Properties

Label 6025.2
Level 6025
Weight 2
Dimension 1333316
Nonzero newspaces 140
Sturm bound 5808000

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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

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