Properties

Label 6015.2
Level 6015
Weight 2
Dimension 881999
Nonzero newspaces 54
Sturm bound 5145600

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Defining parameters

Level: \( N \) = \( 6015 = 3 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 54 \)
Sturm bound: \(5145600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6015))\).

Total New Old
Modular forms 1292800 886783 406017
Cusp forms 1280001 881999 398002
Eisenstein series 12799 4784 8015

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6015))\)

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
6015.2.a \(\chi_{6015}(1, \cdot)\) 6015.2.a.a 2 1
6015.2.a.b 23
6015.2.a.c 28
6015.2.a.d 29
6015.2.a.e 31
6015.2.a.f 36
6015.2.a.g 36
6015.2.a.h 39
6015.2.a.i 43
6015.2.b \(\chi_{6015}(1204, \cdot)\) n/a 400 1
6015.2.c \(\chi_{6015}(4009, \cdot)\) n/a 400 1
6015.2.h \(\chi_{6015}(2806, \cdot)\) n/a 268 1
6015.2.i \(\chi_{6015}(421, \cdot)\) n/a 536 2
6015.2.l \(\chi_{6015}(803, \cdot)\) n/a 1600 2
6015.2.m \(\chi_{6015}(1202, \cdot)\) n/a 1600 2
6015.2.o \(\chi_{6015}(3188, \cdot)\) n/a 1600 2
6015.2.r \(\chi_{6015}(782, \cdot)\) n/a 1600 2
6015.2.t \(\chi_{6015}(1624, \cdot)\) n/a 800 2
6015.2.u \(\chi_{6015}(841, \cdot)\) n/a 1072 4
6015.2.v \(\chi_{6015}(1907, \cdot)\) n/a 3200 4
6015.2.z \(\chi_{6015}(3511, \cdot)\) n/a 1072 4
6015.2.ba \(\chi_{6015}(499, \cdot)\) n/a 1616 4
6015.2.bc \(\chi_{6015}(98, \cdot)\) n/a 3200 4
6015.2.bd \(\chi_{6015}(1966, \cdot)\) n/a 1072 4
6015.2.bi \(\chi_{6015}(484, \cdot)\) n/a 1600 4
6015.2.bj \(\chi_{6015}(874, \cdot)\) n/a 1600 4
6015.2.bo \(\chi_{6015}(133, \cdot)\) n/a 3216 8
6015.2.bp \(\chi_{6015}(371, \cdot)\) n/a 4288 8
6015.2.bq \(\chi_{6015}(254, \cdot)\) n/a 6400 8
6015.2.br \(\chi_{6015}(2152, \cdot)\) n/a 3216 8
6015.2.bs \(\chi_{6015}(379, \cdot)\) n/a 3200 8
6015.2.bu \(\chi_{6015}(623, \cdot)\) n/a 6400 8
6015.2.bx \(\chi_{6015}(3152, \cdot)\) n/a 6400 8
6015.2.bz \(\chi_{6015}(83, \cdot)\) n/a 6400 8
6015.2.ca \(\chi_{6015}(473, \cdot)\) n/a 6400 8
6015.2.cd \(\chi_{6015}(2971, \cdot)\) n/a 2144 8
6015.2.ce \(\chi_{6015}(196, \cdot)\) n/a 5360 20
6015.2.cf \(\chi_{6015}(32, \cdot)\) n/a 12800 16
6015.2.ch \(\chi_{6015}(151, \cdot)\) n/a 4288 16
6015.2.ci \(\chi_{6015}(589, \cdot)\) n/a 6464 16
6015.2.cm \(\chi_{6015}(287, \cdot)\) n/a 12800 16
6015.2.co \(\chi_{6015}(16, \cdot)\) n/a 5360 20
6015.2.cq \(\chi_{6015}(574, \cdot)\) n/a 8000 20
6015.2.cs \(\chi_{6015}(739, \cdot)\) n/a 8000 20
6015.2.cu \(\chi_{6015}(142, \cdot)\) n/a 12864 32
6015.2.cv \(\chi_{6015}(119, \cdot)\) n/a 25600 32
6015.2.cw \(\chi_{6015}(26, \cdot)\) n/a 17152 32
6015.2.cx \(\chi_{6015}(427, \cdot)\) n/a 12864 32
6015.2.dc \(\chi_{6015}(121, \cdot)\) n/a 10720 40
6015.2.de \(\chi_{6015}(338, \cdot)\) n/a 32000 40
6015.2.dg \(\chi_{6015}(113, \cdot)\) n/a 32000 40
6015.2.dh \(\chi_{6015}(197, \cdot)\) n/a 32000 40
6015.2.dk \(\chi_{6015}(77, \cdot)\) n/a 32000 40
6015.2.dm \(\chi_{6015}(4, \cdot)\) n/a 16000 40
6015.2.do \(\chi_{6015}(109, \cdot)\) n/a 32320 80
6015.2.dq \(\chi_{6015}(2, \cdot)\) n/a 64000 80
6015.2.dr \(\chi_{6015}(242, \cdot)\) n/a 64000 80
6015.2.du \(\chi_{6015}(166, \cdot)\) n/a 21440 80
6015.2.dw \(\chi_{6015}(13, \cdot)\) n/a 64320 160
6015.2.dy \(\chi_{6015}(71, \cdot)\) n/a 85760 160
6015.2.dz \(\chi_{6015}(59, \cdot)\) n/a 128000 160
6015.2.ec \(\chi_{6015}(52, \cdot)\) n/a 64320 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6015))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6015)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(401))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1203))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2005))\)\(^{\oplus 2}\)