# Properties

 Label 4030.2 Level 4030 Weight 2 Dimension 145769 Nonzero newspaces 100 Sturm bound 1.93536e+06

## 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

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