Properties

 Label 8044.2 Level 8044 Weight 2 Dimension 1.17752e+06 Nonzero newspaces 16 Sturm bound 8.08824e+06

Defining parameters

 Level: $$N$$ = $$8044 = 2^{2} \cdot 2011$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Sturm bound: $$8088240$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8044))$$.

Total New Old
Modular forms 2027085 1181545 845540
Cusp forms 2017036 1177525 839511
Eisenstein series 10049 4020 6029

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8044))$$

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
8044.2.a $$\chi_{8044}(1, \cdot)$$ 8044.2.a.a 80 1
8044.2.a.b 87
8044.2.d $$\chi_{8044}(8043, \cdot)$$ n/a 1004 1
8044.2.e $$\chi_{8044}(205, \cdot)$$ n/a 336 2
8044.2.f $$\chi_{8044}(2809, \cdot)$$ n/a 668 4
8044.2.g $$\chi_{8044}(6239, \cdot)$$ n/a 2008 2
8044.2.j $$\chi_{8044}(63, \cdot)$$ n/a 4016 4
8044.2.m $$\chi_{8044}(1201, \cdot)$$ n/a 1344 8
8044.2.p $$\chi_{8044}(1099, \cdot)$$ n/a 8032 8
8044.2.q $$\chi_{8044}(133, \cdot)$$ n/a 11022 66
8044.2.r $$\chi_{8044}(147, \cdot)$$ n/a 66264 66
8044.2.u $$\chi_{8044}(117, \cdot)$$ n/a 22176 132
8044.2.v $$\chi_{8044}(13, \cdot)$$ n/a 44088 264
8044.2.y $$\chi_{8044}(15, \cdot)$$ n/a 132528 132
8044.2.bb $$\chi_{8044}(27, \cdot)$$ n/a 265056 264
8044.2.bc $$\chi_{8044}(5, \cdot)$$ n/a 88704 528
8044.2.bd $$\chi_{8044}(3, \cdot)$$ n/a 530112 528

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8044))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8044)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(2011))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4022))$$$$^{\oplus 2}$$