# Properties

 Label 20.3.d Level 20 Weight 3 Character orbit d Rep. character $$\chi_{20}(19,\cdot)$$ Character field $$\Q$$ Dimension 4 Newform subspaces 3 Sturm bound 9 Trace bound 2

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$20 = 2^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 20.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$9$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(20, [\chi])$$.

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

## Trace form

 $$4q - 4q^{5} - 16q^{6} - 4q^{9} + O(q^{10})$$ $$4q - 4q^{5} - 16q^{6} - 4q^{9} + 16q^{10} + 16q^{14} + 64q^{16} - 64q^{20} - 32q^{21} - 64q^{24} + 36q^{25} - 96q^{26} + 40q^{29} + 80q^{30} + 64q^{34} + 128q^{36} - 64q^{40} + 88q^{41} - 124q^{45} - 176q^{46} - 164q^{49} + 96q^{50} + 32q^{54} + 64q^{56} - 72q^{61} + 192q^{65} + 352q^{69} - 80q^{70} - 96q^{74} - 64q^{80} - 28q^{81} - 128q^{84} - 128q^{85} + 304q^{86} - 440q^{89} - 144q^{90} + 16q^{94} - 256q^{96} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(20, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
20.3.d.a $$1$$ $$0.545$$ $$\Q$$ $$\Q(\sqrt{-5})$$ $$-2$$ $$4$$ $$-5$$ $$-4$$ $$q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots$$
20.3.d.b $$1$$ $$0.545$$ $$\Q$$ $$\Q(\sqrt{-5})$$ $$2$$ $$-4$$ $$-5$$ $$4$$ $$q+2q^{2}-4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots$$
20.3.d.c $$2$$ $$0.545$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$6$$ $$0$$ $$q+iq^{2}-4q^{4}+(3-2i)q^{5}-4iq^{8}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 + 2 T$$)($$1 - 2 T$$)($$1 + 4 T^{2}$$)
$3$ ($$1 - 4 T + 9 T^{2}$$)($$1 + 4 T + 9 T^{2}$$)($$( 1 + 9 T^{2} )^{2}$$)
$5$ ($$1 + 5 T$$)($$1 + 5 T$$)($$1 - 6 T + 25 T^{2}$$)
$7$ ($$1 + 4 T + 49 T^{2}$$)($$1 - 4 T + 49 T^{2}$$)($$( 1 + 49 T^{2} )^{2}$$)
$11$ ($$( 1 - 11 T )( 1 + 11 T )$$)($$( 1 - 11 T )( 1 + 11 T )$$)($$( 1 - 11 T )^{2}( 1 + 11 T )^{2}$$)
$13$ ($$( 1 - 13 T )( 1 + 13 T )$$)($$( 1 - 13 T )( 1 + 13 T )$$)($$( 1 - 10 T + 169 T^{2} )( 1 + 10 T + 169 T^{2} )$$)
$17$ ($$( 1 - 17 T )( 1 + 17 T )$$)($$( 1 - 17 T )( 1 + 17 T )$$)($$( 1 - 30 T + 289 T^{2} )( 1 + 30 T + 289 T^{2} )$$)
$19$ ($$( 1 - 19 T )( 1 + 19 T )$$)($$( 1 - 19 T )( 1 + 19 T )$$)($$( 1 - 19 T )^{2}( 1 + 19 T )^{2}$$)
$23$ ($$1 - 44 T + 529 T^{2}$$)($$1 + 44 T + 529 T^{2}$$)($$( 1 + 529 T^{2} )^{2}$$)
$29$ ($$1 + 22 T + 841 T^{2}$$)($$1 + 22 T + 841 T^{2}$$)($$( 1 - 42 T + 841 T^{2} )^{2}$$)
$31$ ($$( 1 - 31 T )( 1 + 31 T )$$)($$( 1 - 31 T )( 1 + 31 T )$$)($$( 1 - 31 T )^{2}( 1 + 31 T )^{2}$$)
$37$ ($$( 1 - 37 T )( 1 + 37 T )$$)($$( 1 - 37 T )( 1 + 37 T )$$)($$( 1 - 70 T + 1369 T^{2} )( 1 + 70 T + 1369 T^{2} )$$)
$41$ ($$1 - 62 T + 1681 T^{2}$$)($$1 - 62 T + 1681 T^{2}$$)($$( 1 + 18 T + 1681 T^{2} )^{2}$$)
$43$ ($$1 + 76 T + 1849 T^{2}$$)($$1 - 76 T + 1849 T^{2}$$)($$( 1 + 1849 T^{2} )^{2}$$)
$47$ ($$1 + 4 T + 2209 T^{2}$$)($$1 - 4 T + 2209 T^{2}$$)($$( 1 + 2209 T^{2} )^{2}$$)
$53$ ($$( 1 - 53 T )( 1 + 53 T )$$)($$( 1 - 53 T )( 1 + 53 T )$$)($$( 1 - 90 T + 2809 T^{2} )( 1 + 90 T + 2809 T^{2} )$$)
$59$ ($$( 1 - 59 T )( 1 + 59 T )$$)($$( 1 - 59 T )( 1 + 59 T )$$)($$( 1 - 59 T )^{2}( 1 + 59 T )^{2}$$)
$61$ ($$1 + 58 T + 3721 T^{2}$$)($$1 + 58 T + 3721 T^{2}$$)($$( 1 - 22 T + 3721 T^{2} )^{2}$$)
$67$ ($$1 - 116 T + 4489 T^{2}$$)($$1 + 116 T + 4489 T^{2}$$)($$( 1 + 4489 T^{2} )^{2}$$)
$71$ ($$( 1 - 71 T )( 1 + 71 T )$$)($$( 1 - 71 T )( 1 + 71 T )$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)
$73$ ($$( 1 - 73 T )( 1 + 73 T )$$)($$( 1 - 73 T )( 1 + 73 T )$$)($$( 1 - 110 T + 5329 T^{2} )( 1 + 110 T + 5329 T^{2} )$$)
$79$ ($$( 1 - 79 T )( 1 + 79 T )$$)($$( 1 - 79 T )( 1 + 79 T )$$)($$( 1 - 79 T )^{2}( 1 + 79 T )^{2}$$)
$83$ ($$1 + 76 T + 6889 T^{2}$$)($$1 - 76 T + 6889 T^{2}$$)($$( 1 + 6889 T^{2} )^{2}$$)
$89$ ($$1 + 142 T + 7921 T^{2}$$)($$1 + 142 T + 7921 T^{2}$$)($$( 1 + 78 T + 7921 T^{2} )^{2}$$)
$97$ ($$( 1 - 97 T )( 1 + 97 T )$$)($$( 1 - 97 T )( 1 + 97 T )$$)($$( 1 - 130 T + 9409 T^{2} )( 1 + 130 T + 9409 T^{2} )$$)