# Properties

 Label 4033.2 Level 4033 Weight 2 Dimension 672309 Nonzero newspaces 156 Sturm bound 2.70864e+06

# Learn more about

## 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

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