# Properties

 Label 20.4.c Level 20 Weight 4 Character orbit c Rep. character $$\chi_{20}(9,\cdot)$$ Character field $$\Q$$ Dimension 2 Newform subspaces 1 Sturm bound 12 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$20 = 2^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 20.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(20, [\chi])$$.

Total New Old
Modular forms 12 2 10
Cusp forms 6 2 4
Eisenstein series 6 0 6

## Trace form

 $$2q + 14q^{5} - 98q^{9} + O(q^{10})$$ $$2q + 14q^{5} - 98q^{9} + 40q^{11} + 152q^{15} - 168q^{19} + 152q^{21} - 54q^{25} + 12q^{29} - 448q^{31} - 152q^{35} + 912q^{39} + 532q^{41} - 686q^{45} + 534q^{49} - 1216q^{51} + 280q^{55} - 56q^{59} + 364q^{61} - 912q^{65} - 1064q^{69} + 816q^{71} + 2128q^{75} + 96q^{79} + 698q^{81} + 1216q^{85} - 3052q^{89} - 912q^{91} - 1176q^{95} - 1960q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(20, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
20.4.c.a $$2$$ $$1.180$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$14$$ $$0$$ $$q-\beta q^{3}+(7+\beta )q^{5}+\beta q^{7}-7^{2}q^{9}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(20, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(20, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(10, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ $$1 + 22 T^{2} + 729 T^{4}$$
$5$ $$1 - 14 T + 125 T^{2}$$
$7$ $$( 1 - 36 T + 343 T^{2} )( 1 + 36 T + 343 T^{2} )$$
$11$ $$( 1 - 20 T + 1331 T^{2} )^{2}$$
$13$ $$1 - 1658 T^{2} + 4826809 T^{4}$$
$17$ $$1 - 4962 T^{2} + 24137569 T^{4}$$
$19$ $$( 1 + 84 T + 6859 T^{2} )^{2}$$
$23$ $$( 1 - 212 T + 12167 T^{2} )( 1 + 212 T + 12167 T^{2} )$$
$29$ $$( 1 - 6 T + 24389 T^{2} )^{2}$$
$31$ $$( 1 + 224 T + 29791 T^{2} )^{2}$$
$37$ $$1 - 86410 T^{2} + 2565726409 T^{4}$$
$41$ $$( 1 - 266 T + 68921 T^{2} )^{2}$$
$43$ $$1 - 65914 T^{2} + 6321363049 T^{4}$$
$47$ $$1 - 67122 T^{2} + 10779215329 T^{4}$$
$53$ $$1 - 163690 T^{2} + 22164361129 T^{4}$$
$59$ $$( 1 + 28 T + 205379 T^{2} )^{2}$$
$61$ $$( 1 - 182 T + 226981 T^{2} )^{2}$$
$67$ $$1 - 419050 T^{2} + 90458382169 T^{4}$$
$71$ $$( 1 - 408 T + 357911 T^{2} )^{2}$$
$73$ $$1 + 390542 T^{2} + 151334226289 T^{4}$$
$79$ $$( 1 - 48 T + 493039 T^{2} )^{2}$$
$83$ $$1 - 1103370 T^{2} + 326940373369 T^{4}$$
$89$ $$( 1 + 1526 T + 704969 T^{2} )^{2}$$
$97$ $$1 - 1514050 T^{2} + 832972004929 T^{4}$$