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Properties

Label 11025.2
Level 11025
Weight 2
Dimension 2955339
Nonzero newspaces 120
Sturm bound 16934400

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Defining parameters

Level: \( N \) = \( 11025 = 3^{2} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 120 \)
Sturm bound: \(16934400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(11025))\).

Total New Old
Modular forms 4260480 2973236 1287244
Cusp forms 4206721 2955339 1251382
Eisenstein series 53759 17897 35862

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(11025))\)

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
11025.2.a \(\chi_{11025}(1, \cdot)\) 11025.2.a.a 1 1
11025.2.a.b 1
11025.2.a.c 1
11025.2.a.d 1
11025.2.a.e 1
11025.2.a.f 1
11025.2.a.g 1
11025.2.a.h 1
11025.2.a.i 1
11025.2.a.j 1
11025.2.a.k 1
11025.2.a.l 1
11025.2.a.m 1
11025.2.a.n 1
11025.2.a.o 1
11025.2.a.p 1
11025.2.a.q 1
11025.2.a.r 1
11025.2.a.s 1
11025.2.a.t 1
11025.2.a.u 1
11025.2.a.v 1
11025.2.a.w 1
11025.2.a.x 1
11025.2.a.y 1
11025.2.a.z 1
11025.2.a.ba 1
11025.2.a.bb 1
11025.2.a.bc 1
11025.2.a.bd 1
11025.2.a.be 1
11025.2.a.bf 1
11025.2.a.bg 1
11025.2.a.bh 1
11025.2.a.bi 1
11025.2.a.bj 1
11025.2.a.bk 1
11025.2.a.bl 1
11025.2.a.bm 1
11025.2.a.bn 1
11025.2.a.bo 1
11025.2.a.bp 1
11025.2.a.bq 1
11025.2.a.br 2
11025.2.a.bs 2
11025.2.a.bt 2
11025.2.a.bu 2
11025.2.a.bv 2
11025.2.a.bw 2
11025.2.a.bx 2
11025.2.a.by 2
11025.2.a.bz 2
11025.2.a.ca 2
11025.2.a.cb 2
11025.2.a.cc 2
11025.2.a.cd 2
11025.2.a.ce 2
11025.2.a.cf 2
11025.2.a.cg 2
11025.2.a.ch 2
11025.2.a.ci 2
11025.2.a.cj 2
11025.2.a.ck 2
11025.2.a.cl 2
11025.2.a.cm 2
11025.2.a.cn 2
11025.2.a.co 2
11025.2.a.cp 2
11025.2.a.cq 2
11025.2.a.cr 2
11025.2.a.cs 2
11025.2.a.ct 2
11025.2.a.cu 2
11025.2.a.cv 2
11025.2.a.cw 2
11025.2.a.cx 2
11025.2.a.cy 2
11025.2.a.cz 3
11025.2.a.da 3
11025.2.a.db 3
11025.2.a.dc 3
11025.2.a.dd 3
11025.2.a.de 3
11025.2.a.df 3
11025.2.a.dg 3
11025.2.a.dh 3
11025.2.a.di 3
11025.2.a.dj 4
11025.2.a.dk 4
11025.2.a.dl 4
11025.2.a.dm 4
11025.2.a.dn 4
11025.2.a.do 4
11025.2.a.dp 4
11025.2.a.dq 4
11025.2.a.dr 4
11025.2.a.ds 4
11025.2.a.dt 4
11025.2.a.du 4
11025.2.a.dv 4
11025.2.a.dw 4
11025.2.a.dx 4
11025.2.a.dy 4
11025.2.a.dz 4
11025.2.a.ea 4
11025.2.a.eb 4
11025.2.a.ec 4
11025.2.a.ed 4
11025.2.a.ee 4
11025.2.a.ef 4
11025.2.a.eg 4
11025.2.a.eh 4
11025.2.a.ei 4
11025.2.a.ej 4
11025.2.a.ek 4
11025.2.a.el 4
11025.2.a.em 4
11025.2.a.en 4
11025.2.a.eo 4
11025.2.a.ep 8
11025.2.a.eq 8
11025.2.a.er 8
11025.2.a.es 8
11025.2.a.et 8
11025.2.a.eu 8
11025.2.b \(\chi_{11025}(9701, \cdot)\) n/a 252 1
11025.2.d \(\chi_{11025}(1324, \cdot)\) n/a 302 1
11025.2.g \(\chi_{11025}(11024, \cdot)\) n/a 240 1
11025.2.i \(\chi_{11025}(3676, \cdot)\) n/a 1528 2
11025.2.j \(\chi_{11025}(226, \cdot)\) n/a 622 2
11025.2.k \(\chi_{11025}(7576, \cdot)\) n/a 1496 2
11025.2.l \(\chi_{11025}(3301, \cdot)\) n/a 1496 2
11025.2.m \(\chi_{11025}(2843, \cdot)\) n/a 492 2
11025.2.p \(\chi_{11025}(6418, \cdot)\) n/a 592 2
11025.2.q \(\chi_{11025}(2206, \cdot)\) n/a 2028 4
11025.2.s \(\chi_{11025}(4624, \cdot)\) n/a 1424 2
11025.2.u \(\chi_{11025}(5801, \cdot)\) n/a 1496 2
11025.2.v \(\chi_{11025}(374, \cdot)\) n/a 1424 2
11025.2.ba \(\chi_{11025}(3674, \cdot)\) n/a 1424 2
11025.2.bc \(\chi_{11025}(4049, \cdot)\) n/a 480 2
11025.2.bf \(\chi_{11025}(2126, \cdot)\) n/a 1496 2
11025.2.bg \(\chi_{11025}(1549, \cdot)\) n/a 592 2
11025.2.bi \(\chi_{11025}(4999, \cdot)\) n/a 1456 2
11025.2.bk \(\chi_{11025}(2726, \cdot)\) n/a 508 2
11025.2.bm \(\chi_{11025}(2351, \cdot)\) n/a 1496 2
11025.2.bp \(\chi_{11025}(949, \cdot)\) n/a 1424 2
11025.2.br \(\chi_{11025}(7124, \cdot)\) n/a 1424 2
11025.2.bt \(\chi_{11025}(1576, \cdot)\) n/a 2646 6
11025.2.bv \(\chi_{11025}(2204, \cdot)\) n/a 1600 4
11025.2.by \(\chi_{11025}(3529, \cdot)\) n/a 2032 4
11025.2.ca \(\chi_{11025}(881, \cdot)\) n/a 1600 4
11025.2.cb \(\chi_{11025}(607, \cdot)\) n/a 2848 4
11025.2.ce \(\chi_{11025}(1157, \cdot)\) n/a 2848 4
11025.2.cg \(\chi_{11025}(6143, \cdot)\) n/a 2848 4
11025.2.ci \(\chi_{11025}(1207, \cdot)\) n/a 1184 4
11025.2.ck \(\chi_{11025}(832, \cdot)\) n/a 2848 4
11025.2.cl \(\chi_{11025}(932, \cdot)\) n/a 2912 4
11025.2.cn \(\chi_{11025}(557, \cdot)\) n/a 960 4
11025.2.cp \(\chi_{11025}(2518, \cdot)\) n/a 2848 4
11025.2.cs \(\chi_{11025}(1574, \cdot)\) n/a 2016 6
11025.2.cv \(\chi_{11025}(2899, \cdot)\) n/a 2508 6
11025.2.cx \(\chi_{11025}(251, \cdot)\) n/a 2136 6
11025.2.cy \(\chi_{11025}(1096, \cdot)\) n/a 9536 8
11025.2.cz \(\chi_{11025}(961, \cdot)\) n/a 9536 8
11025.2.da \(\chi_{11025}(361, \cdot)\) n/a 3968 8
11025.2.db \(\chi_{11025}(736, \cdot)\) n/a 9760 8
11025.2.dc \(\chi_{11025}(1567, \cdot)\) n/a 3968 8
11025.2.df \(\chi_{11025}(197, \cdot)\) n/a 3280 8
11025.2.dg \(\chi_{11025}(151, \cdot)\) n/a 12696 12
11025.2.dh \(\chi_{11025}(1201, \cdot)\) n/a 12696 12
11025.2.di \(\chi_{11025}(676, \cdot)\) n/a 5280 12
11025.2.dj \(\chi_{11025}(526, \cdot)\) n/a 12696 12
11025.2.dl \(\chi_{11025}(118, \cdot)\) n/a 5016 12
11025.2.dm \(\chi_{11025}(1268, \cdot)\) n/a 4032 12
11025.2.dp \(\chi_{11025}(509, \cdot)\) n/a 9536 8
11025.2.dr \(\chi_{11025}(79, \cdot)\) n/a 9536 8
11025.2.du \(\chi_{11025}(146, \cdot)\) n/a 9536 8
11025.2.dw \(\chi_{11025}(521, \cdot)\) n/a 3200 8
11025.2.dy \(\chi_{11025}(589, \cdot)\) n/a 9760 8
11025.2.ea \(\chi_{11025}(1684, \cdot)\) n/a 3968 8
11025.2.eb \(\chi_{11025}(1256, \cdot)\) n/a 9536 8
11025.2.ee \(\chi_{11025}(1844, \cdot)\) n/a 3200 8
11025.2.eg \(\chi_{11025}(734, \cdot)\) n/a 9536 8
11025.2.el \(\chi_{11025}(1244, \cdot)\) n/a 9536 8
11025.2.em \(\chi_{11025}(1391, \cdot)\) n/a 9536 8
11025.2.eo \(\chi_{11025}(214, \cdot)\) n/a 9536 8
11025.2.eq \(\chi_{11025}(316, \cdot)\) n/a 16752 24
11025.2.es \(\chi_{11025}(824, \cdot)\) n/a 12048 12
11025.2.eu \(\chi_{11025}(1024, \cdot)\) n/a 12048 12
11025.2.ex \(\chi_{11025}(776, \cdot)\) n/a 12696 12
11025.2.ez \(\chi_{11025}(26, \cdot)\) n/a 4248 12
11025.2.fb \(\chi_{11025}(274, \cdot)\) n/a 12048 12
11025.2.fd \(\chi_{11025}(424, \cdot)\) n/a 5016 12
11025.2.fe \(\chi_{11025}(551, \cdot)\) n/a 12696 12
11025.2.fh \(\chi_{11025}(899, \cdot)\) n/a 4032 12
11025.2.fj \(\chi_{11025}(524, \cdot)\) n/a 12048 12
11025.2.fo \(\chi_{11025}(299, \cdot)\) n/a 12048 12
11025.2.fp \(\chi_{11025}(101, \cdot)\) n/a 12696 12
11025.2.fr \(\chi_{11025}(499, \cdot)\) n/a 12048 12
11025.2.fu \(\chi_{11025}(313, \cdot)\) n/a 19072 16
11025.2.fw \(\chi_{11025}(422, \cdot)\) n/a 6400 16
11025.2.fy \(\chi_{11025}(1373, \cdot)\) n/a 19520 16
11025.2.fz \(\chi_{11025}(97, \cdot)\) n/a 19072 16
11025.2.gb \(\chi_{11025}(1342, \cdot)\) n/a 7936 16
11025.2.gd \(\chi_{11025}(128, \cdot)\) n/a 19072 16
11025.2.gf \(\chi_{11025}(263, \cdot)\) n/a 19072 16
11025.2.gi \(\chi_{11025}(178, \cdot)\) n/a 19072 16
11025.2.gj \(\chi_{11025}(566, \cdot)\) n/a 13440 24
11025.2.gl \(\chi_{11025}(64, \cdot)\) n/a 16752 24
11025.2.go \(\chi_{11025}(314, \cdot)\) n/a 13440 24
11025.2.gq \(\chi_{11025}(157, \cdot)\) n/a 24096 24
11025.2.gs \(\chi_{11025}(218, \cdot)\) n/a 24096 24
11025.2.gu \(\chi_{11025}(107, \cdot)\) n/a 8064 24
11025.2.gx \(\chi_{11025}(82, \cdot)\) n/a 10032 24
11025.2.gz \(\chi_{11025}(643, \cdot)\) n/a 24096 24
11025.2.hb \(\chi_{11025}(32, \cdot)\) n/a 24096 24
11025.2.hd \(\chi_{11025}(893, \cdot)\) n/a 24096 24
11025.2.he \(\chi_{11025}(418, \cdot)\) n/a 24096 24
11025.2.hg \(\chi_{11025}(106, \cdot)\) n/a 80448 48
11025.2.hh \(\chi_{11025}(46, \cdot)\) n/a 33504 48
11025.2.hi \(\chi_{11025}(16, \cdot)\) n/a 80448 48
11025.2.hj \(\chi_{11025}(121, \cdot)\) n/a 80448 48
11025.2.hl \(\chi_{11025}(8, \cdot)\) n/a 26880 48
11025.2.hm \(\chi_{11025}(433, \cdot)\) n/a 33504 48
11025.2.hp \(\chi_{11025}(184, \cdot)\) n/a 80448 48
11025.2.hr \(\chi_{11025}(131, \cdot)\) n/a 80448 48
11025.2.hs \(\chi_{11025}(59, \cdot)\) n/a 80448 48
11025.2.hx \(\chi_{11025}(104, \cdot)\) n/a 80448 48
11025.2.hz \(\chi_{11025}(89, \cdot)\) n/a 26880 48
11025.2.ic \(\chi_{11025}(236, \cdot)\) n/a 80448 48
11025.2.id \(\chi_{11025}(109, \cdot)\) n/a 33504 48
11025.2.if \(\chi_{11025}(169, \cdot)\) n/a 80448 48
11025.2.ih \(\chi_{11025}(206, \cdot)\) n/a 26880 48
11025.2.ij \(\chi_{11025}(41, \cdot)\) n/a 80448 48
11025.2.im \(\chi_{11025}(4, \cdot)\) n/a 80448 48
11025.2.io \(\chi_{11025}(164, \cdot)\) n/a 80448 48
11025.2.ir \(\chi_{11025}(52, \cdot)\) n/a 160896 96
11025.2.is \(\chi_{11025}(23, \cdot)\) n/a 160896 96
11025.2.iu \(\chi_{11025}(2, \cdot)\) n/a 160896 96
11025.2.iw \(\chi_{11025}(13, \cdot)\) n/a 160896 96
11025.2.iy \(\chi_{11025}(73, \cdot)\) n/a 67008 96
11025.2.jb \(\chi_{11025}(53, \cdot)\) n/a 53760 96
11025.2.jd \(\chi_{11025}(92, \cdot)\) n/a 160896 96
11025.2.jf \(\chi_{11025}(187, \cdot)\) n/a 160896 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(11025))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(11025)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(735))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1225))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1575))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2205))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3675))\)\(^{\oplus 2}\)