Properties

 Label 6036.2 Level 6036 Weight 2 Dimension 441760 Nonzero newspaces 8 Sturm bound 4.04813e+06

Defining parameters

 Level: $$N$$ = $$6036 = 2^{2} \cdot 3 \cdot 503$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Sturm bound: $$4048128$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6036))$$.

Total New Old
Modular forms 1017052 443760 573292
Cusp forms 1007013 441760 565253
Eisenstein series 10039 2000 8039

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6036))$$

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
6036.2.a $$\chi_{6036}(1, \cdot)$$ 6036.2.a.a 1 1
6036.2.a.b 1
6036.2.a.c 1
6036.2.a.d 1
6036.2.a.e 1
6036.2.a.f 14
6036.2.a.g 15
6036.2.a.h 24
6036.2.a.i 26
6036.2.b $$\chi_{6036}(2011, \cdot)$$ n/a 504 1
6036.2.c $$\chi_{6036}(1007, \cdot)$$ n/a 1004 1
6036.2.h $$\chi_{6036}(3017, \cdot)$$ n/a 168 1
6036.2.i $$\chi_{6036}(13, \cdot)$$ n/a 21000 250
6036.2.j $$\chi_{6036}(5, \cdot)$$ n/a 42000 250
6036.2.o $$\chi_{6036}(11, \cdot)$$ n/a 251000 250
6036.2.p $$\chi_{6036}(19, \cdot)$$ n/a 126000 250

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6036))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6036)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(503))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1006))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1509))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2012))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3018))$$$$^{\oplus 2}$$