# Properties

 Label 4012.2.b Level 4012 Weight 2 Character orbit b Rep. character $$\chi_{4012}(237,\cdot)$$ Character field $$\Q$$ Dimension 86 Newform subspaces 2 Sturm bound 1080 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$4012 = 2^{2} \cdot 17 \cdot 59$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 4012.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$17$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$1080$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(4012, [\chi])$$.

Total New Old
Modular forms 546 86 460
Cusp forms 534 86 448
Eisenstein series 12 0 12

## Trace form

 $$86q - 90q^{9} + O(q^{10})$$ $$86q - 90q^{9} + 16q^{13} + 10q^{15} - 7q^{17} - 18q^{21} - 78q^{25} - 12q^{33} - 26q^{35} - 16q^{43} - 4q^{47} - 58q^{49} + 20q^{51} + 16q^{53} - 32q^{55} + 6q^{59} + 24q^{67} - 8q^{69} - 16q^{77} + 86q^{81} - 20q^{83} - 24q^{85} + 26q^{87} - 36q^{89} - 4q^{93} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(4012, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
4012.2.b.a $$40$$ $$32.036$$ None $$0$$ $$0$$ $$0$$ $$0$$
4012.2.b.b $$46$$ $$32.036$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(4012, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(4012, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(34, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(68, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1003, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2006, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database