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Properties

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

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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

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