↑

Properties

Label 6275.2
Level 6275
Weight 2
Dimension 1446476
Nonzero newspaces 51
Sturm bound 6300000

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 6275 = 5^{2} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 51 \)
Sturm bound: \(6300000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6275))\).

Total New Old
Modular forms 1582000 1456684 125316
Cusp forms 1568001 1446476 121525
Eisenstein series 13999 10208 3791

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6275))\)

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
6275.2.a \(\chi_{6275}(1, \cdot)\) 6275.2.a.a 2 1
6275.2.a.b 4
6275.2.a.c 4
6275.2.a.d 14
6275.2.a.e 17
6275.2.a.f 18
6275.2.a.g 21
6275.2.a.h 24
6275.2.a.i 42
6275.2.a.j 42
6275.2.a.k 42
6275.2.a.l 42
6275.2.a.m 48
6275.2.a.n 76
6275.2.b \(\chi_{6275}(5774, \cdot)\) n/a 376 1
6275.2.e \(\chi_{6275}(2007, \cdot)\) n/a 752 2
6275.2.g \(\chi_{6275}(2121, \cdot)\) n/a 2512 4
6275.2.h \(\chi_{6275}(271, \cdot)\) n/a 2512 4
6275.2.i \(\chi_{6275}(1256, \cdot)\) n/a 2504 4
6275.2.j \(\chi_{6275}(721, \cdot)\) n/a 2512 4
6275.2.k \(\chi_{6275}(866, \cdot)\) n/a 2512 4
6275.2.l \(\chi_{6275}(651, \cdot)\) n/a 1584 4
6275.2.n \(\chi_{6275}(149, \cdot)\) n/a 1504 4
6275.2.t \(\chi_{6275}(219, \cdot)\) n/a 2512 4
6275.2.y \(\chi_{6275}(754, \cdot)\) n/a 2496 4
6275.2.z \(\chi_{6275}(3914, \cdot)\) n/a 2512 4
6275.2.ba \(\chi_{6275}(1619, \cdot)\) n/a 2512 4
6275.2.bb \(\chi_{6275}(364, \cdot)\) n/a 2512 4
6275.2.bf \(\chi_{6275}(32, \cdot)\) n/a 3008 8
6275.2.bg \(\chi_{6275}(1608, \cdot)\) n/a 5024 8
6275.2.bl \(\chi_{6275}(138, \cdot)\) n/a 5024 8
6275.2.bm \(\chi_{6275}(1142, \cdot)\) n/a 5024 8
6275.2.bn \(\chi_{6275}(102, \cdot)\) n/a 5024 8
6275.2.bo \(\chi_{6275}(752, \cdot)\) n/a 5024 8
6275.2.bq \(\chi_{6275}(51, \cdot)\) n/a 7920 20
6275.2.br \(\chi_{6275}(91, \cdot)\) n/a 12560 20
6275.2.bs \(\chi_{6275}(331, \cdot)\) n/a 12560 20
6275.2.bt \(\chi_{6275}(16, \cdot)\) n/a 12560 20
6275.2.bu \(\chi_{6275}(1306, \cdot)\) n/a 12560 20
6275.2.bw \(\chi_{6275}(69, \cdot)\) n/a 12560 20
6275.2.cc \(\chi_{6275}(4, \cdot)\) n/a 12560 20
6275.2.cd \(\chi_{6275}(94, \cdot)\) n/a 12560 20
6275.2.cg \(\chi_{6275}(249, \cdot)\) n/a 7520 20
6275.2.ch \(\chi_{6275}(804, \cdot)\) n/a 12560 20
6275.2.cl \(\chi_{6275}(47, \cdot)\) n/a 25120 40
6275.2.cn \(\chi_{6275}(2, \cdot)\) n/a 25120 40
6275.2.cp \(\chi_{6275}(188, \cdot)\) n/a 25120 40
6275.2.cr \(\chi_{6275}(157, \cdot)\) n/a 15040 40
6275.2.ct \(\chi_{6275}(187, \cdot)\) n/a 25120 40
6275.2.cu \(\chi_{6275}(21, \cdot)\) n/a 62800 100
6275.2.cv \(\chi_{6275}(41, \cdot)\) n/a 62800 100
6275.2.cw \(\chi_{6275}(101, \cdot)\) n/a 39600 100
6275.2.cx \(\chi_{6275}(66, \cdot)\) n/a 62800 100
6275.2.cy \(\chi_{6275}(266, \cdot)\) n/a 62800 100
6275.2.df \(\chi_{6275}(89, \cdot)\) n/a 62800 100
6275.2.dg \(\chi_{6275}(9, \cdot)\) n/a 62800 100
6275.2.dk \(\chi_{6275}(49, \cdot)\) n/a 37600 100
6275.2.dl \(\chi_{6275}(154, \cdot)\) n/a 62800 100
6275.2.dm \(\chi_{6275}(79, \cdot)\) n/a 62800 100
6275.2.dp \(\chi_{6275}(37, \cdot)\) n/a 125600 200
6275.2.dq \(\chi_{6275}(33, \cdot)\) n/a 125600 200
6275.2.du \(\chi_{6275}(97, \cdot)\) n/a 125600 200
6275.2.dv \(\chi_{6275}(18, \cdot)\) n/a 75200 200
6275.2.dw \(\chi_{6275}(72, \cdot)\) n/a 125600 200

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6275))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6275)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(251))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1255))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6275))\)\(^{\oplus 1}\)