Properties

Label 6040.2
Level 6040
Weight 2
Dimension 562462
Nonzero newspaces 54
Sturm bound 4377600

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Defining parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 54 \)
Sturm bound: \(4377600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6040))\).

Total New Old
Modular forms 1101600 566038 535562
Cusp forms 1087201 562462 524739
Eisenstein series 14399 3576 10823

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6040))\)

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
6040.2.a \(\chi_{6040}(1, \cdot)\) 6040.2.a.a 1 1
6040.2.a.b 1
6040.2.a.c 1
6040.2.a.d 1
6040.2.a.e 1
6040.2.a.f 1
6040.2.a.g 1
6040.2.a.h 1
6040.2.a.i 1
6040.2.a.j 1
6040.2.a.k 2
6040.2.a.l 9
6040.2.a.m 12
6040.2.a.n 13
6040.2.a.o 15
6040.2.a.p 19
6040.2.a.q 23
6040.2.a.r 23
6040.2.a.s 24
6040.2.b \(\chi_{6040}(6039, \cdot)\) None 0 1
6040.2.d \(\chi_{6040}(1209, \cdot)\) n/a 224 1
6040.2.g \(\chi_{6040}(3021, \cdot)\) n/a 600 1
6040.2.i \(\chi_{6040}(1811, \cdot)\) n/a 608 1
6040.2.j \(\chi_{6040}(4229, \cdot)\) n/a 900 1
6040.2.l \(\chi_{6040}(3019, \cdot)\) n/a 908 1
6040.2.o \(\chi_{6040}(4831, \cdot)\) None 0 1
6040.2.q \(\chi_{6040}(2081, \cdot)\) n/a 304 2
6040.2.r \(\chi_{6040}(2717, \cdot)\) n/a 1816 2
6040.2.u \(\chi_{6040}(303, \cdot)\) None 0 2
6040.2.w \(\chi_{6040}(907, \cdot)\) n/a 1800 2
6040.2.x \(\chi_{6040}(2113, \cdot)\) n/a 456 2
6040.2.z \(\chi_{6040}(321, \cdot)\) n/a 608 4
6040.2.ba \(\chi_{6040}(1931, \cdot)\) n/a 1216 2
6040.2.bc \(\chi_{6040}(2901, \cdot)\) n/a 1216 2
6040.2.bf \(\chi_{6040}(1089, \cdot)\) n/a 456 2
6040.2.bh \(\chi_{6040}(119, \cdot)\) None 0 2
6040.2.bj \(\chi_{6040}(2751, \cdot)\) None 0 2
6040.2.bm \(\chi_{6040}(939, \cdot)\) n/a 1816 2
6040.2.bo \(\chi_{6040}(269, \cdot)\) n/a 1816 2
6040.2.bq \(\chi_{6040}(1351, \cdot)\) None 0 4
6040.2.bt \(\chi_{6040}(1899, \cdot)\) n/a 3632 4
6040.2.bv \(\chi_{6040}(1669, \cdot)\) n/a 3632 4
6040.2.bw \(\chi_{6040}(691, \cdot)\) n/a 2432 4
6040.2.by \(\chi_{6040}(461, \cdot)\) n/a 2432 4
6040.2.cb \(\chi_{6040}(1529, \cdot)\) n/a 912 4
6040.2.cd \(\chi_{6040}(2559, \cdot)\) None 0 4
6040.2.ce \(\chi_{6040}(33, \cdot)\) n/a 912 4
6040.2.ch \(\chi_{6040}(787, \cdot)\) n/a 3632 4
6040.2.cj \(\chi_{6040}(183, \cdot)\) None 0 4
6040.2.ck \(\chi_{6040}(637, \cdot)\) n/a 3632 4
6040.2.cm \(\chi_{6040}(1361, \cdot)\) n/a 1216 8
6040.2.co \(\chi_{6040}(993, \cdot)\) n/a 1824 8
6040.2.cp \(\chi_{6040}(763, \cdot)\) n/a 7264 8
6040.2.cr \(\chi_{6040}(623, \cdot)\) None 0 8
6040.2.cu \(\chi_{6040}(1597, \cdot)\) n/a 7264 8
6040.2.cv \(\chi_{6040}(81, \cdot)\) n/a 3040 20
6040.2.cw \(\chi_{6040}(189, \cdot)\) n/a 7264 8
6040.2.cy \(\chi_{6040}(499, \cdot)\) n/a 7264 8
6040.2.db \(\chi_{6040}(751, \cdot)\) None 0 8
6040.2.dd \(\chi_{6040}(519, \cdot)\) None 0 8
6040.2.df \(\chi_{6040}(529, \cdot)\) n/a 1824 8
6040.2.di \(\chi_{6040}(581, \cdot)\) n/a 4864 8
6040.2.dk \(\chi_{6040}(451, \cdot)\) n/a 4864 8
6040.2.dm \(\chi_{6040}(131, \cdot)\) n/a 12160 20
6040.2.dp \(\chi_{6040}(9, \cdot)\) n/a 4560 20
6040.2.dr \(\chi_{6040}(179, \cdot)\) n/a 18160 20
6040.2.dt \(\chi_{6040}(631, \cdot)\) None 0 20
6040.2.dv \(\chi_{6040}(261, \cdot)\) n/a 12160 20
6040.2.dx \(\chi_{6040}(29, \cdot)\) n/a 18160 20
6040.2.dz \(\chi_{6040}(79, \cdot)\) None 0 20
6040.2.eb \(\chi_{6040}(197, \cdot)\) n/a 14528 16
6040.2.ec \(\chi_{6040}(167, \cdot)\) None 0 16
6040.2.ee \(\chi_{6040}(227, \cdot)\) n/a 14528 16
6040.2.eh \(\chi_{6040}(113, \cdot)\) n/a 3648 16
6040.2.ei \(\chi_{6040}(121, \cdot)\) n/a 6080 40
6040.2.el \(\chi_{6040}(127, \cdot)\) None 0 40
6040.2.em \(\chi_{6040}(53, \cdot)\) n/a 36320 40
6040.2.ep \(\chi_{6040}(123, \cdot)\) n/a 36320 40
6040.2.eq \(\chi_{6040}(57, \cdot)\) n/a 9120 40
6040.2.er \(\chi_{6040}(259, \cdot)\) n/a 36320 40
6040.2.et \(\chi_{6040}(49, \cdot)\) n/a 9120 40
6040.2.ew \(\chi_{6040}(51, \cdot)\) n/a 24320 40
6040.2.ey \(\chi_{6040}(199, \cdot)\) None 0 40
6040.2.fa \(\chi_{6040}(69, \cdot)\) n/a 36320 40
6040.2.fc \(\chi_{6040}(21, \cdot)\) n/a 24320 40
6040.2.fe \(\chi_{6040}(71, \cdot)\) None 0 40
6040.2.fg \(\chi_{6040}(47, \cdot)\) None 0 80
6040.2.fh \(\chi_{6040}(13, \cdot)\) n/a 72640 80
6040.2.fk \(\chi_{6040}(43, \cdot)\) n/a 72640 80
6040.2.fl \(\chi_{6040}(233, \cdot)\) n/a 18240 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6040))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6040)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(151))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(302))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(604))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(755))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1510))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3020))\)\(^{\oplus 2}\)