# Properties

 Label 4034.2 Level 4034 Weight 2 Dimension 169511 Nonzero newspaces 30 Sturm bound 2.03414e+06

## Defining parameters

 Level: $$N$$ = $$4034 = 2 \cdot 2017$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$30$$ Sturm bound: $$2034144$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4034))$$.

Total New Old
Modular forms 510552 169511 341041
Cusp forms 506521 169511 337010
Eisenstein series 4031 0 4031

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4034))$$

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
4034.2.a $$\chi_{4034}(1, \cdot)$$ 4034.2.a.a 33 1
4034.2.a.b 35
4034.2.a.c 49
4034.2.a.d 52
4034.2.b $$\chi_{4034}(4033, \cdot)$$ n/a 170 1
4034.2.c $$\chi_{4034}(2311, \cdot)$$ n/a 340 2
4034.2.d $$\chi_{4034}(229, \cdot)$$ n/a 340 2
4034.2.e $$\chi_{4034}(295, \cdot)$$ n/a 340 2
4034.2.f $$\chi_{4034}(79, \cdot)$$ n/a 1020 6
4034.2.g $$\chi_{4034}(1469, \cdot)$$ n/a 680 4
4034.2.h $$\chi_{4034}(1005, \cdot)$$ n/a 1008 6
4034.2.i $$\chi_{4034}(765, \cdot)$$ n/a 680 4
4034.2.j $$\chi_{4034}(817, \cdot)$$ n/a 1020 6
4034.2.k $$\chi_{4034}(691, \cdot)$$ n/a 1352 8
4034.2.l $$\chi_{4034}(1029, \cdot)$$ n/a 1008 6
4034.2.m $$\chi_{4034}(899, \cdot)$$ n/a 2040 12
4034.2.n $$\chi_{4034}(1701, \cdot)$$ n/a 1360 8
4034.2.o $$\chi_{4034}(783, \cdot)$$ n/a 2040 12
4034.2.q $$\chi_{4034}(207, \cdot)$$ n/a 2016 12
4034.2.r $$\chi_{4034}(175, \cdot)$$ n/a 2040 12
4034.2.s $$\chi_{4034}(77, \cdot)$$ n/a 2704 16
4034.2.t $$\chi_{4034}(313, \cdot)$$ n/a 4080 24
4034.2.u $$\chi_{4034}(139, \cdot)$$ n/a 6048 36
4034.2.v $$\chi_{4034}(99, \cdot)$$ n/a 4032 24
4034.2.w $$\chi_{4034}(75, \cdot)$$ n/a 4080 24
4034.2.y $$\chi_{4034}(61, \cdot)$$ n/a 8112 48
4034.2.z $$\chi_{4034}(93, \cdot)$$ n/a 6048 36
4034.2.ba $$\chi_{4034}(169, \cdot)$$ n/a 8016 48
4034.2.bb $$\chi_{4034}(65, \cdot)$$ n/a 8160 48
4034.2.bd $$\chi_{4034}(11, \cdot)$$ n/a 12096 72
4034.2.bf $$\chi_{4034}(27, \cdot)$$ n/a 16224 96
4034.2.bg $$\chi_{4034}(9, \cdot)$$ n/a 24192 144
4034.2.bi $$\chi_{4034}(3, \cdot)$$ n/a 48096 288

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4034))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4034)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(2017))$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database