T^{2} + 707281 T^{4} )^{2}( 1 + 108194 T^{4} + 500246412961 T^{8} )$$)
$31$ ($$( 1 - 31 T )^{8}( 1 + 31 T )^{8}$$)
$37$ ($$( 1 - 1294 T^{2} + 1874161 T^{4} )^{2}( 1 - 2073886 T^{4} + 3512479453921 T^{8} )$$)
$41$ ($$( 1 + 2825761 T^{4} )^{4}$$)
$43$ ($$( 1 + 58 T + 1849 T^{2} )^{4}( 1 - 6726046 T^{4} + 11688200277601 T^{8} )$$)
$47$ ($$( 1 + 2209 T^{2} )^{8}$$)
$53$ ($$( 1 - 6 T + 2809 T^{2} )^{4}( 1 + 15377762 T^{4} + 62259690411361 T^{8} )$$)
$59$ ($$( 1 + 146830437604321 T^{8} )^{2}$$)
$61$ ($$( 1 + 191707312997281 T^{8} )^{2}$$)
$67$ ($$( 1 + 118 T + 4489 T^{2} )^{4}( 1 - 15839326 T^{4} + 406067677556641 T^{8} )$$)
$71$ ($$( 1 - 42331966 T^{4} + 645753531245761 T^{8} )^{2}$$)
$73$ ($$( 1 + 28398241 T^{4} )^{4}$$)
$79$ ($$( 1 - 64606846 T^{4} + 1517108809906561 T^{8} )^{2}$$)
$83$ ($$( 1 + 2252292232139041 T^{8} )^{2}$$)
$89$ ($$( 1 + 62742241 T^{4} )^{4}$$)
$97$ ($$( 1 - 97 T )^{8}( 1 + 97 T )^{8}$$)