Properties

Label 4536.2
Level 4536
Weight 2
Dimension 237344
Nonzero newspaces 66
Sturm bound 2239488

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Defining parameters

Level: \( N \) = \( 4536 = 2^{3} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 66 \)
Sturm bound: \(2239488\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4536))\).

Total New Old
Modular forms 567648 239584 328064
Cusp forms 552097 237344 314753
Eisenstein series 15551 2240 13311

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4536))\)

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
4536.2.a \(\chi_{4536}(1, \cdot)\) 4536.2.a.a 1 1
4536.2.a.b 1
4536.2.a.c 1
4536.2.a.d 1
4536.2.a.e 1
4536.2.a.f 1
4536.2.a.g 1
4536.2.a.h 1
4536.2.a.i 1
4536.2.a.j 1
4536.2.a.k 2
4536.2.a.l 2
4536.2.a.m 2
4536.2.a.n 2
4536.2.a.o 2
4536.2.a.p 2
4536.2.a.q 2
4536.2.a.r 2
4536.2.a.s 3
4536.2.a.t 3
4536.2.a.u 3
4536.2.a.v 3
4536.2.a.w 4
4536.2.a.x 4
4536.2.a.y 4
4536.2.a.z 4
4536.2.a.ba 4
4536.2.a.bb 4
4536.2.a.bc 5
4536.2.a.bd 5
4536.2.b \(\chi_{4536}(3079, \cdot)\) None 0 1
4536.2.c \(\chi_{4536}(2269, \cdot)\) n/a 288 1
4536.2.h \(\chi_{4536}(2591, \cdot)\) None 0 1
4536.2.i \(\chi_{4536}(1133, \cdot)\) n/a 376 1
4536.2.j \(\chi_{4536}(323, \cdot)\) n/a 288 1
4536.2.k \(\chi_{4536}(3401, \cdot)\) 4536.2.k.a 48 1
4536.2.k.b 48
4536.2.p \(\chi_{4536}(811, \cdot)\) n/a 376 1
4536.2.q \(\chi_{4536}(865, \cdot)\) n/a 192 2
4536.2.r \(\chi_{4536}(1513, \cdot)\) n/a 144 2
4536.2.s \(\chi_{4536}(1297, \cdot)\) n/a 192 2
4536.2.t \(\chi_{4536}(2377, \cdot)\) n/a 192 2
4536.2.w \(\chi_{4536}(109, \cdot)\) n/a 760 2
4536.2.x \(\chi_{4536}(2215, \cdot)\) None 0 2
4536.2.y \(\chi_{4536}(2861, \cdot)\) n/a 760 2
4536.2.z \(\chi_{4536}(2375, \cdot)\) None 0 2
4536.2.be \(\chi_{4536}(2323, \cdot)\) n/a 760 2
4536.2.bf \(\chi_{4536}(2539, \cdot)\) n/a 760 2
4536.2.bk \(\chi_{4536}(1459, \cdot)\) n/a 752 2
4536.2.bl \(\chi_{4536}(2105, \cdot)\) n/a 192 2
4536.2.bm \(\chi_{4536}(1619, \cdot)\) n/a 752 2
4536.2.br \(\chi_{4536}(1835, \cdot)\) n/a 576 2
4536.2.bs \(\chi_{4536}(2537, \cdot)\) n/a 192 2
4536.2.bt \(\chi_{4536}(2699, \cdot)\) n/a 760 2
4536.2.bu \(\chi_{4536}(377, \cdot)\) n/a 192 2
4536.2.bz \(\chi_{4536}(1079, \cdot)\) None 0 2
4536.2.ca \(\chi_{4536}(269, \cdot)\) n/a 760 2
4536.2.cb \(\chi_{4536}(431, \cdot)\) None 0 2
4536.2.cc \(\chi_{4536}(2645, \cdot)\) n/a 760 2
4536.2.ch \(\chi_{4536}(1781, \cdot)\) n/a 752 2
4536.2.ci \(\chi_{4536}(1943, \cdot)\) None 0 2
4536.2.cj \(\chi_{4536}(1621, \cdot)\) n/a 752 2
4536.2.ck \(\chi_{4536}(1783, \cdot)\) None 0 2
4536.2.cp \(\chi_{4536}(55, \cdot)\) None 0 2
4536.2.cq \(\chi_{4536}(2053, \cdot)\) n/a 760 2
4536.2.cr \(\chi_{4536}(271, \cdot)\) None 0 2
4536.2.cs \(\chi_{4536}(757, \cdot)\) n/a 576 2
4536.2.cx \(\chi_{4536}(593, \cdot)\) n/a 192 2
4536.2.cy \(\chi_{4536}(107, \cdot)\) n/a 760 2
4536.2.cz \(\chi_{4536}(1027, \cdot)\) n/a 760 2
4536.2.dc \(\chi_{4536}(505, \cdot)\) n/a 324 6
4536.2.dd \(\chi_{4536}(289, \cdot)\) n/a 432 6
4536.2.de \(\chi_{4536}(793, \cdot)\) n/a 432 6
4536.2.dg \(\chi_{4536}(1367, \cdot)\) None 0 6
4536.2.di \(\chi_{4536}(451, \cdot)\) n/a 1704 6
4536.2.dj \(\chi_{4536}(1207, \cdot)\) None 0 6
4536.2.dl \(\chi_{4536}(611, \cdot)\) n/a 1704 6
4536.2.dn \(\chi_{4536}(773, \cdot)\) n/a 1704 6
4536.2.dr \(\chi_{4536}(125, \cdot)\) n/a 1704 6
4536.2.du \(\chi_{4536}(1045, \cdot)\) n/a 1704 6
4536.2.dv \(\chi_{4536}(881, \cdot)\) n/a 432 6
4536.2.dx \(\chi_{4536}(253, \cdot)\) n/a 1296 6
4536.2.ea \(\chi_{4536}(17, \cdot)\) n/a 432 6
4536.2.eb \(\chi_{4536}(179, \cdot)\) n/a 1704 6
4536.2.ee \(\chi_{4536}(559, \cdot)\) None 0 6
4536.2.eg \(\chi_{4536}(827, \cdot)\) n/a 1296 6
4536.2.eh \(\chi_{4536}(199, \cdot)\) None 0 6
4536.2.ek \(\chi_{4536}(19, \cdot)\) n/a 1704 6
4536.2.el \(\chi_{4536}(71, \cdot)\) None 0 6
4536.2.en \(\chi_{4536}(307, \cdot)\) n/a 1704 6
4536.2.eq \(\chi_{4536}(359, \cdot)\) None 0 6
4536.2.es \(\chi_{4536}(521, \cdot)\) n/a 432 6
4536.2.eu \(\chi_{4536}(37, \cdot)\) n/a 1704 6
4536.2.ew \(\chi_{4536}(341, \cdot)\) n/a 1704 6
4536.2.ey \(\chi_{4536}(193, \cdot)\) n/a 3888 18
4536.2.ez \(\chi_{4536}(169, \cdot)\) n/a 2916 18
4536.2.fa \(\chi_{4536}(25, \cdot)\) n/a 3888 18
4536.2.fb \(\chi_{4536}(277, \cdot)\) n/a 15480 18
4536.2.fd \(\chi_{4536}(115, \cdot)\) n/a 15480 18
4536.2.fg \(\chi_{4536}(257, \cdot)\) n/a 3888 18
4536.2.fi \(\chi_{4536}(23, \cdot)\) None 0 18
4536.2.fl \(\chi_{4536}(223, \cdot)\) None 0 18
4536.2.fm \(\chi_{4536}(31, \cdot)\) None 0 18
4536.2.fr \(\chi_{4536}(293, \cdot)\) n/a 15480 18
4536.2.fs \(\chi_{4536}(173, \cdot)\) n/a 15480 18
4536.2.fv \(\chi_{4536}(347, \cdot)\) n/a 15480 18
4536.2.fw \(\chi_{4536}(155, \cdot)\) n/a 11664 18
4536.2.fz \(\chi_{4536}(187, \cdot)\) n/a 15480 18
4536.2.ga \(\chi_{4536}(139, \cdot)\) n/a 15480 18
4536.2.gd \(\chi_{4536}(85, \cdot)\) n/a 11664 18
4536.2.ge \(\chi_{4536}(205, \cdot)\) n/a 15480 18
4536.2.gf \(\chi_{4536}(239, \cdot)\) None 0 18
4536.2.gg \(\chi_{4536}(95, \cdot)\) None 0 18
4536.2.gj \(\chi_{4536}(185, \cdot)\) n/a 3888 18
4536.2.gk \(\chi_{4536}(41, \cdot)\) n/a 3888 18
4536.2.go \(\chi_{4536}(103, \cdot)\) None 0 18
4536.2.gq \(\chi_{4536}(11, \cdot)\) n/a 15480 18
4536.2.gs \(\chi_{4536}(5, \cdot)\) n/a 15480 18

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4536))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4536)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(378))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(567))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(648))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(756))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1134))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1512))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2268))\)\(^{\oplus 2}\)