Properties

Label 4650.2
Level 4650
Weight 2
Dimension 132446
Nonzero newspaces 84
Sturm bound 2304000

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Defining parameters

Level: \( N \) = \( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 84 \)
Sturm bound: \(2304000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4650))\).

Total New Old
Modular forms 582720 132446 450274
Cusp forms 569281 132446 436835
Eisenstein series 13439 0 13439

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4650))\)

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
4650.2.a \(\chi_{4650}(1, \cdot)\) 4650.2.a.a 1 1
4650.2.a.b 1
4650.2.a.c 1
4650.2.a.d 1
4650.2.a.e 1
4650.2.a.f 1
4650.2.a.g 1
4650.2.a.h 1
4650.2.a.i 1
4650.2.a.j 1
4650.2.a.k 1
4650.2.a.l 1
4650.2.a.m 1
4650.2.a.n 1
4650.2.a.o 1
4650.2.a.p 1
4650.2.a.q 1
4650.2.a.r 1
4650.2.a.s 1
4650.2.a.t 1
4650.2.a.u 1
4650.2.a.v 1
4650.2.a.w 1
4650.2.a.x 1
4650.2.a.y 1
4650.2.a.z 1
4650.2.a.ba 1
4650.2.a.bb 1
4650.2.a.bc 1
4650.2.a.bd 1
4650.2.a.be 1
4650.2.a.bf 1
4650.2.a.bg 1
4650.2.a.bh 1
4650.2.a.bi 1
4650.2.a.bj 1
4650.2.a.bk 1
4650.2.a.bl 1
4650.2.a.bm 1
4650.2.a.bn 1
4650.2.a.bo 1
4650.2.a.bp 1
4650.2.a.bq 1
4650.2.a.br 1
4650.2.a.bs 1
4650.2.a.bt 1
4650.2.a.bu 1
4650.2.a.bv 1
4650.2.a.bw 1
4650.2.a.bx 1
4650.2.a.by 2
4650.2.a.bz 2
4650.2.a.ca 2
4650.2.a.cb 2
4650.2.a.cc 2
4650.2.a.cd 2
4650.2.a.ce 2
4650.2.a.cf 2
4650.2.a.cg 2
4650.2.a.ch 2
4650.2.a.ci 3
4650.2.a.cj 3
4650.2.a.ck 3
4650.2.a.cl 3
4650.2.a.cm 3
4650.2.a.cn 3
4650.2.a.co 3
4650.2.a.cp 3
4650.2.d \(\chi_{4650}(3349, \cdot)\) 4650.2.d.a 2 1
4650.2.d.b 2
4650.2.d.c 2
4650.2.d.d 2
4650.2.d.e 2
4650.2.d.f 2
4650.2.d.g 2
4650.2.d.h 2
4650.2.d.i 2
4650.2.d.j 2
4650.2.d.k 2
4650.2.d.l 2
4650.2.d.m 2
4650.2.d.n 2
4650.2.d.o 2
4650.2.d.p 2
4650.2.d.q 2
4650.2.d.r 2
4650.2.d.s 2
4650.2.d.t 2
4650.2.d.u 2
4650.2.d.v 2
4650.2.d.w 2
4650.2.d.x 2
4650.2.d.y 2
4650.2.d.z 2
4650.2.d.ba 2
4650.2.d.bb 2
4650.2.d.bc 4
4650.2.d.bd 4
4650.2.d.be 4
4650.2.d.bf 4
4650.2.d.bg 4
4650.2.d.bh 4
4650.2.d.bi 6
4650.2.d.bj 6
4650.2.e \(\chi_{4650}(4649, \cdot)\) n/a 192 1
4650.2.h \(\chi_{4650}(1301, \cdot)\) n/a 204 1
4650.2.i \(\chi_{4650}(3001, \cdot)\) n/a 204 2
4650.2.j \(\chi_{4650}(2357, \cdot)\) n/a 360 2
4650.2.k \(\chi_{4650}(2107, \cdot)\) n/a 192 2
4650.2.n \(\chi_{4650}(721, \cdot)\) n/a 640 4
4650.2.o \(\chi_{4650}(901, \cdot)\) n/a 400 4
4650.2.p \(\chi_{4650}(1831, \cdot)\) n/a 640 4
4650.2.q \(\chi_{4650}(1771, \cdot)\) n/a 640 4
4650.2.r \(\chi_{4650}(481, \cdot)\) n/a 640 4
4650.2.s \(\chi_{4650}(931, \cdot)\) n/a 608 4
4650.2.t \(\chi_{4650}(2351, \cdot)\) n/a 404 2
4650.2.w \(\chi_{4650}(1049, \cdot)\) n/a 384 2
4650.2.x \(\chi_{4650}(1699, \cdot)\) n/a 192 2
4650.2.ba \(\chi_{4650}(929, \cdot)\) n/a 1280 4
4650.2.bb \(\chi_{4650}(559, \cdot)\) n/a 592 4
4650.2.bg \(\chi_{4650}(581, \cdot)\) n/a 1280 4
4650.2.bh \(\chi_{4650}(401, \cdot)\) n/a 816 4
4650.2.bi \(\chi_{4650}(3191, \cdot)\) n/a 1280 4
4650.2.bj \(\chi_{4650}(461, \cdot)\) n/a 1280 4
4650.2.bs \(\chi_{4650}(1391, \cdot)\) n/a 1280 4
4650.2.bv \(\chi_{4650}(109, \cdot)\) n/a 640 4
4650.2.bw \(\chi_{4650}(89, \cdot)\) n/a 1280 4
4650.2.bx \(\chi_{4650}(959, \cdot)\) n/a 1280 4
4650.2.by \(\chi_{4650}(449, \cdot)\) n/a 768 4
4650.2.bz \(\chi_{4650}(2209, \cdot)\) n/a 640 4
4650.2.ca \(\chi_{4650}(349, \cdot)\) n/a 384 4
4650.2.cb \(\chi_{4650}(469, \cdot)\) n/a 640 4
4650.2.cc \(\chi_{4650}(1889, \cdot)\) n/a 1280 4
4650.2.cl \(\chi_{4650}(29, \cdot)\) n/a 1280 4
4650.2.cm \(\chi_{4650}(529, \cdot)\) n/a 640 4
4650.2.cn \(\chi_{4650}(371, \cdot)\) n/a 1280 4
4650.2.cs \(\chi_{4650}(3157, \cdot)\) n/a 384 4
4650.2.ct \(\chi_{4650}(707, \cdot)\) n/a 768 4
4650.2.cu \(\chi_{4650}(211, \cdot)\) n/a 1280 8
4650.2.cv \(\chi_{4650}(1291, \cdot)\) n/a 1280 8
4650.2.cw \(\chi_{4650}(661, \cdot)\) n/a 1280 8
4650.2.cx \(\chi_{4650}(751, \cdot)\) n/a 816 8
4650.2.cy \(\chi_{4650}(391, \cdot)\) n/a 1280 8
4650.2.cz \(\chi_{4650}(121, \cdot)\) n/a 1280 8
4650.2.da \(\chi_{4650}(337, \cdot)\) n/a 1280 8
4650.2.db \(\chi_{4650}(233, \cdot)\) n/a 2560 8
4650.2.dm \(\chi_{4650}(977, \cdot)\) n/a 2560 8
4650.2.dn \(\chi_{4650}(247, \cdot)\) n/a 1280 8
4650.2.do \(\chi_{4650}(277, \cdot)\) n/a 1280 8
4650.2.dp \(\chi_{4650}(457, \cdot)\) n/a 768 8
4650.2.dq \(\chi_{4650}(497, \cdot)\) n/a 2400 8
4650.2.dr \(\chi_{4650}(407, \cdot)\) n/a 1536 8
4650.2.ds \(\chi_{4650}(1163, \cdot)\) n/a 2560 8
4650.2.dt \(\chi_{4650}(463, \cdot)\) n/a 1280 8
4650.2.du \(\chi_{4650}(523, \cdot)\) n/a 1280 8
4650.2.dv \(\chi_{4650}(47, \cdot)\) n/a 2560 8
4650.2.ea \(\chi_{4650}(161, \cdot)\) n/a 2560 8
4650.2.eb \(\chi_{4650}(1309, \cdot)\) n/a 1280 8
4650.2.ec \(\chi_{4650}(239, \cdot)\) n/a 2560 8
4650.2.el \(\chi_{4650}(179, \cdot)\) n/a 2560 8
4650.2.em \(\chi_{4650}(19, \cdot)\) n/a 1280 8
4650.2.en \(\chi_{4650}(919, \cdot)\) n/a 1280 8
4650.2.eo \(\chi_{4650}(49, \cdot)\) n/a 768 8
4650.2.ep \(\chi_{4650}(269, \cdot)\) n/a 2560 8
4650.2.eq \(\chi_{4650}(1199, \cdot)\) n/a 1536 8
4650.2.er \(\chi_{4650}(569, \cdot)\) n/a 2560 8
4650.2.es \(\chi_{4650}(169, \cdot)\) n/a 1280 8
4650.2.ev \(\chi_{4650}(611, \cdot)\) n/a 2560 8
4650.2.fe \(\chi_{4650}(641, \cdot)\) n/a 2560 8
4650.2.ff \(\chi_{4650}(251, \cdot)\) n/a 1616 8
4650.2.fg \(\chi_{4650}(11, \cdot)\) n/a 2560 8
4650.2.fh \(\chi_{4650}(911, \cdot)\) n/a 2560 8
4650.2.fm \(\chi_{4650}(439, \cdot)\) n/a 1280 8
4650.2.fn \(\chi_{4650}(119, \cdot)\) n/a 2560 8
4650.2.fq \(\chi_{4650}(127, \cdot)\) n/a 2560 16
4650.2.fr \(\chi_{4650}(227, \cdot)\) n/a 5120 16
4650.2.fs \(\chi_{4650}(107, \cdot)\) n/a 3072 16
4650.2.ft \(\chi_{4650}(377, \cdot)\) n/a 5120 16
4650.2.fu \(\chi_{4650}(43, \cdot)\) n/a 1536 16
4650.2.fv \(\chi_{4650}(13, \cdot)\) n/a 2560 16
4650.2.fw \(\chi_{4650}(37, \cdot)\) n/a 2560 16
4650.2.fx \(\chi_{4650}(173, \cdot)\) n/a 5120 16
4650.2.fy \(\chi_{4650}(803, \cdot)\) n/a 5120 16
4650.2.fz \(\chi_{4650}(73, \cdot)\) n/a 2560 16
4650.2.gk \(\chi_{4650}(113, \cdot)\) n/a 5120 16
4650.2.gl \(\chi_{4650}(613, \cdot)\) n/a 2560 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4650))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4650)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(465))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(775))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(930))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1550))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2325))\)\(^{\oplus 2}\)