↑

Properties

Label 7650.2
Level 7650
Weight 2
Dimension 375626
Nonzero newspaces 72
Sturm bound 6220800

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 7650 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(6220800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7650))\).

Total New Old
Modular forms 1569536 375626 1193910
Cusp forms 1540865 375626 1165239
Eisenstein series 28671 0 28671

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7650))\)

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
7650.2.a \(\chi_{7650}(1, \cdot)\) 7650.2.a.a 1 1
7650.2.a.b 1
7650.2.a.c 1
7650.2.a.d 1
7650.2.a.e 1
7650.2.a.f 1
7650.2.a.g 1
7650.2.a.h 1
7650.2.a.i 1
7650.2.a.j 1
7650.2.a.k 1
7650.2.a.l 1
7650.2.a.m 1
7650.2.a.n 1
7650.2.a.o 1
7650.2.a.p 1
7650.2.a.q 1
7650.2.a.r 1
7650.2.a.s 1
7650.2.a.t 1
7650.2.a.u 1
7650.2.a.v 1
7650.2.a.w 1
7650.2.a.x 1
7650.2.a.y 1
7650.2.a.z 1
7650.2.a.ba 1
7650.2.a.bb 1
7650.2.a.bc 1
7650.2.a.bd 1
7650.2.a.be 1
7650.2.a.bf 1
7650.2.a.bg 1
7650.2.a.bh 1
7650.2.a.bi 1
7650.2.a.bj 1
7650.2.a.bk 1
7650.2.a.bl 1
7650.2.a.bm 1
7650.2.a.bn 1
7650.2.a.bo 1
7650.2.a.bp 1
7650.2.a.bq 1
7650.2.a.br 1
7650.2.a.bs 1
7650.2.a.bt 1
7650.2.a.bu 1
7650.2.a.bv 1
7650.2.a.bw 1
7650.2.a.bx 1
7650.2.a.by 1
7650.2.a.bz 1
7650.2.a.ca 1
7650.2.a.cb 1
7650.2.a.cc 1
7650.2.a.cd 1
7650.2.a.ce 1
7650.2.a.cf 1
7650.2.a.cg 1
7650.2.a.ch 1
7650.2.a.ci 1
7650.2.a.cj 1
7650.2.a.ck 1
7650.2.a.cl 1
7650.2.a.cm 1
7650.2.a.cn 1
7650.2.a.co 1
7650.2.a.cp 1
7650.2.a.cq 2
7650.2.a.cr 2
7650.2.a.cs 2
7650.2.a.ct 2
7650.2.a.cu 2
7650.2.a.cv 2
7650.2.a.cw 2
7650.2.a.cx 2
7650.2.a.cy 2
7650.2.a.cz 2
7650.2.a.da 2
7650.2.a.db 2
7650.2.a.dc 2
7650.2.a.dd 2
7650.2.a.de 2
7650.2.a.df 2
7650.2.a.dg 2
7650.2.a.dh 2
7650.2.a.di 3
7650.2.a.dj 3
7650.2.a.dk 3
7650.2.a.dl 3
7650.2.a.dm 3
7650.2.a.dn 3
7650.2.a.do 3
7650.2.a.dp 3
7650.2.c \(\chi_{7650}(1801, \cdot)\) n/a 142 1
7650.2.d \(\chi_{7650}(2449, \cdot)\) n/a 120 1
7650.2.f \(\chi_{7650}(4249, \cdot)\) n/a 136 1
7650.2.i \(\chi_{7650}(2551, \cdot)\) n/a 608 2
7650.2.j \(\chi_{7650}(1007, \cdot)\) n/a 216 2
7650.2.m \(\chi_{7650}(3707, \cdot)\) n/a 192 2
7650.2.n \(\chi_{7650}(6949, \cdot)\) n/a 272 2
7650.2.q \(\chi_{7650}(4501, \cdot)\) n/a 284 2
7650.2.r \(\chi_{7650}(5507, \cdot)\) n/a 216 2
7650.2.u \(\chi_{7650}(557, \cdot)\) n/a 216 2
7650.2.v \(\chi_{7650}(1531, \cdot)\) n/a 800 4
7650.2.y \(\chi_{7650}(1699, \cdot)\) n/a 648 2
7650.2.ba \(\chi_{7650}(4999, \cdot)\) n/a 576 2
7650.2.bb \(\chi_{7650}(4351, \cdot)\) n/a 684 2
7650.2.bd \(\chi_{7650}(451, \cdot)\) n/a 572 4
7650.2.bf \(\chi_{7650}(2807, \cdot)\) n/a 432 4
7650.2.bi \(\chi_{7650}(593, \cdot)\) n/a 432 4
7650.2.bk \(\chi_{7650}(1549, \cdot)\) n/a 536 4
7650.2.bm \(\chi_{7650}(919, \cdot)\) n/a 800 4
7650.2.bn \(\chi_{7650}(271, \cdot)\) n/a 904 4
7650.2.br \(\chi_{7650}(1189, \cdot)\) n/a 896 4
7650.2.bs \(\chi_{7650}(293, \cdot)\) n/a 1296 4
7650.2.bv \(\chi_{7650}(407, \cdot)\) n/a 1296 4
7650.2.bw \(\chi_{7650}(1951, \cdot)\) n/a 1368 4
7650.2.bz \(\chi_{7650}(1849, \cdot)\) n/a 1296 4
7650.2.ca \(\chi_{7650}(443, \cdot)\) n/a 1152 4
7650.2.cd \(\chi_{7650}(3557, \cdot)\) n/a 1296 4
7650.2.ce \(\chi_{7650}(511, \cdot)\) n/a 3840 8
7650.2.cg \(\chi_{7650}(343, \cdot)\) n/a 1080 8
7650.2.ci \(\chi_{7650}(1151, \cdot)\) n/a 912 8
7650.2.ck \(\chi_{7650}(449, \cdot)\) n/a 864 8
7650.2.cl \(\chi_{7650}(793, \cdot)\) n/a 1080 8
7650.2.co \(\chi_{7650}(863, \cdot)\) n/a 1440 8
7650.2.cq \(\chi_{7650}(917, \cdot)\) n/a 1440 8
7650.2.cr \(\chi_{7650}(361, \cdot)\) n/a 1808 8
7650.2.cu \(\chi_{7650}(829, \cdot)\) n/a 1792 8
7650.2.cv \(\chi_{7650}(647, \cdot)\) n/a 1280 8
7650.2.cx \(\chi_{7650}(1313, \cdot)\) n/a 1440 8
7650.2.cz \(\chi_{7650}(49, \cdot)\) n/a 2592 8
7650.2.dc \(\chi_{7650}(1607, \cdot)\) n/a 2592 8
7650.2.dd \(\chi_{7650}(257, \cdot)\) n/a 2592 8
7650.2.dg \(\chi_{7650}(151, \cdot)\) n/a 2736 8
7650.2.dh \(\chi_{7650}(169, \cdot)\) n/a 4320 8
7650.2.dl \(\chi_{7650}(781, \cdot)\) n/a 4320 8
7650.2.dm \(\chi_{7650}(409, \cdot)\) n/a 3840 8
7650.2.do \(\chi_{7650}(19, \cdot)\) n/a 3616 16
7650.2.dr \(\chi_{7650}(287, \cdot)\) n/a 2880 16
7650.2.ds \(\chi_{7650}(53, \cdot)\) n/a 2880 16
7650.2.dv \(\chi_{7650}(631, \cdot)\) n/a 3584 16
7650.2.dx \(\chi_{7650}(193, \cdot)\) n/a 5184 16
7650.2.dy \(\chi_{7650}(299, \cdot)\) n/a 5184 16
7650.2.ea \(\chi_{7650}(401, \cdot)\) n/a 5472 16
7650.2.ec \(\chi_{7650}(7, \cdot)\) n/a 5184 16
7650.2.ef \(\chi_{7650}(47, \cdot)\) n/a 8640 16
7650.2.eh \(\chi_{7650}(137, \cdot)\) n/a 7680 16
7650.2.ei \(\chi_{7650}(259, \cdot)\) n/a 8640 16
7650.2.el \(\chi_{7650}(421, \cdot)\) n/a 8640 16
7650.2.em \(\chi_{7650}(203, \cdot)\) n/a 8640 16
7650.2.eo \(\chi_{7650}(353, \cdot)\) n/a 8640 16
7650.2.er \(\chi_{7650}(37, \cdot)\) n/a 7200 32
7650.2.et \(\chi_{7650}(269, \cdot)\) n/a 5760 32
7650.2.ev \(\chi_{7650}(71, \cdot)\) n/a 5760 32
7650.2.ew \(\chi_{7650}(73, \cdot)\) n/a 7200 32
7650.2.ey \(\chi_{7650}(121, \cdot)\) n/a 17280 32
7650.2.fa \(\chi_{7650}(77, \cdot)\) n/a 17280 32
7650.2.fd \(\chi_{7650}(263, \cdot)\) n/a 17280 32
7650.2.ff \(\chi_{7650}(229, \cdot)\) n/a 17280 32
7650.2.fh \(\chi_{7650}(133, \cdot)\) n/a 34560 64
7650.2.fi \(\chi_{7650}(11, \cdot)\) n/a 34560 64
7650.2.fk \(\chi_{7650}(29, \cdot)\) n/a 34560 64
7650.2.fm \(\chi_{7650}(97, \cdot)\) n/a 34560 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7650))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7650)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(306))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(510))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(765))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(850))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1530))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2550))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3825))\)\(^{\oplus 2}\)