# Properties

 Label 4004.2.m Level 4004 Weight 2 Character orbit m Rep. character $$\chi_{4004}(2157,\cdot)$$ Character field $$\Q$$ Dimension 68 Newform subspaces 3 Sturm bound 1344 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 4004.m (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$13$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$1344$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(4004, [\chi])$$.

Total New Old
Modular forms 684 68 616
Cusp forms 660 68 592
Eisenstein series 24 0 24

## Trace form

 $$68q + 60q^{9} + O(q^{10})$$ $$68q + 60q^{9} + 8q^{13} - 4q^{23} - 72q^{25} + 12q^{29} - 4q^{35} - 8q^{39} - 12q^{43} - 68q^{49} + 24q^{51} - 28q^{53} - 16q^{61} - 20q^{65} + 80q^{69} - 40q^{75} + 8q^{77} + 28q^{79} + 68q^{81} + 56q^{87} + 8q^{91} + 44q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(4004, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
4004.2.m.a $$2$$ $$31.972$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+2q^{3}+iq^{5}+iq^{7}+q^{9}-iq^{11}+\cdots$$
4004.2.m.b $$30$$ $$31.972$$ None $$0$$ $$0$$ $$0$$ $$0$$
4004.2.m.c $$36$$ $$31.972$$ None $$0$$ $$-4$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(4004, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(4004, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(143, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(182, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(286, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(364, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(572, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1001, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2002, [\chi])$$$$^{\oplus 2}$$