# Properties

 Label 4004.2.e Level 4004 Weight 2 Character orbit e Rep. character $$\chi_{4004}(3849,\cdot)$$ Character field $$\Q$$ Dimension 96 Newform subspaces 2 Sturm bound 1344 Trace bound 7

# Related objects

## Defining parameters

 Level: $$N$$ = $$4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 4004.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$77$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$1344$$ Trace bound: $$7$$

## Dimensions

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

Total New Old
Modular forms 684 96 588
Cusp forms 660 96 564
Eisenstein series 24 0 24

## Trace form

 $$96q - 96q^{9} + O(q^{10})$$ $$96q - 96q^{9} + 4q^{11} + 16q^{15} + 8q^{23} - 88q^{25} - 32q^{37} + 20q^{49} - 16q^{53} + 8q^{67} + 24q^{77} + 128q^{81} - 8q^{91} + 72q^{93} - 80q^{99} + O(q^{100})$$

## 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.e.a $$48$$ $$31.972$$ None $$0$$ $$0$$ $$0$$ $$-4$$
4004.2.e.b $$48$$ $$31.972$$ None $$0$$ $$0$$ $$0$$ $$4$$

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

$$S_{2}^{\mathrm{old}}(4004, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(77, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(154, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(308, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1001, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2002, [\chi])$$$$^{\oplus 2}$$