# Properties

 Label 2002.2.c Level 2002 Weight 2 Character orbit c Rep. character $$\chi_{2002}(1847,\cdot)$$ Character field $$\Q$$ Dimension 96 Newform subspaces 2 Sturm bound 672 Trace bound 7

# Related objects

## Defining parameters

 Level: $$N$$ = $$2002 = 2 \cdot 7 \cdot 11 \cdot 13$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 2002.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$77$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$672$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2002, [\chi])$$.

Total New Old
Modular forms 344 96 248
Cusp forms 328 96 232
Eisenstein series 16 0 16

## Trace form

 $$96q - 96q^{4} - 96q^{9} + O(q^{10})$$ $$96q - 96q^{4} - 96q^{9} - 8q^{11} - 4q^{14} + 16q^{15} + 96q^{16} + 4q^{22} - 64q^{23} - 112q^{25} + 96q^{36} - 32q^{37} + 32q^{42} + 8q^{44} - 76q^{49} + 8q^{53} + 4q^{56} + 48q^{58} - 16q^{60} - 96q^{64} - 16q^{67} - 40q^{70} - 24q^{77} + 32q^{81} - 4q^{88} + 16q^{91} + 64q^{92} - 96q^{93} + 184q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2002, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2002.2.c.a $$48$$ $$15.986$$ None $$0$$ $$0$$ $$0$$ $$-8$$
2002.2.c.b $$48$$ $$15.986$$ None $$0$$ $$0$$ $$0$$ $$8$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2002, [\chi])$$ into lower level spaces

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

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database