Properties

Label 4033.2
Level 4033
Weight 2
Dimension 672309
Nonzero newspaces 156
Sturm bound 2708640

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Defining parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 156 \)
Sturm bound: \(2708640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4033))\).

Total New Old
Modular forms 681048 679801 1247
Cusp forms 673273 672309 964
Eisenstein series 7775 7492 283

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4033))\)

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
4033.2.a \(\chi_{4033}(1, \cdot)\) 4033.2.a.a 1 1
4033.2.a.b 1
4033.2.a.c 77
4033.2.a.d 79
4033.2.a.e 82
4033.2.a.f 85
4033.2.b \(\chi_{4033}(110, \cdot)\) n/a 342 1
4033.2.c \(\chi_{4033}(3923, \cdot)\) n/a 330 1
4033.2.d \(\chi_{4033}(4032, \cdot)\) n/a 344 1
4033.2.e \(\chi_{4033}(935, \cdot)\) n/a 688 2
4033.2.f \(\chi_{4033}(655, \cdot)\) n/a 684 2
4033.2.g \(\chi_{4033}(63, \cdot)\) n/a 688 2
4033.2.h \(\chi_{4033}(2443, \cdot)\) n/a 660 2
4033.2.i \(\chi_{4033}(142, \cdot)\) n/a 690 2
4033.2.n \(\chi_{4033}(512, \cdot)\) n/a 690 2
4033.2.o \(\chi_{4033}(482, \cdot)\) n/a 660 2
4033.2.p \(\chi_{4033}(2552, \cdot)\) n/a 692 2
4033.2.q \(\chi_{4033}(936, \cdot)\) n/a 688 2
4033.2.r \(\chi_{4033}(2506, \cdot)\) n/a 688 2
4033.2.s \(\chi_{4033}(64, \cdot)\) n/a 688 2
4033.2.t \(\chi_{4033}(544, \cdot)\) n/a 692 2
4033.2.u \(\chi_{4033}(2008, \cdot)\) n/a 692 2
4033.2.v \(\chi_{4033}(2617, \cdot)\) n/a 684 2
4033.2.w \(\chi_{4033}(1898, \cdot)\) n/a 692 2
4033.2.x \(\chi_{4033}(1026, \cdot)\) n/a 692 2
4033.2.y \(\chi_{4033}(1136, \cdot)\) n/a 692 2
4033.2.z \(\chi_{4033}(591, \cdot)\) n/a 688 2
4033.2.ba \(\chi_{4033}(38, \cdot)\) n/a 1980 6
4033.2.bb \(\chi_{4033}(1564, \cdot)\) n/a 2064 6
4033.2.bc \(\chi_{4033}(1958, \cdot)\) n/a 2076 6
4033.2.bd \(\chi_{4033}(16, \cdot)\) n/a 2076 6
4033.2.be \(\chi_{4033}(1698, \cdot)\) n/a 2076 6
4033.2.bf \(\chi_{4033}(608, \cdot)\) n/a 2076 6
4033.2.bg \(\chi_{4033}(1117, \cdot)\) n/a 2076 6
4033.2.bh \(\chi_{4033}(1274, \cdot)\) n/a 2076 6
4033.2.bi \(\chi_{4033}(1106, \cdot)\) n/a 2076 6
4033.2.bj \(\chi_{4033}(219, \cdot)\) n/a 2052 6
4033.2.bk \(\chi_{4033}(234, \cdot)\) n/a 2076 6
4033.2.bl \(\chi_{4033}(343, \cdot)\) n/a 2064 6
4033.2.bm \(\chi_{4033}(68, \cdot)\) n/a 1380 4
4033.2.bn \(\chi_{4033}(8, \cdot)\) n/a 1380 4
4033.2.bo \(\chi_{4033}(578, \cdot)\) n/a 1380 4
4033.2.bp \(\chi_{4033}(695, \cdot)\) n/a 1380 4
4033.2.cg \(\chi_{4033}(880, \cdot)\) n/a 1380 4
4033.2.ch \(\chi_{4033}(177, \cdot)\) n/a 1380 4
4033.2.ci \(\chi_{4033}(251, \cdot)\) n/a 1380 4
4033.2.cj \(\chi_{4033}(117, \cdot)\) n/a 1380 4
4033.2.ck \(\chi_{4033}(27, \cdot)\) n/a 2076 6
4033.2.cl \(\chi_{4033}(470, \cdot)\) n/a 2076 6
4033.2.cm \(\chi_{4033}(1183, \cdot)\) n/a 2064 6
4033.2.cn \(\chi_{4033}(529, \cdot)\) n/a 2064 6
4033.2.co \(\chi_{4033}(4, \cdot)\) n/a 2076 6
4033.2.cp \(\chi_{4033}(284, \cdot)\) n/a 2088 6
4033.2.cq \(\chi_{4033}(638, \cdot)\) n/a 2088 6
4033.2.cr \(\chi_{4033}(289, \cdot)\) n/a 2076 6
4033.2.cs \(\chi_{4033}(136, \cdot)\) n/a 2088 6
4033.2.ct \(\chi_{4033}(71, \cdot)\) n/a 2088 6
4033.2.cu \(\chi_{4033}(437, \cdot)\) n/a 2052 6
4033.2.cv \(\chi_{4033}(108, \cdot)\) n/a 2088 6
4033.2.cw \(\chi_{4033}(1027, \cdot)\) n/a 2076 6
4033.2.cx \(\chi_{4033}(173, \cdot)\) n/a 2076 6
4033.2.cy \(\chi_{4033}(152, \cdot)\) n/a 2076 6
4033.2.cz \(\chi_{4033}(300, \cdot)\) n/a 2076 6
4033.2.da \(\chi_{4033}(361, \cdot)\) n/a 2076 6
4033.2.db \(\chi_{4033}(736, \cdot)\) n/a 2088 6
4033.2.dc \(\chi_{4033}(1483, \cdot)\) n/a 2088 6
4033.2.dd \(\chi_{4033}(588, \cdot)\) n/a 2088 6
4033.2.de \(\chi_{4033}(583, \cdot)\) n/a 2088 6
4033.2.df \(\chi_{4033}(432, \cdot)\) n/a 2088 6
4033.2.dg \(\chi_{4033}(1052, \cdot)\) n/a 2088 6
4033.2.dh \(\chi_{4033}(46, \cdot)\) n/a 2088 6
4033.2.di \(\chi_{4033}(1135, \cdot)\) n/a 2088 6
4033.2.dj \(\chi_{4033}(155, \cdot)\) n/a 2088 6
4033.2.dk \(\chi_{4033}(263, \cdot)\) n/a 2088 6
4033.2.dl \(\chi_{4033}(326, \cdot)\) n/a 2076 6
4033.2.dm \(\chi_{4033}(34, \cdot)\) n/a 2088 6
4033.2.dn \(\chi_{4033}(1390, \cdot)\) n/a 2076 6
4033.2.do \(\chi_{4033}(354, \cdot)\) n/a 2088 6
4033.2.dp \(\chi_{4033}(323, \cdot)\) n/a 2076 6
4033.2.dq \(\chi_{4033}(1342, \cdot)\) n/a 2076 6
4033.2.dr \(\chi_{4033}(1074, \cdot)\) n/a 1980 6
4033.2.ds \(\chi_{4033}(147, \cdot)\) n/a 2076 6
4033.2.dt \(\chi_{4033}(915, \cdot)\) n/a 2064 6
4033.2.du \(\chi_{4033}(9, \cdot)\) n/a 6210 18
4033.2.dv \(\chi_{4033}(441, \cdot)\) n/a 6210 18
4033.2.dw \(\chi_{4033}(118, \cdot)\) n/a 6210 18
4033.2.dx \(\chi_{4033}(182, \cdot)\) n/a 6210 18
4033.2.dy \(\chi_{4033}(26, \cdot)\) n/a 6228 18
4033.2.dz \(\chi_{4033}(618, \cdot)\) n/a 6228 18
4033.2.ea \(\chi_{4033}(112, \cdot)\) n/a 5940 18
4033.2.eb \(\chi_{4033}(144, \cdot)\) n/a 6210 18
4033.2.ec \(\chi_{4033}(7, \cdot)\) n/a 6210 18
4033.2.ed \(\chi_{4033}(310, \cdot)\) n/a 4140 12
4033.2.ee \(\chi_{4033}(413, \cdot)\) n/a 4140 12
4033.2.ef \(\chi_{4033}(547, \cdot)\) n/a 4140 12
4033.2.eg \(\chi_{4033}(795, \cdot)\) n/a 4164 12
4033.2.ej \(\chi_{4033}(237, \cdot)\) n/a 4164 12
4033.2.es \(\chi_{4033}(76, \cdot)\) n/a 4164 12
4033.2.et \(\chi_{4033}(335, \cdot)\) n/a 4164 12
4033.2.eu \(\chi_{4033}(368, \cdot)\) n/a 4164 12
4033.2.ev \(\chi_{4033}(19, \cdot)\) n/a 4164 12
4033.2.ew \(\chi_{4033}(459, \cdot)\) n/a 4164 12
4033.2.ex \(\chi_{4033}(346, \cdot)\) n/a 4164 12
4033.2.fw \(\chi_{4033}(235, \cdot)\) n/a 4164 12
4033.2.fx \(\chi_{4033}(350, \cdot)\) n/a 4164 12
4033.2.fy \(\chi_{4033}(54, \cdot)\) n/a 4164 12
4033.2.fz \(\chi_{4033}(150, \cdot)\) n/a 4164 12
4033.2.ga \(\chi_{4033}(553, \cdot)\) n/a 4164 12
4033.2.gb \(\chi_{4033}(294, \cdot)\) n/a 4164 12
4033.2.gk \(\chi_{4033}(468, \cdot)\) n/a 4164 12
4033.2.gn \(\chi_{4033}(17, \cdot)\) n/a 4164 12
4033.2.go \(\chi_{4033}(2, \cdot)\) n/a 4164 12
4033.2.gr \(\chi_{4033}(55, \cdot)\) n/a 4164 12
4033.2.gu \(\chi_{4033}(23, \cdot)\) n/a 4140 12
4033.2.gv \(\chi_{4033}(216, \cdot)\) n/a 4140 12
4033.2.gw \(\chi_{4033}(199, \cdot)\) n/a 4140 12
4033.2.gx \(\chi_{4033}(645, \cdot)\) n/a 6246 18
4033.2.gy \(\chi_{4033}(25, \cdot)\) n/a 6246 18
4033.2.gz \(\chi_{4033}(169, \cdot)\) n/a 6210 18
4033.2.ha \(\chi_{4033}(215, \cdot)\) n/a 6210 18
4033.2.hb \(\chi_{4033}(324, \cdot)\) n/a 6210 18
4033.2.hc \(\chi_{4033}(102, \cdot)\) n/a 6210 18
4033.2.hd \(\chi_{4033}(36, \cdot)\) n/a 6228 18
4033.2.he \(\chi_{4033}(138, \cdot)\) n/a 6228 18
4033.2.hf \(\chi_{4033}(249, \cdot)\) n/a 6228 18
4033.2.hg \(\chi_{4033}(28, \cdot)\) n/a 6210 18
4033.2.hh \(\chi_{4033}(336, \cdot)\) n/a 6246 18
4033.2.hi \(\chi_{4033}(12, \cdot)\) n/a 6246 18
4033.2.hj \(\chi_{4033}(519, \cdot)\) n/a 5940 18
4033.2.hk \(\chi_{4033}(48, \cdot)\) n/a 6264 18
4033.2.hl \(\chi_{4033}(233, \cdot)\) n/a 6264 18
4033.2.hm \(\chi_{4033}(100, \cdot)\) n/a 6264 18
4033.2.hn \(\chi_{4033}(84, \cdot)\) n/a 6264 18
4033.2.ho \(\chi_{4033}(73, \cdot)\) n/a 6264 18
4033.2.hp \(\chi_{4033}(78, \cdot)\) n/a 6246 18
4033.2.hq \(\chi_{4033}(206, \cdot)\) n/a 6246 18
4033.2.hr \(\chi_{4033}(145, \cdot)\) n/a 6246 18
4033.2.hs \(\chi_{4033}(83, \cdot)\) n/a 6246 18
4033.2.ht \(\chi_{4033}(192, \cdot)\) n/a 6246 18
4033.2.hu \(\chi_{4033}(21, \cdot)\) n/a 6246 18
4033.2.hv \(\chi_{4033}(197, \cdot)\) n/a 6246 18
4033.2.hw \(\chi_{4033}(3, \cdot)\) n/a 6246 18
4033.2.hx \(\chi_{4033}(104, \cdot)\) n/a 6210 18
4033.2.hy \(\chi_{4033}(24, \cdot)\) n/a 12456 36
4033.2.hz \(\chi_{4033}(56, \cdot)\) n/a 12456 36
4033.2.ia \(\chi_{4033}(13, \cdot)\) n/a 12456 36
4033.2.if \(\chi_{4033}(52, \cdot)\) n/a 12456 36
4033.2.ig \(\chi_{4033}(18, \cdot)\) n/a 12456 36
4033.2.ih \(\chi_{4033}(14, \cdot)\) n/a 12492 36
4033.2.ii \(\chi_{4033}(171, \cdot)\) n/a 12492 36
4033.2.ij \(\chi_{4033}(179, \cdot)\) n/a 12492 36
4033.2.ik \(\chi_{4033}(133, \cdot)\) n/a 12456 36
4033.2.jj \(\chi_{4033}(57, \cdot)\) n/a 12456 36
4033.2.jk \(\chi_{4033}(156, \cdot)\) n/a 12492 36
4033.2.jl \(\chi_{4033}(6, \cdot)\) n/a 12492 36
4033.2.jm \(\chi_{4033}(103, \cdot)\) n/a 12492 36
4033.2.jn \(\chi_{4033}(42, \cdot)\) n/a 12456 36
4033.2.jo \(\chi_{4033}(153, \cdot)\) n/a 12456 36
4033.2.jx \(\chi_{4033}(39, \cdot)\) n/a 12456 36
4033.2.jy \(\chi_{4033}(146, \cdot)\) n/a 12456 36
4033.2.jz \(\chi_{4033}(69, \cdot)\) n/a 12456 36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4033))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4033)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(109))\)\(^{\oplus 2}\)