# Properties

 Label 7605.2 Level 7605 Weight 2 Dimension 1460457 Nonzero newspaces 100 Sturm bound 8176896

## Defining parameters

 Level: $$N$$ = $$7605 = 3^{2} \cdot 5 \cdot 13^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$100$$ Sturm bound: $$8176896$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(7605))$$.

Total New Old
Modular forms 2058816 1471499 587317
Cusp forms 2029633 1460457 569176
Eisenstein series 29183 11042 18141

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(7605))$$

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
7605.2.a $$\chi_{7605}(1, \cdot)$$ 7605.2.a.a 1 1
7605.2.a.b 1
7605.2.a.c 1
7605.2.a.d 1
7605.2.a.e 1
7605.2.a.f 1
7605.2.a.g 1
7605.2.a.h 1
7605.2.a.i 1
7605.2.a.j 1
7605.2.a.k 1
7605.2.a.l 1
7605.2.a.m 1
7605.2.a.n 1
7605.2.a.o 1
7605.2.a.p 1
7605.2.a.q 1
7605.2.a.r 1
7605.2.a.s 1
7605.2.a.t 1
7605.2.a.u 1
7605.2.a.v 1
7605.2.a.w 2
7605.2.a.x 2
7605.2.a.y 2
7605.2.a.z 2
7605.2.a.ba 2
7605.2.a.bb 2
7605.2.a.bc 2
7605.2.a.bd 2
7605.2.a.be 2
7605.2.a.bf 2
7605.2.a.bg 2
7605.2.a.bh 2
7605.2.a.bi 2
7605.2.a.bj 2
7605.2.a.bk 2
7605.2.a.bl 2
7605.2.a.bm 3
7605.2.a.bn 3
7605.2.a.bo 3
7605.2.a.bp 3
7605.2.a.bq 3
7605.2.a.br 3
7605.2.a.bs 3
7605.2.a.bt 3
7605.2.a.bu 3
7605.2.a.bv 3
7605.2.a.bw 3
7605.2.a.bx 3
7605.2.a.by 3
7605.2.a.bz 3
7605.2.a.ca 3
7605.2.a.cb 3
7605.2.a.cc 3
7605.2.a.cd 3
7605.2.a.ce 3
7605.2.a.cf 4
7605.2.a.cg 4
7605.2.a.ch 4
7605.2.a.ci 4
7605.2.a.cj 4
7605.2.a.ck 4
7605.2.a.cl 5
7605.2.a.cm 5
7605.2.a.cn 5
7605.2.a.co 5
7605.2.a.cp 9
7605.2.a.cq 9
7605.2.a.cr 9
7605.2.a.cs 9
7605.2.a.ct 10
7605.2.a.cu 10
7605.2.a.cv 12
7605.2.a.cw 12
7605.2.a.cx 12
7605.2.a.cy 12
7605.2.b $$\chi_{7605}(1351, \cdot)$$ n/a 258 1
7605.2.c $$\chi_{7605}(4564, \cdot)$$ n/a 376 1
7605.2.h $$\chi_{7605}(5914, \cdot)$$ n/a 376 1
7605.2.i $$\chi_{7605}(2536, \cdot)$$ n/a 1240 2
7605.2.j $$\chi_{7605}(991, \cdot)$$ n/a 512 2
7605.2.k $$\chi_{7605}(3571, \cdot)$$ n/a 1232 2
7605.2.l $$\chi_{7605}(3526, \cdot)$$ n/a 1232 2
7605.2.n $$\chi_{7605}(2098, \cdot)$$ n/a 750 2
7605.2.p $$\chi_{7605}(3212, \cdot)$$ n/a 620 2
7605.2.q $$\chi_{7605}(944, \cdot)$$ n/a 616 2
7605.2.r $$\chi_{7605}(746, \cdot)$$ n/a 416 2
7605.2.v $$\chi_{7605}(4562, \cdot)$$ n/a 616 2
7605.2.w $$\chi_{7605}(577, \cdot)$$ n/a 750 2
7605.2.ba $$\chi_{7605}(2896, \cdot)$$ n/a 1232 2
7605.2.bb $$\chi_{7605}(484, \cdot)$$ n/a 1808 2
7605.2.be $$\chi_{7605}(844, \cdot)$$ n/a 1808 2
7605.2.bf $$\chi_{7605}(4879, \cdot)$$ n/a 752 2
7605.2.bk $$\chi_{7605}(2389, \cdot)$$ n/a 1808 2
7605.2.bl $$\chi_{7605}(529, \cdot)$$ n/a 1808 2
7605.2.bm $$\chi_{7605}(2851, \cdot)$$ n/a 1232 2
7605.2.br $$\chi_{7605}(2029, \cdot)$$ n/a 1816 2
7605.2.bs $$\chi_{7605}(5554, \cdot)$$ n/a 748 2
7605.2.bt $$\chi_{7605}(3886, \cdot)$$ n/a 1232 2
7605.2.bu $$\chi_{7605}(316, \cdot)$$ n/a 512 2
7605.2.bx $$\chi_{7605}(2344, \cdot)$$ n/a 1808 2
7605.2.ca $$\chi_{7605}(3568, \cdot)$$ n/a 3616 4
7605.2.cc $$\chi_{7605}(1948, \cdot)$$ n/a 3616 4
7605.2.cf $$\chi_{7605}(1333, \cdot)$$ n/a 1500 4
7605.2.cg $$\chi_{7605}(268, \cdot)$$ n/a 3616 4
7605.2.ci $$\chi_{7605}(698, \cdot)$$ n/a 3616 4
7605.2.cm $$\chi_{7605}(596, \cdot)$$ n/a 2464 4
7605.2.cn $$\chi_{7605}(3629, \cdot)$$ n/a 3616 4
7605.2.co $$\chi_{7605}(1037, \cdot)$$ n/a 3616 4
7605.2.cr $$\chi_{7605}(23, \cdot)$$ n/a 3616 4
7605.2.cs $$\chi_{7605}(1013, \cdot)$$ n/a 3616 4
7605.2.cv $$\chi_{7605}(3527, \cdot)$$ n/a 1232 4
7605.2.cw $$\chi_{7605}(1601, \cdot)$$ n/a 816 4
7605.2.cx $$\chi_{7605}(89, \cdot)$$ n/a 1232 4
7605.2.dc $$\chi_{7605}(239, \cdot)$$ n/a 3616 4
7605.2.dd $$\chi_{7605}(2216, \cdot)$$ n/a 2464 4
7605.2.de $$\chi_{7605}(1094, \cdot)$$ n/a 3616 4
7605.2.df $$\chi_{7605}(1451, \cdot)$$ n/a 2464 4
7605.2.dj $$\chi_{7605}(677, \cdot)$$ n/a 3632 4
7605.2.dk $$\chi_{7605}(653, \cdot)$$ n/a 3616 4
7605.2.dn $$\chi_{7605}(4202, \cdot)$$ n/a 1232 4
7605.2.dp $$\chi_{7605}(2953, \cdot)$$ n/a 1500 4
7605.2.dq $$\chi_{7605}(1282, \cdot)$$ n/a 3616 4
7605.2.dt $$\chi_{7605}(418, \cdot)$$ n/a 3616 4
7605.2.dv $$\chi_{7605}(2047, \cdot)$$ n/a 3616 4
7605.2.dw $$\chi_{7605}(586, \cdot)$$ n/a 3624 12
7605.2.dx $$\chi_{7605}(64, \cdot)$$ n/a 5424 12
7605.2.ec $$\chi_{7605}(469, \cdot)$$ n/a 5448 12
7605.2.ed $$\chi_{7605}(181, \cdot)$$ n/a 3624 12
7605.2.ee $$\chi_{7605}(16, \cdot)$$ n/a 17472 24
7605.2.ef $$\chi_{7605}(61, \cdot)$$ n/a 17472 24
7605.2.eg $$\chi_{7605}(406, \cdot)$$ n/a 7296 24
7605.2.eh $$\chi_{7605}(196, \cdot)$$ n/a 17472 24
7605.2.ej $$\chi_{7605}(73, \cdot)$$ n/a 10872 24
7605.2.ek $$\chi_{7605}(233, \cdot)$$ n/a 8736 24
7605.2.eo $$\chi_{7605}(161, \cdot)$$ n/a 5760 24
7605.2.ep $$\chi_{7605}(44, \cdot)$$ n/a 8736 24
7605.2.eq $$\chi_{7605}(53, \cdot)$$ n/a 8736 24
7605.2.es $$\chi_{7605}(307, \cdot)$$ n/a 10872 24
7605.2.ew $$\chi_{7605}(4, \cdot)$$ n/a 26112 24
7605.2.ez $$\chi_{7605}(901, \cdot)$$ n/a 7296 24
7605.2.fa $$\chi_{7605}(376, \cdot)$$ n/a 17472 24
7605.2.fb $$\chi_{7605}(289, \cdot)$$ n/a 10896 24
7605.2.fc $$\chi_{7605}(79, \cdot)$$ n/a 26112 24
7605.2.fh $$\chi_{7605}(166, \cdot)$$ n/a 17472 24
7605.2.fi $$\chi_{7605}(94, \cdot)$$ n/a 26112 24
7605.2.fj $$\chi_{7605}(49, \cdot)$$ n/a 26112 24
7605.2.fo $$\chi_{7605}(199, \cdot)$$ n/a 10848 24
7605.2.fp $$\chi_{7605}(259, \cdot)$$ n/a 26112 24
7605.2.fs $$\chi_{7605}(139, \cdot)$$ n/a 26112 24
7605.2.ft $$\chi_{7605}(121, \cdot)$$ n/a 17472 24
7605.2.fw $$\chi_{7605}(292, \cdot)$$ n/a 52224 48
7605.2.fy $$\chi_{7605}(7, \cdot)$$ n/a 52224 48
7605.2.gb $$\chi_{7605}(112, \cdot)$$ n/a 52224 48
7605.2.gc $$\chi_{7605}(28, \cdot)$$ n/a 21744 48
7605.2.ge $$\chi_{7605}(107, \cdot)$$ n/a 17472 48
7605.2.gh $$\chi_{7605}(92, \cdot)$$ n/a 52224 48
7605.2.gi $$\chi_{7605}(68, \cdot)$$ n/a 52224 48
7605.2.gm $$\chi_{7605}(86, \cdot)$$ n/a 34944 48
7605.2.gn $$\chi_{7605}(254, \cdot)$$ n/a 52224 48
7605.2.go $$\chi_{7605}(41, \cdot)$$ n/a 34944 48
7605.2.gp $$\chi_{7605}(164, \cdot)$$ n/a 52224 48
7605.2.gu $$\chi_{7605}(314, \cdot)$$ n/a 17472 48
7605.2.gv $$\chi_{7605}(71, \cdot)$$ n/a 11712 48
7605.2.gw $$\chi_{7605}(17, \cdot)$$ n/a 17472 48
7605.2.gz $$\chi_{7605}(173, \cdot)$$ n/a 52224 48
7605.2.ha $$\chi_{7605}(38, \cdot)$$ n/a 52224 48
7605.2.hd $$\chi_{7605}(212, \cdot)$$ n/a 52224 48
7605.2.he $$\chi_{7605}(59, \cdot)$$ n/a 52224 48
7605.2.hf $$\chi_{7605}(11, \cdot)$$ n/a 34944 48
7605.2.hj $$\chi_{7605}(113, \cdot)$$ n/a 52224 48
7605.2.hl $$\chi_{7605}(187, \cdot)$$ n/a 52224 48
7605.2.hm $$\chi_{7605}(163, \cdot)$$ n/a 21744 48
7605.2.hp $$\chi_{7605}(67, \cdot)$$ n/a 52224 48
7605.2.hr $$\chi_{7605}(58, \cdot)$$ n/a 52224 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(7605))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(7605)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(507))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(585))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(845))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1521))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2535))$$$$^{\oplus 2}$$