Properties

Label 4030.2
Level 4030
Weight 2
Dimension 145769
Nonzero newspaces 100
Sturm bound 1935360

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Defining parameters

Level: \( N \) = \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 100 \)
Sturm bound: \(1935360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4030))\).

Total New Old
Modular forms 489600 145769 343831
Cusp forms 478081 145769 332312
Eisenstein series 11519 0 11519

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4030))\)

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
4030.2.a \(\chi_{4030}(1, \cdot)\) 4030.2.a.a 1 1
4030.2.a.b 2
4030.2.a.c 6
4030.2.a.d 6
4030.2.a.e 6
4030.2.a.f 6
4030.2.a.g 6
4030.2.a.h 7
4030.2.a.i 7
4030.2.a.j 7
4030.2.a.k 8
4030.2.a.l 8
4030.2.a.m 8
4030.2.a.n 8
4030.2.a.o 8
4030.2.a.p 9
4030.2.a.q 9
4030.2.a.r 9
4030.2.c \(\chi_{4030}(2419, \cdot)\) n/a 180 1
4030.2.d \(\chi_{4030}(2729, \cdot)\) n/a 208 1
4030.2.f \(\chi_{4030}(311, \cdot)\) n/a 140 1
4030.2.i \(\chi_{4030}(521, \cdot)\) n/a 256 2
4030.2.j \(\chi_{4030}(2791, \cdot)\) n/a 280 2
4030.2.k \(\chi_{4030}(191, \cdot)\) n/a 296 2
4030.2.l \(\chi_{4030}(1121, \cdot)\) n/a 296 2
4030.2.m \(\chi_{4030}(681, \cdot)\) n/a 288 2
4030.2.o \(\chi_{4030}(187, \cdot)\) n/a 420 2
4030.2.q \(\chi_{4030}(2107, \cdot)\) n/a 384 2
4030.2.t \(\chi_{4030}(2417, \cdot)\) n/a 448 2
4030.2.u \(\chi_{4030}(993, \cdot)\) n/a 420 2
4030.2.w \(\chi_{4030}(619, \cdot)\) n/a 448 2
4030.2.y \(\chi_{4030}(2081, \cdot)\) n/a 512 4
4030.2.ba \(\chi_{4030}(439, \cdot)\) n/a 448 2
4030.2.bb \(\chi_{4030}(1699, \cdot)\) n/a 448 2
4030.2.bd \(\chi_{4030}(1141, \cdot)\) n/a 296 2
4030.2.bj \(\chi_{4030}(621, \cdot)\) n/a 280 2
4030.2.bk \(\chi_{4030}(831, \cdot)\) n/a 304 2
4030.2.bn \(\chi_{4030}(2609, \cdot)\) n/a 448 2
4030.2.bq \(\chi_{4030}(3039, \cdot)\) n/a 416 2
4030.2.br \(\chi_{4030}(129, \cdot)\) n/a 448 2
4030.2.bs \(\chi_{4030}(2939, \cdot)\) n/a 384 2
4030.2.bt \(\chi_{4030}(1179, \cdot)\) n/a 424 2
4030.2.bw \(\chi_{4030}(1369, \cdot)\) n/a 448 2
4030.2.ca \(\chi_{4030}(2051, \cdot)\) n/a 296 2
4030.2.cd \(\chi_{4030}(2391, \cdot)\) n/a 576 4
4030.2.cf \(\chi_{4030}(779, \cdot)\) n/a 896 4
4030.2.cg \(\chi_{4030}(469, \cdot)\) n/a 768 4
4030.2.cj \(\chi_{4030}(1731, \cdot)\) n/a 592 4
4030.2.cl \(\chi_{4030}(1029, \cdot)\) n/a 896 4
4030.2.cm \(\chi_{4030}(99, \cdot)\) n/a 896 4
4030.2.cp \(\chi_{4030}(929, \cdot)\) n/a 896 4
4030.2.cr \(\chi_{4030}(583, \cdot)\) n/a 896 4
4030.2.ct \(\chi_{4030}(397, \cdot)\) n/a 896 4
4030.2.cu \(\chi_{4030}(1513, \cdot)\) n/a 896 4
4030.2.cw \(\chi_{4030}(2853, \cdot)\) n/a 840 4
4030.2.cy \(\chi_{4030}(1297, \cdot)\) n/a 896 4
4030.2.db \(\chi_{4030}(347, \cdot)\) n/a 896 4
4030.2.dc \(\chi_{4030}(243, \cdot)\) n/a 896 4
4030.2.de \(\chi_{4030}(987, \cdot)\) n/a 896 4
4030.2.df \(\chi_{4030}(433, \cdot)\) n/a 896 4
4030.2.dk \(\chi_{4030}(867, \cdot)\) n/a 896 4
4030.2.dl \(\chi_{4030}(677, \cdot)\) n/a 768 4
4030.2.dn \(\chi_{4030}(2207, \cdot)\) n/a 896 4
4030.2.dp \(\chi_{4030}(67, \cdot)\) n/a 896 4
4030.2.dq \(\chi_{4030}(707, \cdot)\) n/a 896 4
4030.2.ds \(\chi_{4030}(63, \cdot)\) n/a 840 4
4030.2.dv \(\chi_{4030}(253, \cdot)\) n/a 896 4
4030.2.dx \(\chi_{4030}(371, \cdot)\) n/a 608 4
4030.2.dy \(\chi_{4030}(161, \cdot)\) n/a 608 4
4030.2.eb \(\chi_{4030}(1111, \cdot)\) n/a 592 4
4030.2.ed \(\chi_{4030}(119, \cdot)\) n/a 896 4
4030.2.ee \(\chi_{4030}(731, \cdot)\) n/a 1184 8
4030.2.ef \(\chi_{4030}(81, \cdot)\) n/a 1184 8
4030.2.eg \(\chi_{4030}(841, \cdot)\) n/a 1216 8
4030.2.eh \(\chi_{4030}(131, \cdot)\) n/a 1024 8
4030.2.ej \(\chi_{4030}(759, \cdot)\) n/a 1792 8
4030.2.el \(\chi_{4030}(47, \cdot)\) n/a 1792 8
4030.2.em \(\chi_{4030}(77, \cdot)\) n/a 1792 8
4030.2.ep \(\chi_{4030}(27, \cdot)\) n/a 1536 8
4030.2.er \(\chi_{4030}(593, \cdot)\) n/a 1792 8
4030.2.et \(\chi_{4030}(151, \cdot)\) n/a 1152 8
4030.2.eu \(\chi_{4030}(121, \cdot)\) n/a 1184 8
4030.2.ey \(\chi_{4030}(979, \cdot)\) n/a 1792 8
4030.2.fb \(\chi_{4030}(159, \cdot)\) n/a 1792 8
4030.2.fc \(\chi_{4030}(599, \cdot)\) n/a 1536 8
4030.2.fd \(\chi_{4030}(909, \cdot)\) n/a 1792 8
4030.2.fe \(\chi_{4030}(1089, \cdot)\) n/a 1792 8
4030.2.fh \(\chi_{4030}(9, \cdot)\) n/a 1792 8
4030.2.fk \(\chi_{4030}(51, \cdot)\) n/a 1216 8
4030.2.fl \(\chi_{4030}(101, \cdot)\) n/a 1216 8
4030.2.fr \(\chi_{4030}(231, \cdot)\) n/a 1184 8
4030.2.ft \(\chi_{4030}(289, \cdot)\) n/a 1792 8
4030.2.fu \(\chi_{4030}(49, \cdot)\) n/a 1792 8
4030.2.fw \(\chi_{4030}(189, \cdot)\) n/a 3584 16
4030.2.fy \(\chi_{4030}(141, \cdot)\) n/a 2368 16
4030.2.gb \(\chi_{4030}(21, \cdot)\) n/a 2432 16
4030.2.gc \(\chi_{4030}(201, \cdot)\) n/a 2432 16
4030.2.ge \(\chi_{4030}(917, \cdot)\) n/a 3584 16
4030.2.gh \(\chi_{4030}(33, \cdot)\) n/a 3584 16
4030.2.gj \(\chi_{4030}(317, \cdot)\) n/a 3584 16
4030.2.gk \(\chi_{4030}(293, \cdot)\) n/a 3584 16
4030.2.gm \(\chi_{4030}(127, \cdot)\) n/a 3584 16
4030.2.go \(\chi_{4030}(53, \cdot)\) n/a 3072 16
4030.2.gp \(\chi_{4030}(263, \cdot)\) n/a 3584 16
4030.2.gu \(\chi_{4030}(23, \cdot)\) n/a 3584 16
4030.2.gv \(\chi_{4030}(207, \cdot)\) n/a 3584 16
4030.2.gx \(\chi_{4030}(3, \cdot)\) n/a 3584 16
4030.2.gy \(\chi_{4030}(393, \cdot)\) n/a 3584 16
4030.2.hb \(\chi_{4030}(17, \cdot)\) n/a 3584 16
4030.2.hd \(\chi_{4030}(903, \cdot)\) n/a 3584 16
4030.2.hf \(\chi_{4030}(307, \cdot)\) n/a 3584 16
4030.2.hg \(\chi_{4030}(7, \cdot)\) n/a 3584 16
4030.2.hi \(\chi_{4030}(193, \cdot)\) n/a 3584 16
4030.2.hk \(\chi_{4030}(89, \cdot)\) n/a 3584 16
4030.2.hn \(\chi_{4030}(229, \cdot)\) n/a 3584 16
4030.2.ho \(\chi_{4030}(579, \cdot)\) n/a 3584 16
4030.2.hq \(\chi_{4030}(11, \cdot)\) n/a 2368 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4030))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4030)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(403))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(806))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2015))\)\(^{\oplus 2}\)