## Defining parameters

 Level: $$N$$ = $$6012 = 2^{2} \cdot 3^{2} \cdot 167$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Sturm bound: $$4015872$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6012))$$.

Total New Old
Modular forms 1010608 465090 545518
Cusp forms 997329 462118 535211
Eisenstein series 13279 2972 10307

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6012))$$

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
6012.2.a $$\chi_{6012}(1, \cdot)$$ 6012.2.a.a 2 1
6012.2.a.b 3
6012.2.a.c 3
6012.2.a.d 5
6012.2.a.e 5
6012.2.a.f 5
6012.2.a.g 7
6012.2.a.h 9
6012.2.a.i 9
6012.2.a.j 10
6012.2.a.k 10
6012.2.b $$\chi_{6012}(667, \cdot)$$ n/a 418 1
6012.2.c $$\chi_{6012}(2339, \cdot)$$ n/a 332 1
6012.2.h $$\chi_{6012}(3005, \cdot)$$ 6012.2.h.a 56 1
6012.2.i $$\chi_{6012}(2005, \cdot)$$ n/a 332 2
6012.2.j $$\chi_{6012}(1001, \cdot)$$ n/a 336 2
6012.2.o $$\chi_{6012}(335, \cdot)$$ n/a 1992 2
6012.2.p $$\chi_{6012}(2671, \cdot)$$ n/a 2008 2
6012.2.q $$\chi_{6012}(181, \cdot)$$ n/a 5740 82
6012.2.r $$\chi_{6012}(17, \cdot)$$ n/a 4592 82
6012.2.w $$\chi_{6012}(107, \cdot)$$ n/a 27552 82
6012.2.x $$\chi_{6012}(55, \cdot)$$ n/a 34276 82
6012.2.y $$\chi_{6012}(25, \cdot)$$ n/a 27552 164
6012.2.z $$\chi_{6012}(43, \cdot)$$ n/a 164656 164
6012.2.ba $$\chi_{6012}(11, \cdot)$$ n/a 164656 164
6012.2.bf $$\chi_{6012}(5, \cdot)$$ n/a 27552 164

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6012))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6012)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(167))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(334))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(501))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(668))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1002))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1503))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2004))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3006))$$$$^{\oplus 2}$$