# Properties

 Label 6001.2 Level 6001 Weight 2 Dimension 1.47962e+06 Nonzero newspaces 76 Sturm bound 5.98118e+06

## Defining parameters

 Level: $$N$$ = $$6001 = 17 \cdot 353$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$76$$ Sturm bound: $$5981184$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6001))$$.

Total New Old
Modular forms 1500928 1490153 10775
Cusp forms 1489665 1479621 10044
Eisenstein series 11263 10532 731

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6001))$$

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
6001.2.a $$\chi_{6001}(1, \cdot)$$ 6001.2.a.a 113 1
6001.2.a.b 114
6001.2.a.c 121
6001.2.a.d 121
6001.2.b $$\chi_{6001}(3178, \cdot)$$ n/a 528 1
6001.2.c $$\chi_{6001}(2823, \cdot)$$ n/a 472 1
6001.2.d $$\chi_{6001}(6000, \cdot)$$ n/a 528 1
6001.2.e $$\chi_{6001}(395, \cdot)$$ n/a 1056 2
6001.2.f $$\chi_{6001}(1058, \cdot)$$ n/a 1056 2
6001.2.g $$\chi_{6001}(4237, \cdot)$$ n/a 1056 2
6001.2.h $$\chi_{6001}(1101, \cdot)$$ n/a 1056 2
6001.2.i $$\chi_{6001}(3841, \cdot)$$ n/a 1056 2
6001.2.j $$\chi_{6001}(664, \cdot)$$ n/a 944 2
6001.2.k $$\chi_{6001}(3061, \cdot)$$ n/a 1888 4
6001.2.l $$\chi_{6001}(237, \cdot)$$ n/a 2112 4
6001.2.m $$\chi_{6001}(70, \cdot)$$ n/a 2120 4
6001.2.n $$\chi_{6001}(1528, \cdot)$$ n/a 2120 4
6001.2.o $$\chi_{6001}(1413, \cdot)$$ n/a 2112 4
6001.2.p $$\chi_{6001}(3572, \cdot)$$ n/a 2120 4
6001.2.q $$\chi_{6001}(42, \cdot)$$ n/a 2120 4
6001.2.r $$\chi_{6001}(705, \cdot)$$ n/a 2120 4
6001.2.s $$\chi_{6001}(1175, \cdot)$$ n/a 2120 4
6001.2.t $$\chi_{6001}(423, \cdot)$$ n/a 2120 4
6001.2.u $$\chi_{6001}(1296, \cdot)$$ n/a 2112 4
6001.2.v $$\chi_{6001}(2002, \cdot)$$ n/a 2112 4
6001.2.w $$\chi_{6001}(256, \cdot)$$ n/a 4720 10
6001.2.x $$\chi_{6001}(2218, \cdot)$$ n/a 4224 8
6001.2.y $$\chi_{6001}(49, \cdot)$$ n/a 4224 8
6001.2.ba $$\chi_{6001}(999, \cdot)$$ n/a 4240 8
6001.2.bb $$\chi_{6001}(1376, \cdot)$$ n/a 4240 8
6001.2.bc $$\chi_{6001}(766, \cdot)$$ n/a 3776 8
6001.2.bd $$\chi_{6001}(293, \cdot)$$ n/a 4240 8
6001.2.bt $$\chi_{6001}(36, \cdot)$$ n/a 4224 8
6001.2.bu $$\chi_{6001}(60, \cdot)$$ n/a 4224 8
6001.2.bv $$\chi_{6001}(16, \cdot)$$ n/a 5280 10
6001.2.bw $$\chi_{6001}(222, \cdot)$$ n/a 4720 10
6001.2.bx $$\chi_{6001}(764, \cdot)$$ n/a 5280 10
6001.2.by $$\chi_{6001}(363, \cdot)$$ n/a 8464 16
6001.2.bz $$\chi_{6001}(294, \cdot)$$ n/a 8464 16
6001.2.ca $$\chi_{6001}(454, \cdot)$$ n/a 8464 16
6001.2.cb $$\chi_{6001}(252, \cdot)$$ n/a 8464 16
6001.2.cc $$\chi_{6001}(346, \cdot)$$ n/a 8464 16
6001.2.cd $$\chi_{6001}(7, \cdot)$$ n/a 8464 16
6001.2.cm $$\chi_{6001}(6, \cdot)$$ n/a 8464 16
6001.2.cn $$\chi_{6001}(10, \cdot)$$ n/a 8464 16
6001.2.co $$\chi_{6001}(35, \cdot)$$ n/a 9440 20
6001.2.cp $$\chi_{6001}(135, \cdot)$$ n/a 10560 20
6001.2.cq $$\chi_{6001}(191, \cdot)$$ n/a 10560 20
6001.2.cr $$\chi_{6001}(140, \cdot)$$ n/a 10560 20
6001.2.cs $$\chi_{6001}(166, \cdot)$$ n/a 10560 20
6001.2.ct $$\chi_{6001}(4, \cdot)$$ n/a 10560 20
6001.2.cu $$\chi_{6001}(81, \cdot)$$ n/a 21120 40
6001.2.cv $$\chi_{6001}(21, \cdot)$$ n/a 21120 40
6001.2.cw $$\chi_{6001}(270, \cdot)$$ n/a 21200 40
6001.2.cx $$\chi_{6001}(111, \cdot)$$ n/a 21200 40
6001.2.cy $$\chi_{6001}(168, \cdot)$$ n/a 21200 40
6001.2.cz $$\chi_{6001}(121, \cdot)$$ n/a 21200 40
6001.2.da $$\chi_{6001}(349, \cdot)$$ n/a 21200 40
6001.2.db $$\chi_{6001}(185, \cdot)$$ n/a 21200 40
6001.2.dc $$\chi_{6001}(2, \cdot)$$ n/a 21200 40
6001.2.dd $$\chi_{6001}(83, \cdot)$$ n/a 21200 40
6001.2.de $$\chi_{6001}(84, \cdot)$$ n/a 21120 40
6001.2.df $$\chi_{6001}(324, \cdot)$$ n/a 18880 40
6001.2.dg $$\chi_{6001}(94, \cdot)$$ n/a 42240 80
6001.2.dh $$\chi_{6001}(43, \cdot)$$ n/a 42240 80
6001.2.dx $$\chi_{6001}(30, \cdot)$$ n/a 42400 80
6001.2.dy $$\chi_{6001}(18, \cdot)$$ n/a 37760 80
6001.2.dz $$\chi_{6001}(50, \cdot)$$ n/a 42400 80
6001.2.ea $$\chi_{6001}(38, \cdot)$$ n/a 42400 80
6001.2.ec $$\chi_{6001}(9, \cdot)$$ n/a 42240 80
6001.2.ed $$\chi_{6001}(19, \cdot)$$ n/a 42240 80
6001.2.ee $$\chi_{6001}(56, \cdot)$$ n/a 84640 160
6001.2.ef $$\chi_{6001}(37, \cdot)$$ n/a 84640 160
6001.2.eo $$\chi_{6001}(48, \cdot)$$ n/a 84640 160
6001.2.ep $$\chi_{6001}(12, \cdot)$$ n/a 84640 160
6001.2.eq $$\chi_{6001}(31, \cdot)$$ n/a 84640 160
6001.2.er $$\chi_{6001}(3, \cdot)$$ n/a 84640 160
6001.2.es $$\chi_{6001}(14, \cdot)$$ n/a 84640 160
6001.2.et $$\chi_{6001}(24, \cdot)$$ n/a 84640 160

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6001))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6001)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(353))$$$$^{\oplus 2}$$