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Properties

Label 8925.2
Level 8925
Weight 2
Dimension 1812672
Nonzero newspaces 144
Sturm bound 11059200

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Defining parameters

Level: \( N \) = \( 8925 = 3 \cdot 5^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 144 \)
Sturm bound: \(11059200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8925))\).

Total New Old
Modular forms 2786304 1824968 961336
Cusp forms 2743297 1812672 930625
Eisenstein series 43007 12296 30711

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8925))\)

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
8925.2.a \(\chi_{8925}(1, \cdot)\) 8925.2.a.a 1 1
8925.2.a.b 1
8925.2.a.c 1
8925.2.a.d 1
8925.2.a.e 1
8925.2.a.f 1
8925.2.a.g 1
8925.2.a.h 1
8925.2.a.i 1
8925.2.a.j 1
8925.2.a.k 1
8925.2.a.l 1
8925.2.a.m 1
8925.2.a.n 1
8925.2.a.o 1
8925.2.a.p 1
8925.2.a.q 1
8925.2.a.r 1
8925.2.a.s 1
8925.2.a.t 1
8925.2.a.u 1
8925.2.a.v 1
8925.2.a.w 1
8925.2.a.x 1
8925.2.a.y 1
8925.2.a.z 1
8925.2.a.ba 1
8925.2.a.bb 1
8925.2.a.bc 1
8925.2.a.bd 2
8925.2.a.be 2
8925.2.a.bf 2
8925.2.a.bg 2
8925.2.a.bh 2
8925.2.a.bi 2
8925.2.a.bj 2
8925.2.a.bk 2
8925.2.a.bl 2
8925.2.a.bm 3
8925.2.a.bn 3
8925.2.a.bo 3
8925.2.a.bp 3
8925.2.a.bq 3
8925.2.a.br 4
8925.2.a.bs 4
8925.2.a.bt 4
8925.2.a.bu 4
8925.2.a.bv 4
8925.2.a.bw 4
8925.2.a.bx 5
8925.2.a.by 5
8925.2.a.bz 5
8925.2.a.ca 5
8925.2.a.cb 6
8925.2.a.cc 6
8925.2.a.cd 6
8925.2.a.ce 6
8925.2.a.cf 6
8925.2.a.cg 7
8925.2.a.ch 7
8925.2.a.ci 7
8925.2.a.cj 7
8925.2.a.ck 7
8925.2.a.cl 7
8925.2.a.cm 7
8925.2.a.cn 7
8925.2.a.co 8
8925.2.a.cp 8
8925.2.a.cq 10
8925.2.a.cr 10
8925.2.a.cs 10
8925.2.a.ct 10
8925.2.a.cu 14
8925.2.a.cv 14
8925.2.a.cw 14
8925.2.a.cx 14
8925.2.b \(\chi_{8925}(3401, \cdot)\) n/a 812 1
8925.2.c \(\chi_{8925}(5524, \cdot)\) n/a 320 1
8925.2.f \(\chi_{8925}(3926, \cdot)\) n/a 900 1
8925.2.g \(\chi_{8925}(4999, \cdot)\) n/a 288 1
8925.2.l \(\chi_{8925}(8399, \cdot)\) n/a 768 1
8925.2.m \(\chi_{8925}(526, \cdot)\) n/a 344 1
8925.2.p \(\chi_{8925}(8924, \cdot)\) n/a 856 1
8925.2.q \(\chi_{8925}(1276, \cdot)\) n/a 812 2
8925.2.t \(\chi_{8925}(3676, \cdot)\) n/a 688 2
8925.2.u \(\chi_{8925}(3149, \cdot)\) n/a 1712 2
8925.2.v \(\chi_{8925}(8093, \cdot)\) n/a 1152 2
8925.2.x \(\chi_{8925}(118, \cdot)\) n/a 864 2
8925.2.z \(\chi_{8925}(3268, \cdot)\) n/a 864 2
8925.2.bc \(\chi_{8925}(3982, \cdot)\) n/a 864 2
8925.2.be \(\chi_{8925}(2843, \cdot)\) n/a 1296 2
8925.2.bf \(\chi_{8925}(3557, \cdot)\) n/a 1296 2
8925.2.bh \(\chi_{8925}(407, \cdot)\) n/a 1296 2
8925.2.bj \(\chi_{8925}(307, \cdot)\) n/a 768 2
8925.2.bl \(\chi_{8925}(1849, \cdot)\) n/a 640 2
8925.2.bm \(\chi_{8925}(251, \cdot)\) n/a 1800 2
8925.2.bp \(\chi_{8925}(1786, \cdot)\) n/a 1920 4
8925.2.bs \(\chi_{8925}(5099, \cdot)\) n/a 1712 2
8925.2.bv \(\chi_{8925}(1801, \cdot)\) n/a 912 2
8925.2.bw \(\chi_{8925}(4574, \cdot)\) n/a 1536 2
8925.2.bx \(\chi_{8925}(6274, \cdot)\) n/a 768 2
8925.2.by \(\chi_{8925}(101, \cdot)\) n/a 1800 2
8925.2.cb \(\chi_{8925}(424, \cdot)\) n/a 864 2
8925.2.cc \(\chi_{8925}(2126, \cdot)\) n/a 1620 2
8925.2.cf \(\chi_{8925}(2218, \cdot)\) n/a 1728 4
8925.2.ci \(\chi_{8925}(2507, \cdot)\) n/a 2592 4
8925.2.ck \(\chi_{8925}(2626, \cdot)\) n/a 1360 4
8925.2.cl \(\chi_{8925}(2099, \cdot)\) n/a 3424 4
8925.2.co \(\chi_{8925}(1301, \cdot)\) n/a 3600 4
8925.2.cp \(\chi_{8925}(274, \cdot)\) n/a 1312 4
8925.2.cr \(\chi_{8925}(1793, \cdot)\) n/a 2592 4
8925.2.cu \(\chi_{8925}(2932, \cdot)\) n/a 1728 4
8925.2.cv \(\chi_{8925}(1784, \cdot)\) n/a 5728 4
8925.2.cy \(\chi_{8925}(2311, \cdot)\) n/a 2144 4
8925.2.cz \(\chi_{8925}(1259, \cdot)\) n/a 5120 4
8925.2.de \(\chi_{8925}(1429, \cdot)\) n/a 1920 4
8925.2.df \(\chi_{8925}(356, \cdot)\) n/a 5728 4
8925.2.di \(\chi_{8925}(169, \cdot)\) n/a 2176 4
8925.2.dj \(\chi_{8925}(1616, \cdot)\) n/a 5120 4
8925.2.dk \(\chi_{8925}(3251, \cdot)\) n/a 3600 4
8925.2.dl \(\chi_{8925}(1024, \cdot)\) n/a 1728 4
8925.2.dp \(\chi_{8925}(4693, \cdot)\) n/a 1536 4
8925.2.dr \(\chi_{8925}(968, \cdot)\) n/a 3424 4
8925.2.ds \(\chi_{8925}(557, \cdot)\) n/a 3424 4
8925.2.dv \(\chi_{8925}(4832, \cdot)\) n/a 3424 4
8925.2.dx \(\chi_{8925}(1993, \cdot)\) n/a 1728 4
8925.2.dy \(\chi_{8925}(157, \cdot)\) n/a 1728 4
8925.2.eb \(\chi_{8925}(5218, \cdot)\) n/a 1728 4
8925.2.ed \(\chi_{8925}(443, \cdot)\) n/a 3072 4
8925.2.eg \(\chi_{8925}(1424, \cdot)\) n/a 3424 4
8925.2.eh \(\chi_{8925}(676, \cdot)\) n/a 1824 4
8925.2.ei \(\chi_{8925}(256, \cdot)\) n/a 5120 8
8925.2.ej \(\chi_{8925}(2918, \cdot)\) n/a 6848 8
8925.2.el \(\chi_{8925}(232, \cdot)\) n/a 2592 8
8925.2.eo \(\chi_{8925}(601, \cdot)\) n/a 3648 8
8925.2.ep \(\chi_{8925}(449, \cdot)\) n/a 5184 8
8925.2.er \(\chi_{8925}(176, \cdot)\) n/a 5472 8
8925.2.eu \(\chi_{8925}(874, \cdot)\) n/a 3456 8
8925.2.ev \(\chi_{8925}(568, \cdot)\) n/a 2592 8
8925.2.ex \(\chi_{8925}(482, \cdot)\) n/a 6848 8
8925.2.fb \(\chi_{8925}(1721, \cdot)\) n/a 11456 8
8925.2.fc \(\chi_{8925}(64, \cdot)\) n/a 4352 8
8925.2.fd \(\chi_{8925}(1378, \cdot)\) n/a 5120 8
8925.2.ff \(\chi_{8925}(1478, \cdot)\) n/a 8640 8
8925.2.fi \(\chi_{8925}(1373, \cdot)\) n/a 8640 8
8925.2.fj \(\chi_{8925}(302, \cdot)\) n/a 8640 8
8925.2.fl \(\chi_{8925}(13, \cdot)\) n/a 5760 8
8925.2.fo \(\chi_{8925}(727, \cdot)\) n/a 5760 8
8925.2.fp \(\chi_{8925}(1903, \cdot)\) n/a 5760 8
8925.2.fr \(\chi_{8925}(953, \cdot)\) n/a 7680 8
8925.2.ft \(\chi_{8925}(1364, \cdot)\) n/a 11456 8
8925.2.fu \(\chi_{8925}(106, \cdot)\) n/a 4288 8
8925.2.fx \(\chi_{8925}(32, \cdot)\) n/a 6848 8
8925.2.ga \(\chi_{8925}(1018, \cdot)\) n/a 3456 8
8925.2.gc \(\chi_{8925}(824, \cdot)\) n/a 6848 8
8925.2.gd \(\chi_{8925}(151, \cdot)\) n/a 3648 8
8925.2.gg \(\chi_{8925}(1549, \cdot)\) n/a 3456 8
8925.2.gh \(\chi_{8925}(26, \cdot)\) n/a 7200 8
8925.2.gj \(\chi_{8925}(682, \cdot)\) n/a 3456 8
8925.2.gm \(\chi_{8925}(1607, \cdot)\) n/a 6848 8
8925.2.gp \(\chi_{8925}(341, \cdot)\) n/a 10240 8
8925.2.gq \(\chi_{8925}(1444, \cdot)\) n/a 5760 8
8925.2.gt \(\chi_{8925}(866, \cdot)\) n/a 11456 8
8925.2.gu \(\chi_{8925}(919, \cdot)\) n/a 5120 8
8925.2.gv \(\chi_{8925}(1004, \cdot)\) n/a 10240 8
8925.2.gw \(\chi_{8925}(16, \cdot)\) n/a 5760 8
8925.2.gz \(\chi_{8925}(509, \cdot)\) n/a 11456 8
8925.2.hd \(\chi_{8925}(8, \cdot)\) n/a 17280 16
8925.2.he \(\chi_{8925}(223, \cdot)\) n/a 11520 16
8925.2.hh \(\chi_{8925}(484, \cdot)\) n/a 8576 16
8925.2.hi \(\chi_{8925}(461, \cdot)\) n/a 22912 16
8925.2.hl \(\chi_{8925}(104, \cdot)\) n/a 22912 16
8925.2.hm \(\chi_{8925}(631, \cdot)\) n/a 8704 16
8925.2.hp \(\chi_{8925}(202, \cdot)\) n/a 11520 16
8925.2.hq \(\chi_{8925}(722, \cdot)\) n/a 17280 16
8925.2.ht \(\chi_{8925}(907, \cdot)\) n/a 6912 16
8925.2.hv \(\chi_{8925}(143, \cdot)\) n/a 13696 16
8925.2.hw \(\chi_{8925}(124, \cdot)\) n/a 6912 16
8925.2.hz \(\chi_{8925}(326, \cdot)\) n/a 14400 16
8925.2.ib \(\chi_{8925}(74, \cdot)\) n/a 13696 16
8925.2.ic \(\chi_{8925}(976, \cdot)\) n/a 7296 16
8925.2.if \(\chi_{8925}(668, \cdot)\) n/a 13696 16
8925.2.ih \(\chi_{8925}(193, \cdot)\) n/a 6912 16
8925.2.ii \(\chi_{8925}(361, \cdot)\) n/a 11520 16
8925.2.ij \(\chi_{8925}(89, \cdot)\) n/a 22912 16
8925.2.in \(\chi_{8925}(137, \cdot)\) n/a 20480 16
8925.2.ip \(\chi_{8925}(577, \cdot)\) n/a 11520 16
8925.2.ir \(\chi_{8925}(523, \cdot)\) n/a 11520 16
8925.2.is \(\chi_{8925}(208, \cdot)\) n/a 11520 16
8925.2.iu \(\chi_{8925}(242, \cdot)\) n/a 22912 16
8925.2.ix \(\chi_{8925}(548, \cdot)\) n/a 22912 16
8925.2.iz \(\chi_{8925}(662, \cdot)\) n/a 22912 16
8925.2.jb \(\chi_{8925}(52, \cdot)\) n/a 10240 16
8925.2.je \(\chi_{8925}(4, \cdot)\) n/a 11520 16
8925.2.jf \(\chi_{8925}(446, \cdot)\) n/a 22912 16
8925.2.jg \(\chi_{8925}(62, \cdot)\) n/a 45824 32
8925.2.ji \(\chi_{8925}(22, \cdot)\) n/a 17280 32
8925.2.jk \(\chi_{8925}(139, \cdot)\) n/a 23040 32
8925.2.jn \(\chi_{8925}(71, \cdot)\) n/a 34560 32
8925.2.jp \(\chi_{8925}(29, \cdot)\) n/a 34560 32
8925.2.jq \(\chi_{8925}(181, \cdot)\) n/a 23040 32
8925.2.js \(\chi_{8925}(148, \cdot)\) n/a 17280 32
8925.2.ju \(\chi_{8925}(167, \cdot)\) n/a 45824 32
8925.2.jx \(\chi_{8925}(178, \cdot)\) n/a 23040 32
8925.2.jy \(\chi_{8925}(53, \cdot)\) n/a 45824 32
8925.2.kb \(\chi_{8925}(206, \cdot)\) n/a 45824 32
8925.2.kc \(\chi_{8925}(529, \cdot)\) n/a 23040 32
8925.2.kf \(\chi_{8925}(121, \cdot)\) n/a 23040 32
8925.2.kg \(\chi_{8925}(59, \cdot)\) n/a 45824 32
8925.2.kj \(\chi_{8925}(2, \cdot)\) n/a 45824 32
8925.2.kk \(\chi_{8925}(502, \cdot)\) n/a 23040 32
8925.2.kn \(\chi_{8925}(37, \cdot)\) n/a 46080 64
8925.2.kp \(\chi_{8925}(173, \cdot)\) n/a 91648 64
8925.2.kr \(\chi_{8925}(31, \cdot)\) n/a 46080 64
8925.2.ks \(\chi_{8925}(44, \cdot)\) n/a 91648 64
8925.2.ku \(\chi_{8925}(11, \cdot)\) n/a 91648 64
8925.2.kx \(\chi_{8925}(334, \cdot)\) n/a 46080 64
8925.2.kz \(\chi_{8925}(122, \cdot)\) n/a 91648 64
8925.2.lb \(\chi_{8925}(88, \cdot)\) n/a 46080 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8925))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8925)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(357))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(595))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1275))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1785))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2975))\)\(^{\oplus 2}\)