# Properties

 Label 4020.2.g Level 4020 Weight 2 Character orbit g Rep. character $$\chi_{4020}(1609,\cdot)$$ Character field $$\Q$$ Dimension 64 Newform subspaces 3 Sturm bound 1632 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4020.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$1632$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(4020, [\chi])$$.

Total New Old
Modular forms 828 64 764
Cusp forms 804 64 740
Eisenstein series 24 0 24

## Trace form

 $$64q - 4q^{5} - 64q^{9} + O(q^{10})$$ $$64q - 4q^{5} - 64q^{9} + 16q^{11} + 4q^{15} - 8q^{21} + 8q^{25} - 32q^{29} - 8q^{31} - 4q^{35} + 24q^{41} + 4q^{45} - 56q^{49} + 8q^{55} - 32q^{59} + 24q^{61} + 4q^{65} + 8q^{75} - 24q^{79} + 64q^{81} - 8q^{85} - 24q^{89} + 24q^{91} + 32q^{95} - 16q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(4020, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
4020.2.g.a $$2$$ $$32.100$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{3}+(1-2i)q^{5}-q^{9}+2iq^{13}+\cdots$$
4020.2.g.b $$24$$ $$32.100$$ None $$0$$ $$0$$ $$-4$$ $$0$$
4020.2.g.c $$38$$ $$32.100$$ None $$0$$ $$0$$ $$-2$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(4020, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(4020, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(335, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(670, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1005, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1340, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2010, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ ($$1 + T^{2}$$)
$5$ ($$1 - 2 T + 5 T^{2}$$)
$7$ ($$( 1 - 7 T^{2} )^{2}$$)
$11$ ($$( 1 + 11 T^{2} )^{2}$$)
$13$ ($$1 - 22 T^{2} + 169 T^{4}$$)
$17$ ($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)
$19$ ($$( 1 + 19 T^{2} )^{2}$$)
$23$ ($$1 + 18 T^{2} + 529 T^{4}$$)
$29$ ($$( 1 + 6 T + 29 T^{2} )^{2}$$)
$31$ ($$( 1 + 2 T + 31 T^{2} )^{2}$$)
$37$ ($$( 1 - 37 T^{2} )^{2}$$)
$41$ ($$( 1 + 6 T + 41 T^{2} )^{2}$$)
$43$ ($$1 - 70 T^{2} + 1849 T^{4}$$)
$47$ ($$( 1 - 47 T^{2} )^{2}$$)
$53$ ($$( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} )$$)
$59$ ($$( 1 + 2 T + 59 T^{2} )^{2}$$)
$61$ ($$( 1 + 10 T + 61 T^{2} )^{2}$$)
$67$ ($$1 + T^{2}$$)
$71$ ($$( 1 + 10 T + 71 T^{2} )^{2}$$)
$73$ ($$1 - 82 T^{2} + 5329 T^{4}$$)
$79$ ($$( 1 - 14 T + 79 T^{2} )^{2}$$)
$83$ ($$1 - 22 T^{2} + 6889 T^{4}$$)
$89$ ($$( 1 - 2 T + 89 T^{2} )^{2}$$)
$97$ ($$1 + 2 T^{2} + 9409 T^{4}$$)