Properties

Label 6003.2
Level 6003
Weight 2
Dimension 1041768
Nonzero newspaces 48
Sturm bound 5322240

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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

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