Properties

 Label 6525.2 Level 6525 Weight 2 Dimension 1095627 Nonzero newspaces 80 Sturm bound 6048000

Defining parameters

 Level: $$N$$ = $$6525 = 3^{2} \cdot 5^{2} \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$80$$ Sturm bound: $$6048000$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6525))$$.

Total New Old
Modular forms 1524544 1105589 418955
Cusp forms 1499457 1095627 403830
Eisenstein series 25087 9962 15125

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6525))$$

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
6525.2.a $$\chi_{6525}(1, \cdot)$$ 6525.2.a.a 1 1
6525.2.a.b 1
6525.2.a.c 1
6525.2.a.d 1
6525.2.a.e 1
6525.2.a.f 1
6525.2.a.g 1
6525.2.a.h 1
6525.2.a.i 1
6525.2.a.j 1
6525.2.a.k 1
6525.2.a.l 1
6525.2.a.m 1
6525.2.a.n 2
6525.2.a.o 2
6525.2.a.p 2
6525.2.a.q 2
6525.2.a.r 2
6525.2.a.s 2
6525.2.a.t 2
6525.2.a.u 2
6525.2.a.v 2
6525.2.a.w 2
6525.2.a.x 2
6525.2.a.y 2
6525.2.a.z 2
6525.2.a.ba 2
6525.2.a.bb 2
6525.2.a.bc 2
6525.2.a.bd 2
6525.2.a.be 3
6525.2.a.bf 3
6525.2.a.bg 3
6525.2.a.bh 3
6525.2.a.bi 4
6525.2.a.bj 4
6525.2.a.bk 4
6525.2.a.bl 5
6525.2.a.bm 5
6525.2.a.bn 5
6525.2.a.bo 5
6525.2.a.bp 5
6525.2.a.bq 5
6525.2.a.br 5
6525.2.a.bs 5
6525.2.a.bt 6
6525.2.a.bu 7
6525.2.a.bv 7
6525.2.a.bw 7
6525.2.a.bx 7
6525.2.a.by 8
6525.2.a.bz 8
6525.2.a.ca 9
6525.2.a.cb 9
6525.2.a.cc 9
6525.2.a.cd 9
6525.2.a.ce 12
6525.2.a.cf 12
6525.2.c $$\chi_{6525}(4699, \cdot)$$ n/a 210 1
6525.2.d $$\chi_{6525}(4726, \cdot)$$ n/a 234 1
6525.2.f $$\chi_{6525}(2899, \cdot)$$ n/a 224 1
6525.2.i $$\chi_{6525}(2176, \cdot)$$ n/a 1064 2
6525.2.k $$\chi_{6525}(568, \cdot)$$ n/a 446 2
6525.2.m $$\chi_{6525}(3149, \cdot)$$ n/a 360 2
6525.2.n $$\chi_{6525}(2582, \cdot)$$ n/a 336 2
6525.2.q $$\chi_{6525}(782, \cdot)$$ n/a 360 2
6525.2.r $$\chi_{6525}(476, \cdot)$$ n/a 380 2
6525.2.t $$\chi_{6525}(307, \cdot)$$ n/a 446 2
6525.2.v $$\chi_{6525}(1306, \cdot)$$ n/a 1400 4
6525.2.x $$\chi_{6525}(724, \cdot)$$ n/a 1072 2
6525.2.z $$\chi_{6525}(376, \cdot)$$ n/a 1128 2
6525.2.bc $$\chi_{6525}(349, \cdot)$$ n/a 1008 2
6525.2.bd $$\chi_{6525}(226, \cdot)$$ n/a 1410 6
6525.2.bf $$\chi_{6525}(289, \cdot)$$ n/a 1488 4
6525.2.bh $$\chi_{6525}(784, \cdot)$$ n/a 1400 4
6525.2.bk $$\chi_{6525}(811, \cdot)$$ n/a 1496 4
6525.2.bl $$\chi_{6525}(418, \cdot)$$ n/a 2144 4
6525.2.bo $$\chi_{6525}(626, \cdot)$$ n/a 2256 4
6525.2.bq $$\chi_{6525}(2957, \cdot)$$ n/a 2144 4
6525.2.br $$\chi_{6525}(407, \cdot)$$ n/a 2016 4
6525.2.bt $$\chi_{6525}(824, \cdot)$$ n/a 2144 4
6525.2.bw $$\chi_{6525}(157, \cdot)$$ n/a 2144 4
6525.2.bz $$\chi_{6525}(874, \cdot)$$ n/a 1344 6
6525.2.cb $$\chi_{6525}(676, \cdot)$$ n/a 1404 6
6525.2.cc $$\chi_{6525}(199, \cdot)$$ n/a 1332 6
6525.2.ce $$\chi_{6525}(436, \cdot)$$ n/a 6720 8
6525.2.cg $$\chi_{6525}(1288, \cdot)$$ n/a 2984 8
6525.2.ch $$\chi_{6525}(539, \cdot)$$ n/a 2400 8
6525.2.cj $$\chi_{6525}(2087, \cdot)$$ n/a 2400 8
6525.2.cm $$\chi_{6525}(233, \cdot)$$ n/a 2240 8
6525.2.co $$\chi_{6525}(1061, \cdot)$$ n/a 2400 8
6525.2.cp $$\chi_{6525}(1027, \cdot)$$ n/a 2984 8
6525.2.cr $$\chi_{6525}(1051, \cdot)$$ n/a 6768 12
6525.2.ct $$\chi_{6525}(757, \cdot)$$ n/a 2676 12
6525.2.cv $$\chi_{6525}(26, \cdot)$$ n/a 2280 12
6525.2.cw $$\chi_{6525}(332, \cdot)$$ n/a 2160 12
6525.2.cz $$\chi_{6525}(107, \cdot)$$ n/a 2160 12
6525.2.da $$\chi_{6525}(224, \cdot)$$ n/a 2160 12
6525.2.dc $$\chi_{6525}(118, \cdot)$$ n/a 2676 12
6525.2.df $$\chi_{6525}(1246, \cdot)$$ n/a 7168 8
6525.2.dg $$\chi_{6525}(1219, \cdot)$$ n/a 6720 8
6525.2.dk $$\chi_{6525}(1159, \cdot)$$ n/a 7168 8
6525.2.dl $$\chi_{6525}(136, \cdot)$$ n/a 8928 24
6525.2.dm $$\chi_{6525}(49, \cdot)$$ n/a 6432 12
6525.2.dp $$\chi_{6525}(151, \cdot)$$ n/a 6768 12
6525.2.dr $$\chi_{6525}(274, \cdot)$$ n/a 6432 12
6525.2.dt $$\chi_{6525}(133, \cdot)$$ n/a 14336 16
6525.2.dv $$\chi_{6525}(41, \cdot)$$ n/a 14336 16
6525.2.dy $$\chi_{6525}(842, \cdot)$$ n/a 13440 16
6525.2.dz $$\chi_{6525}(173, \cdot)$$ n/a 14336 16
6525.2.ec $$\chi_{6525}(104, \cdot)$$ n/a 14336 16
6525.2.ee $$\chi_{6525}(742, \cdot)$$ n/a 14336 16
6525.2.ef $$\chi_{6525}(91, \cdot)$$ n/a 8976 24
6525.2.ei $$\chi_{6525}(604, \cdot)$$ n/a 8976 24
6525.2.ek $$\chi_{6525}(64, \cdot)$$ n/a 8928 24
6525.2.em $$\chi_{6525}(43, \cdot)$$ n/a 12864 24
6525.2.ep $$\chi_{6525}(374, \cdot)$$ n/a 12864 24
6525.2.er $$\chi_{6525}(257, \cdot)$$ n/a 12864 24
6525.2.es $$\chi_{6525}(932, \cdot)$$ n/a 12864 24
6525.2.eu $$\chi_{6525}(101, \cdot)$$ n/a 13536 24
6525.2.ex $$\chi_{6525}(868, \cdot)$$ n/a 12864 24
6525.2.ey $$\chi_{6525}(16, \cdot)$$ n/a 43008 48
6525.2.fa $$\chi_{6525}(37, \cdot)$$ n/a 17904 48
6525.2.fb $$\chi_{6525}(206, \cdot)$$ n/a 14400 48
6525.2.fd $$\chi_{6525}(53, \cdot)$$ n/a 14400 48
6525.2.fg $$\chi_{6525}(62, \cdot)$$ n/a 14400 48
6525.2.fi $$\chi_{6525}(44, \cdot)$$ n/a 14400 48
6525.2.fj $$\chi_{6525}(73, \cdot)$$ n/a 17904 48
6525.2.fl $$\chi_{6525}(4, \cdot)$$ n/a 43008 48
6525.2.fp $$\chi_{6525}(94, \cdot)$$ n/a 43008 48
6525.2.fq $$\chi_{6525}(121, \cdot)$$ n/a 43008 48
6525.2.fs $$\chi_{6525}(292, \cdot)$$ n/a 86016 96
6525.2.fu $$\chi_{6525}(14, \cdot)$$ n/a 86016 96
6525.2.fx $$\chi_{6525}(38, \cdot)$$ n/a 86016 96
6525.2.fy $$\chi_{6525}(23, \cdot)$$ n/a 86016 96
6525.2.gb $$\chi_{6525}(11, \cdot)$$ n/a 86016 96
6525.2.gd $$\chi_{6525}(97, \cdot)$$ n/a 86016 96

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6525))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6525)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(87))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(145))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(261))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(435))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(725))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1305))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2175))$$$$^{\oplus 2}$$