## Defining parameters

 Level: $$N$$ = $$6003 = 3^{2} \cdot 23 \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$5322240$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6003))$$.

Total New Old
Modular forms 1340416 1051976 288440
Cusp forms 1320705 1041768 278937
Eisenstein series 19711 10208 9503

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6003))$$

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
6003.2.a $$\chi_{6003}(1, \cdot)$$ 6003.2.a.a 1 1
6003.2.a.b 1
6003.2.a.c 1
6003.2.a.d 2
6003.2.a.e 2
6003.2.a.f 2
6003.2.a.g 4
6003.2.a.h 5
6003.2.a.i 7
6003.2.a.j 7
6003.2.a.k 10
6003.2.a.l 10
6003.2.a.m 11
6003.2.a.n 12
6003.2.a.o 13
6003.2.a.p 14
6003.2.a.q 16
6003.2.a.r 16
6003.2.a.s 20
6003.2.a.t 22
6003.2.a.u 22
6003.2.a.v 30
6003.2.a.w 30
6003.2.d $$\chi_{6003}(3104, \cdot)$$ n/a 224 1
6003.2.e $$\chi_{6003}(2899, \cdot)$$ n/a 274 1
6003.2.h $$\chi_{6003}(6002, \cdot)$$ n/a 240 1
6003.2.i $$\chi_{6003}(2002, \cdot)$$ n/a 1232 2
6003.2.l $$\chi_{6003}(505, \cdot)$$ n/a 596 2
6003.2.m $$\chi_{6003}(737, \cdot)$$ n/a 440 2
6003.2.n $$\chi_{6003}(2000, \cdot)$$ n/a 1432 2
6003.2.q $$\chi_{6003}(898, \cdot)$$ n/a 1320 2
6003.2.r $$\chi_{6003}(1103, \cdot)$$ n/a 1344 2
6003.2.u $$\chi_{6003}(1243, \cdot)$$ n/a 1656 6
6003.2.v $$\chi_{6003}(262, \cdot)$$ n/a 2800 10
6003.2.w $$\chi_{6003}(1496, \cdot)$$ n/a 2640 4
6003.2.x $$\chi_{6003}(1264, \cdot)$$ n/a 2864 4
6003.2.ba $$\chi_{6003}(1862, \cdot)$$ n/a 1440 6
6003.2.bd $$\chi_{6003}(208, \cdot)$$ n/a 1644 6
6003.2.be $$\chi_{6003}(413, \cdot)$$ n/a 1440 6
6003.2.bh $$\chi_{6003}(139, \cdot)$$ n/a 7920 12
6003.2.bi $$\chi_{6003}(260, \cdot)$$ n/a 2400 10
6003.2.bl $$\chi_{6003}(289, \cdot)$$ n/a 2980 10
6003.2.bm $$\chi_{6003}(494, \cdot)$$ n/a 2240 10
6003.2.bp $$\chi_{6003}(530, \cdot)$$ n/a 2640 12
6003.2.bq $$\chi_{6003}(298, \cdot)$$ n/a 3576 12
6003.2.bt $$\chi_{6003}(349, \cdot)$$ n/a 13440 20
6003.2.bw $$\chi_{6003}(344, \cdot)$$ n/a 8592 12
6003.2.bx $$\chi_{6003}(760, \cdot)$$ n/a 7920 12
6003.2.ca $$\chi_{6003}(689, \cdot)$$ n/a 8592 12
6003.2.cb $$\chi_{6003}(215, \cdot)$$ n/a 4800 20
6003.2.cc $$\chi_{6003}(244, \cdot)$$ n/a 5960 20
6003.2.ch $$\chi_{6003}(320, \cdot)$$ n/a 13440 20
6003.2.ci $$\chi_{6003}(202, \cdot)$$ n/a 14320 20
6003.2.cl $$\chi_{6003}(86, \cdot)$$ n/a 14320 20
6003.2.cm $$\chi_{6003}(82, \cdot)$$ n/a 17880 60
6003.2.cp $$\chi_{6003}(160, \cdot)$$ n/a 17184 24
6003.2.cq $$\chi_{6003}(47, \cdot)$$ n/a 15840 24
6003.2.ct $$\chi_{6003}(157, \cdot)$$ n/a 28640 40
6003.2.cu $$\chi_{6003}(41, \cdot)$$ n/a 28640 40
6003.2.cx $$\chi_{6003}(53, \cdot)$$ n/a 14400 60
6003.2.cy $$\chi_{6003}(64, \cdot)$$ n/a 17880 60
6003.2.db $$\chi_{6003}(80, \cdot)$$ n/a 14400 60
6003.2.dc $$\chi_{6003}(16, \cdot)$$ n/a 85920 120
6003.2.df $$\chi_{6003}(10, \cdot)$$ n/a 35760 120
6003.2.dg $$\chi_{6003}(8, \cdot)$$ n/a 28800 120
6003.2.dh $$\chi_{6003}(5, \cdot)$$ n/a 85920 120
6003.2.dk $$\chi_{6003}(4, \cdot)$$ n/a 85920 120
6003.2.dl $$\chi_{6003}(20, \cdot)$$ n/a 85920 120
6003.2.do $$\chi_{6003}(2, \cdot)$$ n/a 171840 240
6003.2.dp $$\chi_{6003}(40, \cdot)$$ n/a 171840 240

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6003))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6003)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(87))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(207))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(261))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(667))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2001))$$$$^{\oplus 2}$$