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Properties

Label 6005.2
Level 6005
Weight 2
Dimension 1318599
Nonzero newspaces 60
Sturm bound 5769600

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Defining parameters

Level: \( N \) = \( 6005 = 5 \cdot 1201 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(5769600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6005))\).

Total New Old
Modular forms 1447200 1325795 121405
Cusp forms 1437601 1318599 119002
Eisenstein series 9599 7196 2403

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6005))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
6005.2.a \(\chi_{6005}(1, \cdot)\) 6005.2.a.a 1 1
6005.2.a.b 1
6005.2.a.c 4
6005.2.a.d 83
6005.2.a.e 88
6005.2.a.f 111
6005.2.a.g 113
6005.2.b \(\chi_{6005}(6004, \cdot)\) n/a 600 1
6005.2.c \(\chi_{6005}(3604, \cdot)\) n/a 600 1
6005.2.d \(\chi_{6005}(2401, \cdot)\) n/a 402 1
6005.2.e \(\chi_{6005}(1771, \cdot)\) n/a 800 2
6005.2.f \(\chi_{6005}(49, \cdot)\) n/a 1200 2
6005.2.k \(\chi_{6005}(2451, \cdot)\) n/a 804 2
6005.2.l \(\chi_{6005}(216, \cdot)\) n/a 1608 4
6005.2.m \(\chi_{6005}(571, \cdot)\) n/a 800 2
6005.2.n \(\chi_{6005}(5374, \cdot)\) n/a 1200 2
6005.2.o \(\chi_{6005}(4174, \cdot)\) n/a 1200 2
6005.2.p \(\chi_{6005}(3596, \cdot)\) n/a 1608 4
6005.2.s \(\chi_{6005}(1194, \cdot)\) n/a 2392 4
6005.2.t \(\chi_{6005}(1096, \cdot)\) n/a 1608 4
6005.2.u \(\chi_{6005}(2219, \cdot)\) n/a 2400 4
6005.2.v \(\chi_{6005}(139, \cdot)\) n/a 2400 4
6005.2.w \(\chi_{6005}(356, \cdot)\) n/a 1600 4
6005.2.bb \(\chi_{6005}(894, \cdot)\) n/a 2400 4
6005.2.bc \(\chi_{6005}(6, \cdot)\) n/a 3200 8
6005.2.bd \(\chi_{6005}(292, \cdot)\) n/a 4792 8
6005.2.bg \(\chi_{6005}(1493, \cdot)\) n/a 4792 8
6005.2.bh \(\chi_{6005}(341, \cdot)\) n/a 3216 8
6005.2.bm \(\chi_{6005}(3944, \cdot)\) n/a 4800 8
6005.2.bn \(\chi_{6005}(394, \cdot)\) n/a 4784 8
6005.2.bq \(\chi_{6005}(1111, \cdot)\) n/a 3200 8
6005.2.br \(\chi_{6005}(96, \cdot)\) n/a 8040 20
6005.2.bs \(\chi_{6005}(834, \cdot)\) n/a 4800 8
6005.2.bt \(\chi_{6005}(1304, \cdot)\) n/a 4800 8
6005.2.bu \(\chi_{6005}(1106, \cdot)\) n/a 3200 8
6005.2.bv \(\chi_{6005}(374, \cdot)\) n/a 9568 16
6005.2.by \(\chi_{6005}(311, \cdot)\) n/a 6432 16
6005.2.bz \(\chi_{6005}(142, \cdot)\) n/a 9584 16
6005.2.cc \(\chi_{6005}(207, \cdot)\) n/a 9584 16
6005.2.cd \(\chi_{6005}(319, \cdot)\) n/a 12000 20
6005.2.ce \(\chi_{6005}(64, \cdot)\) n/a 12000 20
6005.2.cf \(\chi_{6005}(326, \cdot)\) n/a 8040 20
6005.2.cg \(\chi_{6005}(149, \cdot)\) n/a 9600 16
6005.2.cl \(\chi_{6005}(266, \cdot)\) n/a 6400 16
6005.2.cm \(\chi_{6005}(16, \cdot)\) n/a 16000 40
6005.2.cn \(\chi_{6005}(87, \cdot)\) n/a 19168 32
6005.2.cq \(\chi_{6005}(83, \cdot)\) n/a 19168 32
6005.2.cr \(\chi_{6005}(206, \cdot)\) n/a 16080 40
6005.2.cw \(\chi_{6005}(59, \cdot)\) n/a 24000 40
6005.2.cx \(\chi_{6005}(536, \cdot)\) n/a 12800 32
6005.2.da \(\chi_{6005}(199, \cdot)\) n/a 19136 32
6005.2.db \(\chi_{6005}(4, \cdot)\) n/a 24000 40
6005.2.dc \(\chi_{6005}(274, \cdot)\) n/a 24000 40
6005.2.dd \(\chi_{6005}(411, \cdot)\) n/a 16000 40
6005.2.df \(\chi_{6005}(19, \cdot)\) n/a 47840 80
6005.2.dg \(\chi_{6005}(56, \cdot)\) n/a 32160 80
6005.2.di \(\chi_{6005}(97, \cdot)\) n/a 38336 64
6005.2.dl \(\chi_{6005}(287, \cdot)\) n/a 38336 64
6005.2.dm \(\chi_{6005}(61, \cdot)\) n/a 32000 80
6005.2.dr \(\chi_{6005}(229, \cdot)\) n/a 48000 80
6005.2.ds \(\chi_{6005}(13, \cdot)\) n/a 95840 160
6005.2.dv \(\chi_{6005}(47, \cdot)\) n/a 95840 160
6005.2.dx \(\chi_{6005}(21, \cdot)\) n/a 64000 160
6005.2.dy \(\chi_{6005}(14, \cdot)\) n/a 95680 160
6005.2.ea \(\chi_{6005}(17, \cdot)\) n/a 191680 320
6005.2.ed \(\chi_{6005}(33, \cdot)\) n/a 191680 320

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6005))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6005)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1201))\)\(^{\oplus 2}\)