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Properties

Label 5994.2
Level 5994
Weight 2
Dimension 262272
Nonzero newspaces 78
Sturm bound 3989088

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Defining parameters

Level: \( N \) = \( 5994 = 2 \cdot 3^{4} \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 78 \)
Sturm bound: \(3989088\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5994))\).

Total New Old
Modular forms 1005048 262272 742776
Cusp forms 989497 262272 727225
Eisenstein series 15551 0 15551

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5994))\)

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
5994.2.a \(\chi_{5994}(1, \cdot)\) 5994.2.a.a 1 1
5994.2.a.b 1
5994.2.a.c 1
5994.2.a.d 1
5994.2.a.e 1
5994.2.a.f 1
5994.2.a.g 1
5994.2.a.h 1
5994.2.a.i 2
5994.2.a.j 2
5994.2.a.k 3
5994.2.a.l 3
5994.2.a.m 4
5994.2.a.n 4
5994.2.a.o 4
5994.2.a.p 4
5994.2.a.q 5
5994.2.a.r 5
5994.2.a.s 6
5994.2.a.t 6
5994.2.a.u 7
5994.2.a.v 7
5994.2.a.w 8
5994.2.a.x 8
5994.2.a.y 8
5994.2.a.z 8
5994.2.a.ba 10
5994.2.a.bb 10
5994.2.a.bc 11
5994.2.a.bd 11
5994.2.c \(\chi_{5994}(3403, \cdot)\) n/a 152 1
5994.2.e \(\chi_{5994}(1999, \cdot)\) n/a 288 2
5994.2.f \(\chi_{5994}(2431, \cdot)\) n/a 304 2
5994.2.g \(\chi_{5994}(433, \cdot)\) n/a 304 2
5994.2.h \(\chi_{5994}(3673, \cdot)\) n/a 304 2
5994.2.j \(\chi_{5994}(3077, \cdot)\) n/a 304 2
5994.2.k \(\chi_{5994}(1729, \cdot)\) n/a 304 2
5994.2.q \(\chi_{5994}(1405, \cdot)\) n/a 304 2
5994.2.s \(\chi_{5994}(973, \cdot)\) n/a 304 2
5994.2.t \(\chi_{5994}(4969, \cdot)\) n/a 304 2
5994.2.w \(\chi_{5994}(145, \cdot)\) n/a 684 6
5994.2.x \(\chi_{5994}(127, \cdot)\) n/a 684 6
5994.2.y \(\chi_{5994}(1477, \cdot)\) n/a 684 6
5994.2.z \(\chi_{5994}(793, \cdot)\) n/a 684 6
5994.2.ba \(\chi_{5994}(271, \cdot)\) n/a 912 6
5994.2.bb \(\chi_{5994}(811, \cdot)\) n/a 912 6
5994.2.bc \(\chi_{5994}(667, \cdot)\) n/a 648 6
5994.2.bd \(\chi_{5994}(1009, \cdot)\) n/a 684 6
5994.2.be \(\chi_{5994}(343, \cdot)\) n/a 684 6
5994.2.bf \(\chi_{5994}(379, \cdot)\) n/a 912 6
5994.2.bg \(\chi_{5994}(181, \cdot)\) n/a 684 6
5994.2.bh \(\chi_{5994}(937, \cdot)\) n/a 684 6
5994.2.bj \(\chi_{5994}(917, \cdot)\) n/a 608 4
5994.2.bk \(\chi_{5994}(1079, \cdot)\) n/a 608 4
5994.2.bn \(\chi_{5994}(1133, \cdot)\) n/a 608 4
5994.2.bo \(\chi_{5994}(1673, \cdot)\) n/a 608 4
5994.2.br \(\chi_{5994}(955, \cdot)\) n/a 684 6
5994.2.bu \(\chi_{5994}(559, \cdot)\) n/a 684 6
5994.2.by \(\chi_{5994}(361, \cdot)\) n/a 684 6
5994.2.cc \(\chi_{5994}(1135, \cdot)\) n/a 912 6
5994.2.cd \(\chi_{5994}(3025, \cdot)\) n/a 912 6
5994.2.ce \(\chi_{5994}(307, \cdot)\) n/a 684 6
5994.2.ck \(\chi_{5994}(1063, \cdot)\) n/a 684 6
5994.2.cl \(\chi_{5994}(73, \cdot)\) n/a 684 6
5994.2.cr \(\chi_{5994}(595, \cdot)\) n/a 912 6
5994.2.cu \(\chi_{5994}(289, \cdot)\) n/a 684 6
5994.2.cv \(\chi_{5994}(613, \cdot)\) n/a 684 6
5994.2.cx \(\chi_{5994}(1801, \cdot)\) n/a 684 6
5994.2.da \(\chi_{5994}(715, \cdot)\) n/a 6156 18
5994.2.db \(\chi_{5994}(157, \cdot)\) n/a 6156 18
5994.2.dc \(\chi_{5994}(229, \cdot)\) n/a 6156 18
5994.2.dd \(\chi_{5994}(589, \cdot)\) n/a 6156 18
5994.2.de \(\chi_{5994}(121, \cdot)\) n/a 6156 18
5994.2.df \(\chi_{5994}(223, \cdot)\) n/a 5832 18
5994.2.dg \(\chi_{5994}(211, \cdot)\) n/a 6156 18
5994.2.dh \(\chi_{5994}(601, \cdot)\) n/a 6156 18
5994.2.di \(\chi_{5994}(7, \cdot)\) n/a 6156 18
5994.2.dk \(\chi_{5994}(143, \cdot)\) n/a 1368 12
5994.2.dm \(\chi_{5994}(1277, \cdot)\) n/a 1368 12
5994.2.do \(\chi_{5994}(431, \cdot)\) n/a 1824 12
5994.2.dp \(\chi_{5994}(161, \cdot)\) n/a 1824 12
5994.2.dq \(\chi_{5994}(35, \cdot)\) n/a 1368 12
5994.2.ds \(\chi_{5994}(179, \cdot)\) n/a 1368 12
5994.2.dv \(\chi_{5994}(125, \cdot)\) n/a 1368 12
5994.2.dw \(\chi_{5994}(341, \cdot)\) n/a 1368 12
5994.2.dz \(\chi_{5994}(89, \cdot)\) n/a 1368 12
5994.2.eb \(\chi_{5994}(449, \cdot)\) n/a 1368 12
5994.2.ee \(\chi_{5994}(755, \cdot)\) n/a 1824 12
5994.2.ef \(\chi_{5994}(17, \cdot)\) n/a 1368 12
5994.2.ei \(\chi_{5994}(151, \cdot)\) n/a 6156 18
5994.2.el \(\chi_{5994}(25, \cdot)\) n/a 6156 18
5994.2.er \(\chi_{5994}(295, \cdot)\) n/a 6156 18
5994.2.es \(\chi_{5994}(175, \cdot)\) n/a 6156 18
5994.2.ex \(\chi_{5994}(85, \cdot)\) n/a 6156 18
5994.2.ez \(\chi_{5994}(67, \cdot)\) n/a 6156 18
5994.2.fb \(\chi_{5994}(169, \cdot)\) n/a 6156 18
5994.2.fd \(\chi_{5994}(247, \cdot)\) n/a 6156 18
5994.2.ff \(\chi_{5994}(115, \cdot)\) n/a 6156 18
5994.2.fi \(\chi_{5994}(245, \cdot)\) n/a 12312 36
5994.2.fl \(\chi_{5994}(167, \cdot)\) n/a 12312 36
5994.2.fo \(\chi_{5994}(59, \cdot)\) n/a 12312 36
5994.2.fp \(\chi_{5994}(311, \cdot)\) n/a 12312 36
5994.2.fs \(\chi_{5994}(113, \cdot)\) n/a 12312 36
5994.2.fu \(\chi_{5994}(5, \cdot)\) n/a 12312 36
5994.2.fv \(\chi_{5994}(365, \cdot)\) n/a 12312 36
5994.2.fx \(\chi_{5994}(191, \cdot)\) n/a 12312 36
5994.2.fy \(\chi_{5994}(23, \cdot)\) n/a 12312 36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5994))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5994)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(333))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(666))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(999))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1998))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2997))\)\(^{\oplus 2}\)