# Properties

 Label 4028.2.c Level 4028 Weight 2 Character orbit c Rep. character $$\chi_{4028}(3497,\cdot)$$ Character field $$\Q$$ Dimension 82 Newform subspaces 1 Sturm bound 1080 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$4028 = 2^{2} \cdot 19 \cdot 53$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 4028.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$53$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$1080$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(4028, [\chi])$$.

Total New Old
Modular forms 546 82 464
Cusp forms 534 82 452
Eisenstein series 12 0 12

## Trace form

 $$82q - 8q^{7} - 82q^{9} + O(q^{10})$$ $$82q - 8q^{7} - 82q^{9} + 4q^{13} + 4q^{15} - 4q^{17} - 58q^{25} - 16q^{29} - 12q^{37} - 32q^{43} + 8q^{47} + 98q^{49} + 6q^{53} - 4q^{57} + 4q^{59} + 8q^{63} + 28q^{69} - 8q^{77} + 154q^{81} - 20q^{89} + 48q^{91} - 56q^{93} - 44q^{97} - 8q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(4028, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
4028.2.c.a $$82$$ $$32.164$$ None $$0$$ $$0$$ $$0$$ $$-8$$

## Decomposition of $$S_{2}^{\mathrm{old}}(4028, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(4028, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(53, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(106, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(212, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1007, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2014, [\chi])$$$$^{\oplus 2}$$