# Properties

 Label 7400.2 Level 7400 Weight 2 Dimension 846953 Nonzero newspaces 96 Sturm bound 6566400

## Defining parameters

 Level: $$N$$ = $$7400 = 2^{3} \cdot 5^{2} \cdot 37$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$96$$ Sturm bound: $$6566400$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(7400))$$.

Total New Old
Modular forms 1653696 852693 801003
Cusp forms 1629505 846953 782552
Eisenstein series 24191 5740 18451

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(7400))$$

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
7400.2.a $$\chi_{7400}(1, \cdot)$$ 7400.2.a.a 1 1
7400.2.a.b 1
7400.2.a.c 1
7400.2.a.d 1
7400.2.a.e 1
7400.2.a.f 1
7400.2.a.g 1
7400.2.a.h 1
7400.2.a.i 1
7400.2.a.j 1
7400.2.a.k 3
7400.2.a.l 3
7400.2.a.m 3
7400.2.a.n 4
7400.2.a.o 5
7400.2.a.p 5
7400.2.a.q 5
7400.2.a.r 5
7400.2.a.s 6
7400.2.a.t 8
7400.2.a.u 8
7400.2.a.v 8
7400.2.a.w 8
7400.2.a.x 9
7400.2.a.y 9
7400.2.a.z 10
7400.2.a.ba 10
7400.2.a.bb 10
7400.2.a.bc 10
7400.2.a.bd 16
7400.2.a.be 16
7400.2.d $$\chi_{7400}(3849, \cdot)$$ n/a 162 1
7400.2.e $$\chi_{7400}(1849, \cdot)$$ n/a 172 1
7400.2.f $$\chi_{7400}(3701, \cdot)$$ n/a 684 1
7400.2.g $$\chi_{7400}(1701, \cdot)$$ n/a 716 1
7400.2.j $$\chi_{7400}(5549, \cdot)$$ n/a 680 1
7400.2.k $$\chi_{7400}(149, \cdot)$$ n/a 648 1
7400.2.p $$\chi_{7400}(5401, \cdot)$$ n/a 180 1
7400.2.q $$\chi_{7400}(1601, \cdot)$$ n/a 362 2
7400.2.r $$\chi_{7400}(2251, \cdot)$$ n/a 1432 2
7400.2.u $$\chi_{7400}(2399, \cdot)$$ None 0 2
7400.2.w $$\chi_{7400}(3657, \cdot)$$ n/a 342 2
7400.2.y $$\chi_{7400}(4143, \cdot)$$ None 0 2
7400.2.ba $$\chi_{7400}(1407, \cdot)$$ None 0 2
7400.2.bb $$\chi_{7400}(857, \cdot)$$ n/a 342 2
7400.2.bd $$\chi_{7400}(4557, \cdot)$$ n/a 1360 2
7400.2.bf $$\chi_{7400}(2443, \cdot)$$ n/a 1296 2
7400.2.bh $$\chi_{7400}(443, \cdot)$$ n/a 1360 2
7400.2.bk $$\chi_{7400}(1893, \cdot)$$ n/a 1360 2
7400.2.bm $$\chi_{7400}(3151, \cdot)$$ None 0 2
7400.2.bn $$\chi_{7400}(3299, \cdot)$$ n/a 1360 2
7400.2.bp $$\chi_{7400}(1481, \cdot)$$ n/a 1080 4
7400.2.bs $$\chi_{7400}(2601, \cdot)$$ n/a 360 2
7400.2.bt $$\chi_{7400}(1749, \cdot)$$ n/a 1360 2
7400.2.bu $$\chi_{7400}(2749, \cdot)$$ n/a 1360 2
7400.2.bx $$\chi_{7400}(101, \cdot)$$ n/a 1432 2
7400.2.by $$\chi_{7400}(5301, \cdot)$$ n/a 1432 2
7400.2.cd $$\chi_{7400}(249, \cdot)$$ n/a 344 2
7400.2.ce $$\chi_{7400}(5449, \cdot)$$ n/a 340 2
7400.2.cf $$\chi_{7400}(201, \cdot)$$ n/a 1086 6
7400.2.ci $$\chi_{7400}(1629, \cdot)$$ n/a 4320 4
7400.2.cj $$\chi_{7400}(1109, \cdot)$$ n/a 4544 4
7400.2.ck $$\chi_{7400}(961, \cdot)$$ n/a 1144 4
7400.2.cn $$\chi_{7400}(369, \cdot)$$ n/a 1136 4
7400.2.co $$\chi_{7400}(889, \cdot)$$ n/a 1080 4
7400.2.ct $$\chi_{7400}(221, \cdot)$$ n/a 4544 4
7400.2.cu $$\chi_{7400}(741, \cdot)$$ n/a 4320 4
7400.2.cv $$\chi_{7400}(3899, \cdot)$$ n/a 2720 4
7400.2.cy $$\chi_{7400}(3751, \cdot)$$ None 0 4
7400.2.da $$\chi_{7400}(2857, \cdot)$$ n/a 684 4
7400.2.db $$\chi_{7400}(343, \cdot)$$ None 0 4
7400.2.dd $$\chi_{7400}(1343, \cdot)$$ None 0 4
7400.2.df $$\chi_{7400}(193, \cdot)$$ n/a 684 4
7400.2.dh $$\chi_{7400}(3893, \cdot)$$ n/a 2720 4
7400.2.dk $$\chi_{7400}(307, \cdot)$$ n/a 2720 4
7400.2.dm $$\chi_{7400}(507, \cdot)$$ n/a 2720 4
7400.2.do $$\chi_{7400}(2493, \cdot)$$ n/a 2720 4
7400.2.dq $$\chi_{7400}(199, \cdot)$$ None 0 4
7400.2.dr $$\chi_{7400}(51, \cdot)$$ n/a 2864 4
7400.2.dt $$\chi_{7400}(121, \cdot)$$ n/a 2272 8
7400.2.dw $$\chi_{7400}(1249, \cdot)$$ n/a 1032 6
7400.2.dx $$\chi_{7400}(1801, \cdot)$$ n/a 1080 6
7400.2.dz $$\chi_{7400}(49, \cdot)$$ n/a 1020 6
7400.2.eb $$\chi_{7400}(1949, \cdot)$$ n/a 4080 6
7400.2.ed $$\chi_{7400}(2301, \cdot)$$ n/a 4296 6
7400.2.eg $$\chi_{7400}(349, \cdot)$$ n/a 4080 6
7400.2.ei $$\chi_{7400}(1101, \cdot)$$ n/a 4296 6
7400.2.ej $$\chi_{7400}(31, \cdot)$$ None 0 8
7400.2.em $$\chi_{7400}(179, \cdot)$$ n/a 9088 8
7400.2.en $$\chi_{7400}(413, \cdot)$$ n/a 9088 8
7400.2.eq $$\chi_{7400}(147, \cdot)$$ n/a 9088 8
7400.2.es $$\chi_{7400}(667, \cdot)$$ n/a 8640 8
7400.2.eu $$\chi_{7400}(117, \cdot)$$ n/a 9088 8
7400.2.ew $$\chi_{7400}(2337, \cdot)$$ n/a 2280 8
7400.2.ex $$\chi_{7400}(223, \cdot)$$ None 0 8
7400.2.ez $$\chi_{7400}(887, \cdot)$$ None 0 8
7400.2.fb $$\chi_{7400}(697, \cdot)$$ n/a 2280 8
7400.2.fe $$\chi_{7400}(771, \cdot)$$ n/a 9088 8
7400.2.ff $$\chi_{7400}(919, \cdot)$$ None 0 8
7400.2.fj $$\chi_{7400}(581, \cdot)$$ n/a 9088 8
7400.2.fk $$\chi_{7400}(381, \cdot)$$ n/a 9088 8
7400.2.fl $$\chi_{7400}(729, \cdot)$$ n/a 2288 8
7400.2.fm $$\chi_{7400}(529, \cdot)$$ n/a 2272 8
7400.2.fp $$\chi_{7400}(841, \cdot)$$ n/a 2288 8
7400.2.fu $$\chi_{7400}(989, \cdot)$$ n/a 9088 8
7400.2.fv $$\chi_{7400}(269, \cdot)$$ n/a 9088 8
7400.2.fw $$\chi_{7400}(757, \cdot)$$ n/a 8160 12
7400.2.fz $$\chi_{7400}(351, \cdot)$$ None 0 12
7400.2.ga $$\chi_{7400}(107, \cdot)$$ n/a 8160 12
7400.2.gd $$\chi_{7400}(243, \cdot)$$ n/a 8160 12
7400.2.ge $$\chi_{7400}(799, \cdot)$$ None 0 12
7400.2.gh $$\chi_{7400}(93, \cdot)$$ n/a 8160 12
7400.2.gj $$\chi_{7400}(257, \cdot)$$ n/a 2052 12
7400.2.gk $$\chi_{7400}(499, \cdot)$$ n/a 8160 12
7400.2.gm $$\chi_{7400}(543, \cdot)$$ None 0 12
7400.2.gp $$\chi_{7400}(7, \cdot)$$ None 0 12
7400.2.gr $$\chi_{7400}(651, \cdot)$$ n/a 8592 12
7400.2.gs $$\chi_{7400}(57, \cdot)$$ n/a 2052 12
7400.2.gu $$\chi_{7400}(81, \cdot)$$ n/a 6816 24
7400.2.gv $$\chi_{7400}(119, \cdot)$$ None 0 16
7400.2.gy $$\chi_{7400}(171, \cdot)$$ n/a 18176 16
7400.2.gz $$\chi_{7400}(637, \cdot)$$ n/a 18176 16
7400.2.hb $$\chi_{7400}(787, \cdot)$$ n/a 18176 16
7400.2.hd $$\chi_{7400}(27, \cdot)$$ n/a 18176 16
7400.2.hg $$\chi_{7400}(717, \cdot)$$ n/a 18176 16
7400.2.hi $$\chi_{7400}(177, \cdot)$$ n/a 4560 16
7400.2.hk $$\chi_{7400}(767, \cdot)$$ None 0 16
7400.2.hm $$\chi_{7400}(47, \cdot)$$ None 0 16
7400.2.hn $$\chi_{7400}(97, \cdot)$$ n/a 4560 16
7400.2.hq $$\chi_{7400}(859, \cdot)$$ n/a 18176 16
7400.2.hr $$\chi_{7400}(711, \cdot)$$ None 0 16
7400.2.hu $$\chi_{7400}(21, \cdot)$$ n/a 27264 24
7400.2.hw $$\chi_{7400}(229, \cdot)$$ n/a 27264 24
7400.2.hx $$\chi_{7400}(181, \cdot)$$ n/a 27264 24
7400.2.hz $$\chi_{7400}(189, \cdot)$$ n/a 27264 24
7400.2.ib $$\chi_{7400}(9, \cdot)$$ n/a 6864 24
7400.2.id $$\chi_{7400}(41, \cdot)$$ n/a 6864 24
7400.2.ig $$\chi_{7400}(169, \cdot)$$ n/a 6816 24
7400.2.ii $$\chi_{7400}(153, \cdot)$$ n/a 13680 48
7400.2.ik $$\chi_{7400}(91, \cdot)$$ n/a 54528 48
7400.2.in $$\chi_{7400}(127, \cdot)$$ None 0 48
7400.2.io $$\chi_{7400}(247, \cdot)$$ None 0 48
7400.2.ir $$\chi_{7400}(19, \cdot)$$ n/a 54528 48
7400.2.it $$\chi_{7400}(17, \cdot)$$ n/a 13680 48
7400.2.iv $$\chi_{7400}(13, \cdot)$$ n/a 54528 48
7400.2.ix $$\chi_{7400}(39, \cdot)$$ None 0 48
7400.2.iz $$\chi_{7400}(3, \cdot)$$ n/a 54528 48
7400.2.ja $$\chi_{7400}(83, \cdot)$$ n/a 54528 48
7400.2.jc $$\chi_{7400}(311, \cdot)$$ None 0 48
7400.2.je $$\chi_{7400}(533, \cdot)$$ n/a 54528 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(7400))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(7400)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(37))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(74))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(148))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(185))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(200))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(296))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(370))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(740))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(925))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1480))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1850))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3700))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7400))$$$$^{\oplus 1}$$