Properties

Label 6001.2
Level 6001
Weight 2
Dimension 1479621
Nonzero newspaces 76
Sturm bound 5981184

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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

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