# Properties

 Label 7600.2 Level 7600 Weight 2 Dimension 887747 Nonzero newspaces 84 Sturm bound 6912000

## Defining parameters

 Level: $$N$$ = $$7600 = 2^{4} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$84$$ Sturm bound: $$6912000$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(7600))$$.

Total New Old
Modular forms 1742112 894019 848093
Cusp forms 1713889 887747 826142
Eisenstein series 28223 6272 21951

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(7600))$$

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
7600.2.a $$\chi_{7600}(1, \cdot)$$ 7600.2.a.a 1 1
7600.2.a.b 1
7600.2.a.c 1
7600.2.a.d 1
7600.2.a.e 1
7600.2.a.f 1
7600.2.a.g 1
7600.2.a.h 1
7600.2.a.i 1
7600.2.a.j 1
7600.2.a.k 1
7600.2.a.l 1
7600.2.a.m 1
7600.2.a.n 1
7600.2.a.o 1
7600.2.a.p 1
7600.2.a.q 1
7600.2.a.r 1
7600.2.a.s 1
7600.2.a.t 1
7600.2.a.u 2
7600.2.a.v 2
7600.2.a.w 2
7600.2.a.x 2
7600.2.a.y 2
7600.2.a.z 2
7600.2.a.ba 2
7600.2.a.bb 2
7600.2.a.bc 2
7600.2.a.bd 2
7600.2.a.be 2
7600.2.a.bf 2
7600.2.a.bg 2
7600.2.a.bh 3
7600.2.a.bi 3
7600.2.a.bj 3
7600.2.a.bk 3
7600.2.a.bl 3
7600.2.a.bm 3
7600.2.a.bn 3
7600.2.a.bo 3
7600.2.a.bp 3
7600.2.a.bq 3
7600.2.a.br 3
7600.2.a.bs 3
7600.2.a.bt 3
7600.2.a.bu 3
7600.2.a.bv 3
7600.2.a.bw 3
7600.2.a.bx 3
7600.2.a.by 3
7600.2.a.bz 3
7600.2.a.ca 3
7600.2.a.cb 3
7600.2.a.cc 3
7600.2.a.cd 3
7600.2.a.ce 4
7600.2.a.cf 4
7600.2.a.cg 6
7600.2.a.ch 6
7600.2.a.ci 6
7600.2.a.cj 6
7600.2.a.ck 6
7600.2.a.cl 6
7600.2.a.cm 6
7600.2.a.cn 6
7600.2.d $$\chi_{7600}(3649, \cdot)$$ n/a 162 1
7600.2.e $$\chi_{7600}(151, \cdot)$$ None 0 1
7600.2.f $$\chi_{7600}(3801, \cdot)$$ None 0 1
7600.2.g $$\chi_{7600}(7599, \cdot)$$ n/a 180 1
7600.2.j $$\chi_{7600}(3951, \cdot)$$ n/a 190 1
7600.2.k $$\chi_{7600}(7449, \cdot)$$ None 0 1
7600.2.p $$\chi_{7600}(3799, \cdot)$$ None 0 1
7600.2.q $$\chi_{7600}(2401, \cdot)$$ n/a 374 2
7600.2.r $$\chi_{7600}(4293, \cdot)$$ n/a 1432 2
7600.2.t $$\chi_{7600}(6043, \cdot)$$ n/a 1296 2
7600.2.w $$\chi_{7600}(1899, \cdot)$$ n/a 1432 2
7600.2.y $$\chi_{7600}(1901, \cdot)$$ n/a 1368 2
7600.2.bb $$\chi_{7600}(2393, \cdot)$$ None 0 2
7600.2.bc $$\chi_{7600}(1407, \cdot)$$ n/a 324 2
7600.2.bd $$\chi_{7600}(3457, \cdot)$$ n/a 356 2
7600.2.be $$\chi_{7600}(343, \cdot)$$ None 0 2
7600.2.bi $$\chi_{7600}(1749, \cdot)$$ n/a 1296 2
7600.2.bk $$\chi_{7600}(2051, \cdot)$$ n/a 1508 2
7600.2.bl $$\chi_{7600}(2243, \cdot)$$ n/a 1296 2
7600.2.bn $$\chi_{7600}(493, \cdot)$$ n/a 1432 2
7600.2.bp $$\chi_{7600}(1521, \cdot)$$ n/a 1080 4
7600.2.bq $$\chi_{7600}(2249, \cdot)$$ None 0 2
7600.2.br $$\chi_{7600}(1551, \cdot)$$ n/a 380 2
7600.2.bw $$\chi_{7600}(1399, \cdot)$$ None 0 2
7600.2.bz $$\chi_{7600}(3751, \cdot)$$ None 0 2
7600.2.ca $$\chi_{7600}(49, \cdot)$$ n/a 356 2
7600.2.cb $$\chi_{7600}(3599, \cdot)$$ n/a 360 2
7600.2.cc $$\chi_{7600}(201, \cdot)$$ None 0 2
7600.2.cf $$\chi_{7600}(1201, \cdot)$$ n/a 1122 6
7600.2.ci $$\chi_{7600}(1369, \cdot)$$ None 0 4
7600.2.cj $$\chi_{7600}(911, \cdot)$$ n/a 1200 4
7600.2.ck $$\chi_{7600}(759, \cdot)$$ None 0 4
7600.2.cn $$\chi_{7600}(1671, \cdot)$$ None 0 4
7600.2.co $$\chi_{7600}(609, \cdot)$$ n/a 1080 4
7600.2.ct $$\chi_{7600}(1519, \cdot)$$ n/a 1200 4
7600.2.cu $$\chi_{7600}(761, \cdot)$$ None 0 4
7600.2.cv $$\chi_{7600}(4093, \cdot)$$ n/a 2864 4
7600.2.cx $$\chi_{7600}(4643, \cdot)$$ n/a 2864 4
7600.2.da $$\chi_{7600}(501, \cdot)$$ n/a 3016 4
7600.2.dc $$\chi_{7600}(1699, \cdot)$$ n/a 2864 4
7600.2.dd $$\chi_{7600}(3257, \cdot)$$ None 0 4
7600.2.de $$\chi_{7600}(543, \cdot)$$ n/a 720 4
7600.2.dj $$\chi_{7600}(1057, \cdot)$$ n/a 712 4
7600.2.dk $$\chi_{7600}(7, \cdot)$$ None 0 4
7600.2.dm $$\chi_{7600}(1851, \cdot)$$ n/a 3016 4
7600.2.do $$\chi_{7600}(349, \cdot)$$ n/a 2864 4
7600.2.dp $$\chi_{7600}(843, \cdot)$$ n/a 2864 4
7600.2.dr $$\chi_{7600}(293, \cdot)$$ n/a 2864 4
7600.2.dt $$\chi_{7600}(881, \cdot)$$ n/a 2384 8
7600.2.du $$\chi_{7600}(599, \cdot)$$ None 0 6
7600.2.dz $$\chi_{7600}(2201, \cdot)$$ None 0 6
7600.2.ea $$\chi_{7600}(1199, \cdot)$$ n/a 1080 6
7600.2.ed $$\chi_{7600}(2049, \cdot)$$ n/a 1068 6
7600.2.ee $$\chi_{7600}(1351, \cdot)$$ None 0 6
7600.2.ef $$\chi_{7600}(751, \cdot)$$ n/a 1140 6
7600.2.eg $$\chi_{7600}(1049, \cdot)$$ None 0 6
7600.2.ek $$\chi_{7600}(37, \cdot)$$ n/a 9568 8
7600.2.em $$\chi_{7600}(267, \cdot)$$ n/a 8640 8
7600.2.en $$\chi_{7600}(381, \cdot)$$ n/a 8640 8
7600.2.ep $$\chi_{7600}(379, \cdot)$$ n/a 9568 8
7600.2.et $$\chi_{7600}(647, \cdot)$$ None 0 8
7600.2.eu $$\chi_{7600}(113, \cdot)$$ n/a 2384 8
7600.2.ev $$\chi_{7600}(1103, \cdot)$$ n/a 2160 8
7600.2.ew $$\chi_{7600}(873, \cdot)$$ None 0 8
7600.2.ez $$\chi_{7600}(531, \cdot)$$ n/a 9568 8
7600.2.fb $$\chi_{7600}(229, \cdot)$$ n/a 8640 8
7600.2.fe $$\chi_{7600}(1027, \cdot)$$ n/a 8640 8
7600.2.fg $$\chi_{7600}(797, \cdot)$$ n/a 9568 8
7600.2.fh $$\chi_{7600}(1489, \cdot)$$ n/a 2384 8
7600.2.fi $$\chi_{7600}(711, \cdot)$$ None 0 8
7600.2.fn $$\chi_{7600}(121, \cdot)$$ None 0 8
7600.2.fo $$\chi_{7600}(559, \cdot)$$ n/a 2400 8
7600.2.fr $$\chi_{7600}(31, \cdot)$$ n/a 2400 8
7600.2.fs $$\chi_{7600}(729, \cdot)$$ None 0 8
7600.2.ft $$\chi_{7600}(1319, \cdot)$$ None 0 8
7600.2.fw $$\chi_{7600}(149, \cdot)$$ n/a 8592 12
7600.2.fx $$\chi_{7600}(51, \cdot)$$ n/a 9048 12
7600.2.gc $$\chi_{7600}(193, \cdot)$$ n/a 2136 12
7600.2.gd $$\chi_{7600}(807, \cdot)$$ None 0 12
7600.2.gg $$\chi_{7600}(643, \cdot)$$ n/a 8592 12
7600.2.gh $$\chi_{7600}(357, \cdot)$$ n/a 8592 12
7600.2.gk $$\chi_{7600}(1093, \cdot)$$ n/a 8592 12
7600.2.gl $$\chi_{7600}(43, \cdot)$$ n/a 8592 12
7600.2.go $$\chi_{7600}(393, \cdot)$$ None 0 12
7600.2.gp $$\chi_{7600}(207, \cdot)$$ n/a 2160 12
7600.2.gq $$\chi_{7600}(101, \cdot)$$ n/a 9048 12
7600.2.gr $$\chi_{7600}(299, \cdot)$$ n/a 8592 12
7600.2.gu $$\chi_{7600}(81, \cdot)$$ n/a 7152 24
7600.2.gw $$\chi_{7600}(373, \cdot)$$ n/a 19136 16
7600.2.gy $$\chi_{7600}(387, \cdot)$$ n/a 19136 16
7600.2.gz $$\chi_{7600}(179, \cdot)$$ n/a 19136 16
7600.2.hb $$\chi_{7600}(581, \cdot)$$ n/a 19136 16
7600.2.hd $$\chi_{7600}(87, \cdot)$$ None 0 16
7600.2.he $$\chi_{7600}(673, \cdot)$$ n/a 4768 16
7600.2.hj $$\chi_{7600}(463, \cdot)$$ n/a 4800 16
7600.2.hk $$\chi_{7600}(217, \cdot)$$ None 0 16
7600.2.hl $$\chi_{7600}(429, \cdot)$$ n/a 19136 16
7600.2.hn $$\chi_{7600}(331, \cdot)$$ n/a 19136 16
7600.2.hq $$\chi_{7600}(83, \cdot)$$ n/a 19136 16
7600.2.hs $$\chi_{7600}(597, \cdot)$$ n/a 19136 16
7600.2.ht $$\chi_{7600}(79, \cdot)$$ n/a 7200 24
7600.2.hu $$\chi_{7600}(441, \cdot)$$ None 0 24
7600.2.hz $$\chi_{7600}(279, \cdot)$$ None 0 24
7600.2.ic $$\chi_{7600}(9, \cdot)$$ None 0 24
7600.2.id $$\chi_{7600}(431, \cdot)$$ n/a 7200 24
7600.2.ie $$\chi_{7600}(71, \cdot)$$ None 0 24
7600.2.if $$\chi_{7600}(289, \cdot)$$ n/a 7152 24
7600.2.ik $$\chi_{7600}(91, \cdot)$$ n/a 57408 48
7600.2.il $$\chi_{7600}(309, \cdot)$$ n/a 57408 48
7600.2.im $$\chi_{7600}(47, \cdot)$$ n/a 14400 48
7600.2.in $$\chi_{7600}(553, \cdot)$$ None 0 48
7600.2.iq $$\chi_{7600}(123, \cdot)$$ n/a 57408 48
7600.2.ir $$\chi_{7600}(53, \cdot)$$ n/a 57408 48
7600.2.iu $$\chi_{7600}(13, \cdot)$$ n/a 57408 48
7600.2.iv $$\chi_{7600}(187, \cdot)$$ n/a 57408 48
7600.2.iy $$\chi_{7600}(23, \cdot)$$ None 0 48
7600.2.iz $$\chi_{7600}(33, \cdot)$$ n/a 14304 48
7600.2.je $$\chi_{7600}(59, \cdot)$$ n/a 57408 48
7600.2.jf $$\chi_{7600}(61, \cdot)$$ n/a 57408 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(7600))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(7600)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(200))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(380))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(400))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(475))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(760))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(950))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1520))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1900))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3800))$$$$^{\oplus 2}$$