# Properties

 Label 4018.2 Level 4018 Weight 2 Dimension 157800 Nonzero newspaces 32 Sturm bound 1.97568e+06

## Defining parameters

 Level: $$N$$ = $$4018 = 2 \cdot 7^{2} \cdot 41$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$1975680$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4018))$$.

Total New Old
Modular forms 498720 157800 340920
Cusp forms 489121 157800 331321
Eisenstein series 9599 0 9599

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4018))$$

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
4018.2.a $$\chi_{4018}(1, \cdot)$$ 4018.2.a.a 1 1
4018.2.a.b 1
4018.2.a.c 1
4018.2.a.d 1
4018.2.a.e 1
4018.2.a.f 1
4018.2.a.g 1
4018.2.a.h 1
4018.2.a.i 1
4018.2.a.j 1
4018.2.a.k 1
4018.2.a.l 1
4018.2.a.m 1
4018.2.a.n 1
4018.2.a.o 1
4018.2.a.p 1
4018.2.a.q 1
4018.2.a.r 1
4018.2.a.s 1
4018.2.a.t 2
4018.2.a.u 2
4018.2.a.v 2
4018.2.a.w 2
4018.2.a.x 2
4018.2.a.y 2
4018.2.a.z 2
4018.2.a.ba 2
4018.2.a.bb 2
4018.2.a.bc 2
4018.2.a.bd 3
4018.2.a.be 3
4018.2.a.bf 3
4018.2.a.bg 3
4018.2.a.bh 3
4018.2.a.bi 4
4018.2.a.bj 4
4018.2.a.bk 4
4018.2.a.bl 4
4018.2.a.bm 4
4018.2.a.bn 6
4018.2.a.bo 6
4018.2.a.bp 6
4018.2.a.bq 6
4018.2.a.br 10
4018.2.a.bs 10
4018.2.a.bt 10
4018.2.a.bu 10
4018.2.c $$\chi_{4018}(491, \cdot)$$ n/a 144 1
4018.2.e $$\chi_{4018}(165, \cdot)$$ n/a 264 2
4018.2.f $$\chi_{4018}(2059, \cdot)$$ n/a 286 2
4018.2.h $$\chi_{4018}(1863, \cdot)$$ n/a 576 4
4018.2.j $$\chi_{4018}(655, \cdot)$$ n/a 280 2
4018.2.l $$\chi_{4018}(575, \cdot)$$ n/a 1104 6
4018.2.n $$\chi_{4018}(489, \cdot)$$ n/a 560 4
4018.2.o $$\chi_{4018}(687, \cdot)$$ n/a 576 4
4018.2.s $$\chi_{4018}(1157, \cdot)$$ n/a 560 4
4018.2.u $$\chi_{4018}(1065, \cdot)$$ n/a 1176 6
4018.2.w $$\chi_{4018}(961, \cdot)$$ n/a 1120 8
4018.2.y $$\chi_{4018}(197, \cdot)$$ n/a 1144 8
4018.2.z $$\chi_{4018}(247, \cdot)$$ n/a 2256 12
4018.2.ba $$\chi_{4018}(325, \cdot)$$ n/a 1120 8
4018.2.bd $$\chi_{4018}(155, \cdot)$$ n/a 2352 12
4018.2.bg $$\chi_{4018}(373, \cdot)$$ n/a 1120 8
4018.2.bh $$\chi_{4018}(57, \cdot)$$ n/a 4704 24
4018.2.bi $$\chi_{4018}(97, \cdot)$$ n/a 2240 16
4018.2.bl $$\chi_{4018}(81, \cdot)$$ n/a 2352 12
4018.2.bo $$\chi_{4018}(27, \cdot)$$ n/a 4704 24
4018.2.bp $$\chi_{4018}(361, \cdot)$$ n/a 2240 16
4018.2.bt $$\chi_{4018}(113, \cdot)$$ n/a 4704 24
4018.2.bu $$\chi_{4018}(9, \cdot)$$ n/a 4704 24
4018.2.bw $$\chi_{4018}(37, \cdot)$$ n/a 9408 48
4018.2.by $$\chi_{4018}(19, \cdot)$$ n/a 4480 32
4018.2.bz $$\chi_{4018}(43, \cdot)$$ n/a 9408 48
4018.2.cb $$\chi_{4018}(3, \cdot)$$ n/a 9408 48
4018.2.cd $$\chi_{4018}(23, \cdot)$$ n/a 9408 48
4018.2.cg $$\chi_{4018}(13, \cdot)$$ n/a 18816 96
4018.2.cj $$\chi_{4018}(39, \cdot)$$ n/a 18816 96
4018.2.cl $$\chi_{4018}(17, \cdot)$$ n/a 37632 192

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4018))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4018)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(41))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(82))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(287))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(574))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2009))$$$$^{\oplus 2}$$