# Properties

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

## 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 the 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

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