# Properties

 Label 20.6.e Level 20 Weight 6 Character orbit e Rep. character $$\chi_{20}(3,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 26 Newform subspaces 2 Sturm bound 18 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$20 = 2^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 20.e (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$18$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(20, [\chi])$$.

Total New Old
Modular forms 34 34 0
Cusp forms 26 26 0
Eisenstein series 8 8 0

## Trace form

 $$26q - 2q^{2} - 4q^{5} - 184q^{6} + 244q^{8} + O(q^{10})$$ $$26q - 2q^{2} - 4q^{5} - 184q^{6} + 244q^{8} + 566q^{10} - 1280q^{12} + 118q^{13} + 1976q^{16} + 1006q^{17} - 3246q^{18} - 1364q^{20} + 1632q^{21} - 2440q^{22} - 7794q^{25} + 6836q^{26} + 5920q^{28} + 8600q^{30} + 17608q^{32} + 10400q^{33} - 27908q^{36} - 9414q^{37} - 22160q^{38} - 31444q^{40} - 9648q^{41} - 39400q^{42} + 27886q^{45} + 29416q^{46} + 108160q^{48} + 114186q^{50} + 38476q^{52} - 58982q^{53} - 85984q^{56} + 40320q^{57} - 183672q^{58} - 263840q^{60} + 96152q^{61} - 109400q^{62} - 68198q^{65} + 186000q^{66} + 313988q^{68} + 364240q^{70} + 309828q^{72} + 39298q^{73} - 297600q^{76} - 53280q^{77} - 586200q^{78} - 467824q^{80} - 184842q^{81} - 458744q^{82} - 27578q^{85} + 545416q^{86} + 690080q^{88} + 945366q^{90} + 576800q^{92} + 182240q^{93} - 841984q^{96} + 129426q^{97} - 1036906q^{98} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(20, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
20.6.e.a $$2$$ $$3.208$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$8$$ $$0$$ $$76$$ $$0$$ $$q+(4+4i)q^{2}+2^{5}iq^{4}+(38+41i)q^{5}+\cdots$$
20.6.e.b $$24$$ $$3.208$$ None $$-10$$ $$0$$ $$-80$$ $$0$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 - 8 T + 32 T^{2}$$)
$3$ ($$1 + 59049 T^{4}$$)
$5$ ($$1 - 76 T + 3125 T^{2}$$)
$7$ ($$1 + 282475249 T^{4}$$)
$11$ ($$( 1 - 161051 T^{2} )^{2}$$)
$13$ ($$( 1 - 1194 T + 371293 T^{2} )( 1 - 244 T + 371293 T^{2} )$$)
$17$ ($$( 1 - 808 T + 1419857 T^{2} )( 1 + 2242 T + 1419857 T^{2} )$$)
$19$ ($$( 1 + 2476099 T^{2} )^{2}$$)
$23$ ($$1 + 41426511213649 T^{4}$$)
$29$ ($$( 1 - 2950 T + 20511149 T^{2} )( 1 + 2950 T + 20511149 T^{2} )$$)
$31$ ($$( 1 - 28629151 T^{2} )^{2}$$)
$37$ ($$( 1 + 11292 T + 69343957 T^{2} )( 1 + 12242 T + 69343957 T^{2} )$$)
$41$ ($$( 1 - 4952 T + 115856201 T^{2} )^{2}$$)
$43$ ($$1 + 21611482313284249 T^{4}$$)
$47$ ($$1 + 52599132235830049 T^{4}$$)
$53$ ($$( 1 - 40244 T + 418195493 T^{2} )( 1 - 7294 T + 418195493 T^{2} )$$)
$59$ ($$( 1 + 714924299 T^{2} )^{2}$$)
$61$ ($$( 1 + 54948 T + 844596301 T^{2} )^{2}$$)
$67$ ($$1 + 1822837804551761449 T^{4}$$)
$71$ ($$( 1 - 1804229351 T^{2} )^{2}$$)
$73$ ($$( 1 - 20144 T + 2073071593 T^{2} )( 1 + 88806 T + 2073071593 T^{2} )$$)
$79$ ($$( 1 + 3077056399 T^{2} )^{2}$$)
$83$ ($$1 + 15516041187205853449 T^{4}$$)
$89$ ($$( 1 - 51050 T + 5584059449 T^{2} )( 1 + 51050 T + 5584059449 T^{2} )$$)
$97$ ($$( 1 - 160808 T + 8587340257 T^{2} )( 1 + 92142 T + 8587340257 T^{2} )$$)