# Properties

 Label 6018.2 Level 6018 Weight 2 Dimension 248673 Nonzero newspaces 20 Sturm bound 4.00896e+06

## Defining parameters

 Level: $$N$$ = $$6018 = 2 \cdot 3 \cdot 17 \cdot 59$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$20$$ Sturm bound: $$4008960$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6018))$$.

Total New Old
Modular forms 1009664 248673 760991
Cusp forms 994817 248673 746144
Eisenstein series 14847 0 14847

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6018))$$

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
6018.2.a $$\chi_{6018}(1, \cdot)$$ 6018.2.a.a 1 1
6018.2.a.b 1
6018.2.a.c 1
6018.2.a.d 1
6018.2.a.e 1
6018.2.a.f 1
6018.2.a.g 1
6018.2.a.h 1
6018.2.a.i 1
6018.2.a.j 1
6018.2.a.k 1
6018.2.a.l 1
6018.2.a.m 3
6018.2.a.n 4
6018.2.a.o 4
6018.2.a.p 5
6018.2.a.q 6
6018.2.a.r 6
6018.2.a.s 8
6018.2.a.t 8
6018.2.a.u 9
6018.2.a.v 9
6018.2.a.w 9
6018.2.a.x 10
6018.2.a.y 10
6018.2.a.z 11
6018.2.a.ba 12
6018.2.a.bb 13
6018.2.a.bc 14
6018.2.b $$\chi_{6018}(4249, \cdot)$$ n/a 176 1
6018.2.e $$\chi_{6018}(1769, \cdot)$$ n/a 320 1
6018.2.f $$\chi_{6018}(6017, \cdot)$$ n/a 360 1
6018.2.i $$\chi_{6018}(353, \cdot)$$ n/a 720 2
6018.2.l $$\chi_{6018}(4603, \cdot)$$ n/a 352 2
6018.2.n $$\chi_{6018}(355, \cdot)$$ n/a 688 4
6018.2.o $$\chi_{6018}(2123, \cdot)$$ n/a 1440 4
6018.2.q $$\chi_{6018}(473, \cdot)$$ n/a 2784 8
6018.2.t $$\chi_{6018}(235, \cdot)$$ n/a 1440 8
6018.2.u $$\chi_{6018}(205, \cdot)$$ n/a 4480 28
6018.2.x $$\chi_{6018}(101, \cdot)$$ n/a 10080 28
6018.2.y $$\chi_{6018}(443, \cdot)$$ n/a 8960 28
6018.2.bb $$\chi_{6018}(169, \cdot)$$ n/a 5040 28
6018.2.bc $$\chi_{6018}(361, \cdot)$$ n/a 10080 56
6018.2.bf $$\chi_{6018}(47, \cdot)$$ n/a 20160 56
6018.2.bh $$\chi_{6018}(77, \cdot)$$ n/a 40320 112
6018.2.bi $$\chi_{6018}(19, \cdot)$$ n/a 20160 112
6018.2.bk $$\chi_{6018}(31, \cdot)$$ n/a 40320 224
6018.2.bn $$\chi_{6018}(5, \cdot)$$ n/a 80640 224

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6018))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6018)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(59))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(102))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(118))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(177))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(354))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1003))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2006))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3009))$$$$^{\oplus 2}$$