# Properties

 Label 6025.2 Level 6025 Weight 2 Dimension 1.33332e+06 Nonzero newspaces 140 Sturm bound 5.808e+06

## Defining parameters

 Level: $$N$$ = $$6025 = 5^{2} \cdot 241$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$140$$ Sturm bound: $$5808000$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6025))$$.

Total New Old
Modular forms 1458720 1343114 115606
Cusp forms 1445281 1333316 111965
Eisenstein series 13439 9798 3641

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6025))$$

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
6025.2.a $$\chi_{6025}(1, \cdot)$$ 6025.2.a.a 2 1
6025.2.a.b 2
6025.2.a.c 2
6025.2.a.d 2
6025.2.a.e 5
6025.2.a.f 7
6025.2.a.g 11
6025.2.a.h 12
6025.2.a.i 15
6025.2.a.j 25
6025.2.a.k 25
6025.2.a.l 40
6025.2.a.m 40
6025.2.a.n 40
6025.2.a.o 40
6025.2.a.p 46
6025.2.a.q 66
6025.2.b $$\chi_{6025}(724, \cdot)$$ n/a 360 1
6025.2.c $$\chi_{6025}(6024, \cdot)$$ n/a 360 1
6025.2.d $$\chi_{6025}(5301, \cdot)$$ n/a 380 1
6025.2.e $$\chi_{6025}(2876, \cdot)$$ n/a 762 2
6025.2.f $$\chi_{6025}(1751, \cdot)$$ n/a 760 2
6025.2.k $$\chi_{6025}(2474, \cdot)$$ n/a 720 2
6025.2.l $$\chi_{6025}(1296, \cdot)$$ n/a 2408 4
6025.2.m $$\chi_{6025}(821, \cdot)$$ n/a 2408 4
6025.2.n $$\chi_{6025}(1206, \cdot)$$ n/a 2400 4
6025.2.o $$\chi_{6025}(91, \cdot)$$ n/a 2408 4
6025.2.p $$\chi_{6025}(2856, \cdot)$$ n/a 2408 4
6025.2.q $$\chi_{6025}(1051, \cdot)$$ n/a 1520 4
6025.2.r $$\chi_{6025}(226, \cdot)$$ n/a 762 2
6025.2.s $$\chi_{6025}(949, \cdot)$$ n/a 720 2
6025.2.t $$\chi_{6025}(3599, \cdot)$$ n/a 720 2
6025.2.v $$\chi_{6025}(249, \cdot)$$ n/a 1448 4
6025.2.w $$\chi_{6025}(1476, \cdot)$$ n/a 1516 4
6025.2.y $$\chi_{6025}(3524, \cdot)$$ n/a 1440 4
6025.2.z $$\chi_{6025}(1774, \cdot)$$ n/a 1440 4
6025.2.ba $$\chi_{6025}(481, \cdot)$$ n/a 2408 4
6025.2.bb $$\chi_{6025}(36, \cdot)$$ n/a 2408 4
6025.2.bc $$\chi_{6025}(636, \cdot)$$ n/a 2408 4
6025.2.bd $$\chi_{6025}(391, \cdot)$$ n/a 2408 4
6025.2.be $$\chi_{6025}(866, \cdot)$$ n/a 2408 4
6025.2.bf $$\chi_{6025}(154, \cdot)$$ n/a 2416 4
6025.2.bg $$\chi_{6025}(814, \cdot)$$ n/a 2416 4
6025.2.bh $$\chi_{6025}(1929, \cdot)$$ n/a 2400 4
6025.2.bi $$\chi_{6025}(759, \cdot)$$ n/a 2416 4
6025.2.bj $$\chi_{6025}(1359, \cdot)$$ n/a 2416 4
6025.2.bk $$\chi_{6025}(2019, \cdot)$$ n/a 2416 4
6025.2.bl $$\chi_{6025}(1544, \cdot)$$ n/a 2416 4
6025.2.bm $$\chi_{6025}(1204, \cdot)$$ n/a 2416 4
6025.2.bn $$\chi_{6025}(1589, \cdot)$$ n/a 2416 4
6025.2.bo $$\chi_{6025}(339, \cdot)$$ n/a 2416 4
6025.2.bp $$\chi_{6025}(2801, \cdot)$$ n/a 1520 4
6025.2.bq $$\chi_{6025}(1024, \cdot)$$ n/a 1440 4
6025.2.bv $$\chi_{6025}(301, \cdot)$$ n/a 1524 4
6025.2.bw $$\chi_{6025}(401, \cdot)$$ n/a 3048 8
6025.2.bx $$\chi_{6025}(906, \cdot)$$ n/a 4816 8
6025.2.by $$\chi_{6025}(256, \cdot)$$ n/a 4816 8
6025.2.bz $$\chi_{6025}(231, \cdot)$$ n/a 4816 8
6025.2.ca $$\chi_{6025}(341, \cdot)$$ n/a 4816 8
6025.2.cb $$\chi_{6025}(1711, \cdot)$$ n/a 4816 8
6025.2.cc $$\chi_{6025}(1557, \cdot)$$ n/a 2888 8
6025.2.cd $$\chi_{6025}(593, \cdot)$$ n/a 2888 8
6025.2.cg $$\chi_{6025}(201, \cdot)$$ n/a 3040 8
6025.2.ch $$\chi_{6025}(1004, \cdot)$$ n/a 4832 8
6025.2.ci $$\chi_{6025}(64, \cdot)$$ n/a 4832 8
6025.2.cj $$\chi_{6025}(729, \cdot)$$ n/a 4832 8
6025.2.ck $$\chi_{6025}(829, \cdot)$$ n/a 4832 8
6025.2.cl $$\chi_{6025}(1934, \cdot)$$ n/a 4832 8
6025.2.dk $$\chi_{6025}(106, \cdot)$$ n/a 4816 8
6025.2.dl $$\chi_{6025}(281, \cdot)$$ n/a 4816 8
6025.2.dm $$\chi_{6025}(546, \cdot)$$ n/a 4816 8
6025.2.dn $$\chi_{6025}(6, \cdot)$$ n/a 4816 8
6025.2.do $$\chi_{6025}(1211, \cdot)$$ n/a 4816 8
6025.2.dp $$\chi_{6025}(924, \cdot)$$ n/a 2880 8
6025.2.dr $$\chi_{6025}(851, \cdot)$$ n/a 3040 8
6025.2.ds $$\chi_{6025}(1574, \cdot)$$ n/a 2896 8
6025.2.du $$\chi_{6025}(251, \cdot)$$ n/a 3048 8
6025.2.dv $$\chi_{6025}(739, \cdot)$$ n/a 4832 8
6025.2.dw $$\chi_{6025}(119, \cdot)$$ n/a 4832 8
6025.2.dx $$\chi_{6025}(1064, \cdot)$$ n/a 4832 8
6025.2.dy $$\chi_{6025}(804, \cdot)$$ n/a 4832 8
6025.2.dz $$\chi_{6025}(604, \cdot)$$ n/a 4832 8
6025.2.ea $$\chi_{6025}(979, \cdot)$$ n/a 4832 8
6025.2.eb $$\chi_{6025}(1629, \cdot)$$ n/a 4832 8
6025.2.ec $$\chi_{6025}(629, \cdot)$$ n/a 4832 8
6025.2.ed $$\chi_{6025}(54, \cdot)$$ n/a 4832 8
6025.2.ee $$\chi_{6025}(1809, \cdot)$$ n/a 4832 8
6025.2.ef $$\chi_{6025}(781, \cdot)$$ n/a 4816 8
6025.2.eg $$\chi_{6025}(81, \cdot)$$ n/a 4816 8
6025.2.eh $$\chi_{6025}(141, \cdot)$$ n/a 4816 8
6025.2.ei $$\chi_{6025}(16, \cdot)$$ n/a 4816 8
6025.2.ej $$\chi_{6025}(1086, \cdot)$$ n/a 4816 8
6025.2.ek $$\chi_{6025}(24, \cdot)$$ n/a 2880 8
6025.2.el $$\chi_{6025}(299, \cdot)$$ n/a 2880 8
6025.2.es $$\chi_{6025}(676, \cdot)$$ n/a 6064 16
6025.2.et $$\chi_{6025}(1399, \cdot)$$ n/a 5792 16
6025.2.eu $$\chi_{6025}(61, \cdot)$$ n/a 9664 16
6025.2.ev $$\chi_{6025}(289, \cdot)$$ n/a 9632 16
6025.2.ew $$\chi_{6025}(236, \cdot)$$ n/a 9664 16
6025.2.ex $$\chi_{6025}(194, \cdot)$$ n/a 9632 16
6025.2.ey $$\chi_{6025}(41, \cdot)$$ n/a 9664 16
6025.2.ez $$\chi_{6025}(79, \cdot)$$ n/a 9632 16
6025.2.fa $$\chi_{6025}(214, \cdot)$$ n/a 9632 16
6025.2.fb $$\chi_{6025}(116, \cdot)$$ n/a 9664 16
6025.2.fc $$\chi_{6025}(211, \cdot)$$ n/a 9664 16
6025.2.fd $$\chi_{6025}(934, \cdot)$$ n/a 9632 16
6025.2.fm $$\chi_{6025}(393, \cdot)$$ n/a 5776 16
6025.2.fn $$\chi_{6025}(493, \cdot)$$ n/a 5776 16
6025.2.fo $$\chi_{6025}(324, \cdot)$$ n/a 5760 16
6025.2.fp $$\chi_{6025}(331, \cdot)$$ n/a 9632 16
6025.2.fq $$\chi_{6025}(181, \cdot)$$ n/a 9632 16
6025.2.fr $$\chi_{6025}(96, \cdot)$$ n/a 9632 16
6025.2.fs $$\chi_{6025}(386, \cdot)$$ n/a 9632 16
6025.2.ft $$\chi_{6025}(1046, \cdot)$$ n/a 9632 16
6025.2.gs $$\chi_{6025}(144, \cdot)$$ n/a 9664 16
6025.2.gt $$\chi_{6025}(9, \cdot)$$ n/a 9664 16
6025.2.gu $$\chi_{6025}(4, \cdot)$$ n/a 9664 16
6025.2.gv $$\chi_{6025}(134, \cdot)$$ n/a 9664 16
6025.2.gw $$\chi_{6025}(359, \cdot)$$ n/a 9664 16
6025.2.gx $$\chi_{6025}(151, \cdot)$$ n/a 6096 16
6025.2.ha $$\chi_{6025}(43, \cdot)$$ n/a 11552 32
6025.2.hb $$\chi_{6025}(57, \cdot)$$ n/a 11552 32
6025.2.hc $$\chi_{6025}(352, \cdot)$$ n/a 19296 32
6025.2.hd $$\chi_{6025}(197, \cdot)$$ n/a 19296 32
6025.2.hm $$\chi_{6025}(258, \cdot)$$ n/a 19296 32
6025.2.hn $$\chi_{6025}(17, \cdot)$$ n/a 19296 32
6025.2.ho $$\chi_{6025}(377, \cdot)$$ n/a 19296 32
6025.2.hp $$\chi_{6025}(138, \cdot)$$ n/a 19296 32
6025.2.hq $$\chi_{6025}(567, \cdot)$$ n/a 19296 32
6025.2.hr $$\chi_{6025}(28, \cdot)$$ n/a 19296 32
6025.2.hs $$\chi_{6025}(33, \cdot)$$ n/a 19296 32
6025.2.ht $$\chi_{6025}(213, \cdot)$$ n/a 19296 32
6025.2.ic $$\chi_{6025}(29, \cdot)$$ n/a 19264 32
6025.2.id $$\chi_{6025}(166, \cdot)$$ n/a 19328 32
6025.2.ie $$\chi_{6025}(209, \cdot)$$ n/a 19264 32
6025.2.if $$\chi_{6025}(121, \cdot)$$ n/a 19328 32
6025.2.ig $$\chi_{6025}(196, \cdot)$$ n/a 19328 32
6025.2.ih $$\chi_{6025}(164, \cdot)$$ n/a 19264 32
6025.2.ii $$\chi_{6025}(244, \cdot)$$ n/a 19264 32
6025.2.ij $$\chi_{6025}(191, \cdot)$$ n/a 19328 32
6025.2.ik $$\chi_{6025}(169, \cdot)$$ n/a 19264 32
6025.2.il $$\chi_{6025}(161, \cdot)$$ n/a 19328 32
6025.2.im $$\chi_{6025}(49, \cdot)$$ n/a 11584 32
6025.2.in $$\chi_{6025}(651, \cdot)$$ n/a 12160 32
6025.2.iw $$\chi_{6025}(52, \cdot)$$ n/a 38592 64
6025.2.ix $$\chi_{6025}(37, \cdot)$$ n/a 38592 64
6025.2.iy $$\chi_{6025}(278, \cdot)$$ n/a 38592 64
6025.2.iz $$\chi_{6025}(62, \cdot)$$ n/a 38592 64
6025.2.ja $$\chi_{6025}(272, \cdot)$$ n/a 38592 64
6025.2.jb $$\chi_{6025}(13, \cdot)$$ n/a 38592 64
6025.2.jc $$\chi_{6025}(167, \cdot)$$ n/a 38592 64
6025.2.jd $$\chi_{6025}(42, \cdot)$$ n/a 38592 64
6025.2.jm $$\chi_{6025}(38, \cdot)$$ n/a 38592 64
6025.2.jn $$\chi_{6025}(22, \cdot)$$ n/a 38592 64
6025.2.jo $$\chi_{6025}(132, \cdot)$$ n/a 23104 64
6025.2.jp $$\chi_{6025}(7, \cdot)$$ n/a 23104 64

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6025))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6025)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(241))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1205))$$$$^{\oplus 2}$$