# Properties

 Label 8027.2 Level 8027 Weight 2 Dimension 2.66212e+06 Nonzero newspaces 24 Sturm bound 1.07184e+07

## Defining parameters

 Level: $$N$$ = $$8027 = 23 \cdot 349$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$10718400$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8027))$$.

Total New Old
Modular forms 2687256 2676693 10563
Cusp forms 2671945 2662117 9828
Eisenstein series 15311 14576 735

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8027))$$

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
8027.2.a $$\chi_{8027}(1, \cdot)$$ 8027.2.a.a 1 1
8027.2.a.b 1
8027.2.a.c 143
8027.2.a.d 149
8027.2.a.e 169
8027.2.a.f 176
8027.2.c $$\chi_{8027}(4187, \cdot)$$ n/a 642 1
8027.2.e $$\chi_{8027}(2669, \cdot)$$ n/a 1284 2
8027.2.g $$\chi_{8027}(1609, \cdot)$$ n/a 1396 2
8027.2.i $$\chi_{8027}(576, \cdot)$$ n/a 1280 2
8027.2.k $$\chi_{8027}(699, \cdot)$$ n/a 6960 10
8027.2.l $$\chi_{8027}(160, \cdot)$$ n/a 2792 4
8027.2.o $$\chi_{8027}(348, \cdot)$$ n/a 6980 10
8027.2.q $$\chi_{8027}(415, \cdot)$$ n/a 18032 28
8027.2.r $$\chi_{8027}(924, \cdot)$$ n/a 13960 20
8027.2.s $$\chi_{8027}(136, \cdot)$$ n/a 13960 20
8027.2.v $$\chi_{8027}(139, \cdot)$$ n/a 17976 28
8027.2.y $$\chi_{8027}(123, \cdot)$$ n/a 13960 20
8027.2.ba $$\chi_{8027}(116, \cdot)$$ n/a 35952 56
8027.2.bb $$\chi_{8027}(321, \cdot)$$ n/a 39088 56
8027.2.be $$\chi_{8027}(189, \cdot)$$ n/a 27920 40
8027.2.bg $$\chi_{8027}(70, \cdot)$$ n/a 35840 56
8027.2.bi $$\chi_{8027}(31, \cdot)$$ n/a 195440 280
8027.2.bk $$\chi_{8027}(114, \cdot)$$ n/a 78176 112
8027.2.bm $$\chi_{8027}(27, \cdot)$$ n/a 195440 280
8027.2.bo $$\chi_{8027}(9, \cdot)$$ n/a 390880 560
8027.2.bq $$\chi_{8027}(10, \cdot)$$ n/a 390880 560
8027.2.bs $$\chi_{8027}(3, \cdot)$$ n/a 390880 560
8027.2.bu $$\chi_{8027}(7, \cdot)$$ n/a 781760 1120

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8027))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8027)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(349))$$$$^{\oplus 2}$$