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Properties

Label 4440.2
Level 4440
Weight 2
Dimension 202012
Nonzero newspaces 90
Sturm bound 2101248

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Defining parameters

Level: \( N \) = \( 4440 = 2^{3} \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 90 \)
Sturm bound: \(2101248\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4440))\).

Total New Old
Modular forms 532224 203692 328532
Cusp forms 518401 202012 316389
Eisenstein series 13823 1680 12143

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4440))\)

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
4440.2.a \(\chi_{4440}(1, \cdot)\) 4440.2.a.a 1 1
4440.2.a.b 1
4440.2.a.c 1
4440.2.a.d 1
4440.2.a.e 1
4440.2.a.f 1
4440.2.a.g 1
4440.2.a.h 1
4440.2.a.i 1
4440.2.a.j 2
4440.2.a.k 2
4440.2.a.l 2
4440.2.a.m 2
4440.2.a.n 2
4440.2.a.o 3
4440.2.a.p 3
4440.2.a.q 3
4440.2.a.r 3
4440.2.a.s 3
4440.2.a.t 4
4440.2.a.u 4
4440.2.a.v 4
4440.2.a.w 5
4440.2.a.x 5
4440.2.a.y 5
4440.2.a.z 5
4440.2.a.ba 6
4440.2.c \(\chi_{4440}(371, \cdot)\) n/a 576 1
4440.2.e \(\chi_{4440}(4069, \cdot)\) n/a 456 1
4440.2.f \(\chi_{4440}(3109, \cdot)\) n/a 432 1
4440.2.h \(\chi_{4440}(1331, \cdot)\) n/a 608 1
4440.2.k \(\chi_{4440}(889, \cdot)\) n/a 108 1
4440.2.m \(\chi_{4440}(3551, \cdot)\) None 0 1
4440.2.n \(\chi_{4440}(2591, \cdot)\) None 0 1
4440.2.p \(\chi_{4440}(1849, \cdot)\) n/a 116 1
4440.2.r \(\chi_{4440}(2219, \cdot)\) n/a 904 1
4440.2.t \(\chi_{4440}(2221, \cdot)\) n/a 288 1
4440.2.w \(\chi_{4440}(3181, \cdot)\) n/a 304 1
4440.2.y \(\chi_{4440}(1259, \cdot)\) n/a 864 1
4440.2.z \(\chi_{4440}(961, \cdot)\) 4440.2.z.a 2 1
4440.2.z.b 2
4440.2.z.c 2
4440.2.z.d 16
4440.2.z.e 16
4440.2.z.f 18
4440.2.z.g 20
4440.2.bb \(\chi_{4440}(3479, \cdot)\) None 0 1
4440.2.be \(\chi_{4440}(4439, \cdot)\) None 0 1
4440.2.bg \(\chi_{4440}(121, \cdot)\) n/a 152 2
4440.2.bh \(\chi_{4440}(931, \cdot)\) n/a 608 2
4440.2.bj \(\chi_{4440}(2189, \cdot)\) n/a 1808 2
4440.2.bm \(\chi_{4440}(31, \cdot)\) None 0 2
4440.2.bo \(\chi_{4440}(1289, \cdot)\) n/a 456 2
4440.2.bq \(\chi_{4440}(3287, \cdot)\) None 0 2
4440.2.br \(\chi_{4440}(697, \cdot)\) n/a 228 2
4440.2.bv \(\chi_{4440}(593, \cdot)\) n/a 432 2
4440.2.bw \(\chi_{4440}(1183, \cdot)\) None 0 2
4440.2.bx \(\chi_{4440}(1553, \cdot)\) n/a 456 2
4440.2.by \(\chi_{4440}(223, \cdot)\) None 0 2
4440.2.cb \(\chi_{4440}(2473, \cdot)\) n/a 228 2
4440.2.ce \(\chi_{4440}(623, \cdot)\) None 0 2
4440.2.cf \(\chi_{4440}(253, \cdot)\) n/a 912 2
4440.2.ci \(\chi_{4440}(2843, \cdot)\) n/a 1808 2
4440.2.cl \(\chi_{4440}(1997, \cdot)\) n/a 1808 2
4440.2.cm \(\chi_{4440}(667, \cdot)\) n/a 864 2
4440.2.cn \(\chi_{4440}(1037, \cdot)\) n/a 1728 2
4440.2.co \(\chi_{4440}(1627, \cdot)\) n/a 912 2
4440.2.cs \(\chi_{4440}(1067, \cdot)\) n/a 1808 2
4440.2.ct \(\chi_{4440}(2917, \cdot)\) n/a 912 2
4440.2.cw \(\chi_{4440}(1819, \cdot)\) n/a 912 2
4440.2.cy \(\chi_{4440}(1301, \cdot)\) n/a 1216 2
4440.2.cz \(\chi_{4440}(919, \cdot)\) None 0 2
4440.2.db \(\chi_{4440}(401, \cdot)\) n/a 304 2
4440.2.de \(\chi_{4440}(1379, \cdot)\) n/a 1808 2
4440.2.dg \(\chi_{4440}(1861, \cdot)\) n/a 608 2
4440.2.dh \(\chi_{4440}(2341, \cdot)\) n/a 608 2
4440.2.dj \(\chi_{4440}(899, \cdot)\) n/a 1808 2
4440.2.dn \(\chi_{4440}(3119, \cdot)\) None 0 2
4440.2.do \(\chi_{4440}(359, \cdot)\) None 0 2
4440.2.dq \(\chi_{4440}(841, \cdot)\) n/a 152 2
4440.2.ds \(\chi_{4440}(11, \cdot)\) n/a 1216 2
4440.2.du \(\chi_{4440}(3229, \cdot)\) n/a 912 2
4440.2.dx \(\chi_{4440}(2749, \cdot)\) n/a 912 2
4440.2.dz \(\chi_{4440}(491, \cdot)\) n/a 1216 2
4440.2.ea \(\chi_{4440}(529, \cdot)\) n/a 232 2
4440.2.ec \(\chi_{4440}(2711, \cdot)\) None 0 2
4440.2.ef \(\chi_{4440}(2231, \cdot)\) None 0 2
4440.2.eh \(\chi_{4440}(1009, \cdot)\) n/a 224 2
4440.2.ei \(\chi_{4440}(601, \cdot)\) n/a 456 6
4440.2.ej \(\chi_{4440}(341, \cdot)\) n/a 2432 4
4440.2.el \(\chi_{4440}(859, \cdot)\) n/a 1824 4
4440.2.eo \(\chi_{4440}(1361, \cdot)\) n/a 608 4
4440.2.eq \(\chi_{4440}(199, \cdot)\) None 0 4
4440.2.er \(\chi_{4440}(1007, \cdot)\) None 0 4
4440.2.eu \(\chi_{4440}(97, \cdot)\) n/a 456 4
4440.2.ev \(\chi_{4440}(343, \cdot)\) None 0 4
4440.2.ew \(\chi_{4440}(233, \cdot)\) n/a 912 4
4440.2.fb \(\chi_{4440}(1063, \cdot)\) None 0 4
4440.2.fc \(\chi_{4440}(137, \cdot)\) n/a 912 4
4440.2.fe \(\chi_{4440}(193, \cdot)\) n/a 456 4
4440.2.ff \(\chi_{4440}(23, \cdot)\) None 0 4
4440.2.fi \(\chi_{4440}(2197, \cdot)\) n/a 1824 4
4440.2.fj \(\chi_{4440}(347, \cdot)\) n/a 3616 4
4440.2.fl \(\chi_{4440}(307, \cdot)\) n/a 1824 4
4440.2.fm \(\chi_{4440}(1157, \cdot)\) n/a 3616 4
4440.2.fr \(\chi_{4440}(787, \cdot)\) n/a 1824 4
4440.2.fs \(\chi_{4440}(677, \cdot)\) n/a 3616 4
4440.2.ft \(\chi_{4440}(467, \cdot)\) n/a 3616 4
4440.2.fw \(\chi_{4440}(637, \cdot)\) n/a 1824 4
4440.2.fy \(\chi_{4440}(29, \cdot)\) n/a 3616 4
4440.2.ga \(\chi_{4440}(1531, \cdot)\) n/a 1216 4
4440.2.gb \(\chi_{4440}(569, \cdot)\) n/a 912 4
4440.2.gd \(\chi_{4440}(991, \cdot)\) None 0 4
4440.2.gf \(\chi_{4440}(839, \cdot)\) None 0 6
4440.2.gj \(\chi_{4440}(71, \cdot)\) None 0 6
4440.2.gk \(\chi_{4440}(169, \cdot)\) n/a 696 6
4440.2.gm \(\chi_{4440}(49, \cdot)\) n/a 672 6
4440.2.gp \(\chi_{4440}(1151, \cdot)\) None 0 6
4440.2.gr \(\chi_{4440}(361, \cdot)\) n/a 456 6
4440.2.gs \(\chi_{4440}(599, \cdot)\) None 0 6
4440.2.gu \(\chi_{4440}(469, \cdot)\) n/a 2736 6
4440.2.gx \(\chi_{4440}(971, \cdot)\) n/a 3648 6
4440.2.gz \(\chi_{4440}(181, \cdot)\) n/a 1824 6
4440.2.ha \(\chi_{4440}(299, \cdot)\) n/a 5424 6
4440.2.hc \(\chi_{4440}(419, \cdot)\) n/a 5424 6
4440.2.hf \(\chi_{4440}(781, \cdot)\) n/a 1824 6
4440.2.hh \(\chi_{4440}(731, \cdot)\) n/a 3648 6
4440.2.hi \(\chi_{4440}(229, \cdot)\) n/a 2736 6
4440.2.hl \(\chi_{4440}(757, \cdot)\) n/a 5472 12
4440.2.hn \(\chi_{4440}(203, \cdot)\) n/a 10848 12
4440.2.hp \(\chi_{4440}(77, \cdot)\) n/a 10848 12
4440.2.hq \(\chi_{4440}(403, \cdot)\) n/a 5472 12
4440.2.hu \(\chi_{4440}(89, \cdot)\) n/a 2736 12
4440.2.hv \(\chi_{4440}(79, \cdot)\) None 0 12
4440.2.hw \(\chi_{4440}(161, \cdot)\) n/a 1824 12
4440.2.hx \(\chi_{4440}(631, \cdot)\) None 0 12
4440.2.ia \(\chi_{4440}(53, \cdot)\) n/a 10848 12
4440.2.id \(\chi_{4440}(67, \cdot)\) n/a 5472 12
4440.2.ie \(\chi_{4440}(587, \cdot)\) n/a 10848 12
4440.2.ig \(\chi_{4440}(13, \cdot)\) n/a 5472 12
4440.2.ij \(\chi_{4440}(143, \cdot)\) None 0 12
4440.2.il \(\chi_{4440}(457, \cdot)\) n/a 1368 12
4440.2.in \(\chi_{4440}(247, \cdot)\) None 0 12
4440.2.io \(\chi_{4440}(377, \cdot)\) n/a 2736 12
4440.2.is \(\chi_{4440}(19, \cdot)\) n/a 5472 12
4440.2.it \(\chi_{4440}(389, \cdot)\) n/a 10848 12
4440.2.iu \(\chi_{4440}(91, \cdot)\) n/a 3648 12
4440.2.iv \(\chi_{4440}(461, \cdot)\) n/a 7296 12
4440.2.iy \(\chi_{4440}(7, \cdot)\) None 0 12
4440.2.jb \(\chi_{4440}(617, \cdot)\) n/a 2736 12
4440.2.jc \(\chi_{4440}(217, \cdot)\) n/a 1368 12
4440.2.je \(\chi_{4440}(383, \cdot)\) None 0 12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4440))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4440)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(370))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(444))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(555))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(740))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(888))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1110))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2220))\)\(^{\oplus 2}\)