Properties

Label 6027.2
Level 6027
Weight 2
Dimension 943026
Nonzero newspaces 64
Sturm bound 5268480

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Defining parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(5268480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6027))\).

Total New Old
Modular forms 1326720 950594 376126
Cusp forms 1307521 943026 364495
Eisenstein series 19199 7568 11631

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6027))\)

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
6027.2.a \(\chi_{6027}(1, \cdot)\) 6027.2.a.a 1 1
6027.2.a.b 1
6027.2.a.c 1
6027.2.a.d 1
6027.2.a.e 1
6027.2.a.f 1
6027.2.a.g 1
6027.2.a.h 1
6027.2.a.i 2
6027.2.a.j 2
6027.2.a.k 2
6027.2.a.l 2
6027.2.a.m 2
6027.2.a.n 2
6027.2.a.o 3
6027.2.a.p 3
6027.2.a.q 3
6027.2.a.r 3
6027.2.a.s 3
6027.2.a.t 3
6027.2.a.u 4
6027.2.a.v 5
6027.2.a.w 5
6027.2.a.x 5
6027.2.a.y 7
6027.2.a.z 8
6027.2.a.ba 8
6027.2.a.bb 8
6027.2.a.bc 8
6027.2.a.bd 10
6027.2.a.be 10
6027.2.a.bf 12
6027.2.a.bg 12
6027.2.a.bh 13
6027.2.a.bi 13
6027.2.a.bj 14
6027.2.a.bk 14
6027.2.a.bl 16
6027.2.a.bm 16
6027.2.a.bn 24
6027.2.a.bo 24
6027.2.d \(\chi_{6027}(3527, \cdot)\) n/a 532 1
6027.2.e \(\chi_{6027}(6026, \cdot)\) n/a 552 1
6027.2.h \(\chi_{6027}(2500, \cdot)\) n/a 288 1
6027.2.i \(\chi_{6027}(1108, \cdot)\) n/a 532 2
6027.2.j \(\chi_{6027}(442, \cdot)\) n/a 572 2
6027.2.l \(\chi_{6027}(3968, \cdot)\) n/a 1104 2
6027.2.n \(\chi_{6027}(2353, \cdot)\) n/a 1152 4
6027.2.o \(\chi_{6027}(655, \cdot)\) n/a 560 2
6027.2.r \(\chi_{6027}(1844, \cdot)\) n/a 1104 2
6027.2.s \(\chi_{6027}(2420, \cdot)\) n/a 1068 2
6027.2.v \(\chi_{6027}(862, \cdot)\) n/a 2232 6
6027.2.w \(\chi_{6027}(3037, \cdot)\) n/a 1120 4
6027.2.z \(\chi_{6027}(1520, \cdot)\) n/a 2256 4
6027.2.ba \(\chi_{6027}(148, \cdot)\) n/a 1152 4
6027.2.bd \(\chi_{6027}(146, \cdot)\) n/a 2208 4
6027.2.be \(\chi_{6027}(734, \cdot)\) n/a 2208 4
6027.2.bi \(\chi_{6027}(1403, \cdot)\) n/a 2208 4
6027.2.bk \(\chi_{6027}(214, \cdot)\) n/a 1120 4
6027.2.bl \(\chi_{6027}(778, \cdot)\) n/a 2352 6
6027.2.bo \(\chi_{6027}(860, \cdot)\) n/a 4680 6
6027.2.bp \(\chi_{6027}(83, \cdot)\) n/a 4488 6
6027.2.bs \(\chi_{6027}(508, \cdot)\) n/a 2240 8
6027.2.bu \(\chi_{6027}(881, \cdot)\) n/a 4416 8
6027.2.bw \(\chi_{6027}(295, \cdot)\) n/a 2288 8
6027.2.bx \(\chi_{6027}(247, \cdot)\) n/a 4488 12
6027.2.by \(\chi_{6027}(998, \cdot)\) n/a 4416 8
6027.2.cb \(\chi_{6027}(178, \cdot)\) n/a 2240 8
6027.2.cd \(\chi_{6027}(419, \cdot)\) n/a 9360 12
6027.2.cf \(\chi_{6027}(337, \cdot)\) n/a 4704 12
6027.2.ci \(\chi_{6027}(215, \cdot)\) n/a 4416 8
6027.2.cj \(\chi_{6027}(1097, \cdot)\) n/a 4416 8
6027.2.cm \(\chi_{6027}(373, \cdot)\) n/a 2240 8
6027.2.cn \(\chi_{6027}(379, \cdot)\) n/a 9408 24
6027.2.co \(\chi_{6027}(785, \cdot)\) n/a 9024 16
6027.2.cr \(\chi_{6027}(97, \cdot)\) n/a 4480 16
6027.2.cu \(\chi_{6027}(206, \cdot)\) n/a 8952 12
6027.2.cv \(\chi_{6027}(122, \cdot)\) n/a 9360 12
6027.2.cy \(\chi_{6027}(163, \cdot)\) n/a 4704 12
6027.2.cz \(\chi_{6027}(260, \cdot)\) n/a 18720 24
6027.2.dc \(\chi_{6027}(55, \cdot)\) n/a 9408 24
6027.2.dd \(\chi_{6027}(226, \cdot)\) n/a 4480 16
6027.2.df \(\chi_{6027}(80, \cdot)\) n/a 8832 16
6027.2.dj \(\chi_{6027}(461, \cdot)\) n/a 18720 24
6027.2.dk \(\chi_{6027}(209, \cdot)\) n/a 18720 24
6027.2.dn \(\chi_{6027}(64, \cdot)\) n/a 9408 24
6027.2.do \(\chi_{6027}(319, \cdot)\) n/a 9408 24
6027.2.dq \(\chi_{6027}(173, \cdot)\) n/a 18720 24
6027.2.ds \(\chi_{6027}(16, \cdot)\) n/a 18816 48
6027.2.dt \(\chi_{6027}(19, \cdot)\) n/a 8960 32
6027.2.dw \(\chi_{6027}(116, \cdot)\) n/a 17664 32
6027.2.dx \(\chi_{6027}(43, \cdot)\) n/a 18816 48
6027.2.dz \(\chi_{6027}(20, \cdot)\) n/a 37440 48
6027.2.eb \(\chi_{6027}(208, \cdot)\) n/a 18816 48
6027.2.ee \(\chi_{6027}(44, \cdot)\) n/a 37440 48
6027.2.ef \(\chi_{6027}(4, \cdot)\) n/a 18816 48
6027.2.ei \(\chi_{6027}(236, \cdot)\) n/a 37440 48
6027.2.ej \(\chi_{6027}(59, \cdot)\) n/a 37440 48
6027.2.em \(\chi_{6027}(13, \cdot)\) n/a 37632 96
6027.2.ep \(\chi_{6027}(29, \cdot)\) n/a 74880 96
6027.2.er \(\chi_{6027}(5, \cdot)\) n/a 74880 96
6027.2.et \(\chi_{6027}(46, \cdot)\) n/a 37632 96
6027.2.eu \(\chi_{6027}(11, \cdot)\) n/a 149760 192
6027.2.ex \(\chi_{6027}(52, \cdot)\) n/a 75264 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6027))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6027)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(287))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(861))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2009))\)\(^{\oplus 2}\)