# Properties

 Label 16.5.c Level 16 Weight 5 Character orbit c Rep. character $$\chi_{16}(15,\cdot)$$ Character field $$\Q$$ Dimension 2 Newform subspaces 1 Sturm bound 10 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$16 = 2^{4}$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 16.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$10$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(16, [\chi])$$.

Total New Old
Modular forms 11 2 9
Cusp forms 5 2 3
Eisenstein series 6 0 6

## Trace form

 $$2q + 36q^{5} - 222q^{9} + O(q^{10})$$ $$2q + 36q^{5} - 222q^{9} + 356q^{13} - 252q^{17} + 768q^{21} - 602q^{25} - 2844q^{29} + 3456q^{33} + 1060q^{37} + 324q^{41} - 3996q^{45} + 3266q^{49} + 1188q^{53} - 11136q^{57} + 1252q^{61} + 6408q^{65} + 20736q^{69} - 13372q^{73} - 6912q^{77} - 6462q^{81} - 4536q^{85} + 16452q^{89} - 9216q^{93} - 3196q^{97} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(16, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
16.5.c.a $$2$$ $$1.654$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$36$$ $$0$$ $$q-\zeta_{6}q^{3}+18q^{5}+2\zeta_{6}q^{7}-111q^{9}+\cdots$$

## Decomposition of $$S_{5}^{\mathrm{old}}(16, [\chi])$$ into lower level spaces

$$S_{5}^{\mathrm{old}}(16, [\chi]) \cong$$ $$S_{5}^{\mathrm{new}}(4, [\chi])$$$$^{\oplus 3}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ $$1 + 30 T^{2} + 6561 T^{4}$$
$5$ $$( 1 - 18 T + 625 T^{2} )^{2}$$
$7$ $$( 1 - 94 T + 2401 T^{2} )( 1 + 94 T + 2401 T^{2} )$$
$11$ $$1 - 13730 T^{2} + 214358881 T^{4}$$
$13$ $$( 1 - 178 T + 28561 T^{2} )^{2}$$
$17$ $$( 1 + 126 T + 83521 T^{2} )^{2}$$
$19$ $$1 - 99170 T^{2} + 16983563041 T^{4}$$
$23$ $$1 + 190 T^{2} + 78310985281 T^{4}$$
$29$ $$( 1 + 1422 T + 707281 T^{2} )^{2}$$
$31$ $$1 - 1736450 T^{2} + 852891037441 T^{4}$$
$37$ $$( 1 - 530 T + 1874161 T^{2} )^{2}$$
$41$ $$( 1 - 162 T + 2825761 T^{2} )^{2}$$
$43$ $$1 - 4471970 T^{2} + 11688200277601 T^{4}$$
$47$ $$1 + 2433406 T^{2} + 23811286661761 T^{4}$$
$53$ $$( 1 - 594 T + 7890481 T^{2} )^{2}$$
$59$ $$1 - 18620450 T^{2} + 146830437604321 T^{4}$$
$61$ $$( 1 - 626 T + 13845841 T^{2} )^{2}$$
$67$ $$1 - 39103970 T^{2} + 406067677556641 T^{4}$$
$71$ $$1 + 8958526 T^{2} + 645753531245761 T^{4}$$
$73$ $$( 1 + 6686 T + 28398241 T^{2} )^{2}$$
$79$ $$1 - 75980162 T^{2} + 1517108809906561 T^{4}$$
$83$ $$1 - 73625954 T^{2} + 2252292232139041 T^{4}$$
$89$ $$( 1 - 8226 T + 62742241 T^{2} )^{2}$$
$97$ $$( 1 + 1598 T + 88529281 T^{2} )^{2}$$