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Properties

Label 19275.2
Level 19275
Weight 2
Dimension 9120402
Nonzero newspaces 68
Sturm bound 52838400

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Defining parameters

Level: \( N \) = \( 19275 = 3 \cdot 5^{2} \cdot 257 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 68 \)
Sturm bound: \(52838400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(19275))\).

Total New Old
Modular forms 13238272 9141314 4096958
Cusp forms 13180929 9120402 4060527
Eisenstein series 57343 20912 36431

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(19275))\)

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
19275.2.a \(\chi_{19275}(1, \cdot)\) n/a 810 1
19275.2.c \(\chi_{19275}(10024, \cdot)\) n/a 768 1
19275.2.e \(\chi_{19275}(6424, \cdot)\) n/a 776 1
19275.2.g \(\chi_{19275}(15676, \cdot)\) n/a 816 1
19275.2.j \(\chi_{19275}(17749, \cdot)\) n/a 1552 2
19275.2.k \(\chi_{19275}(2843, \cdot)\) n/a 3088 2
19275.2.m \(\chi_{19275}(10793, \cdot)\) n/a 3088 2
19275.2.n \(\chi_{19275}(2057, \cdot)\) n/a 3072 2
19275.2.q \(\chi_{19275}(3068, \cdot)\) n/a 3088 2
19275.2.t \(\chi_{19275}(7726, \cdot)\) n/a 1632 2
19275.2.u \(\chi_{19275}(3856, \cdot)\) n/a 5120 4
19275.2.v \(\chi_{19275}(1024, \cdot)\) n/a 3104 4
19275.2.z \(\chi_{19275}(7457, \cdot)\) n/a 6176 4
19275.2.ba \(\chi_{19275}(518, \cdot)\) n/a 6176 4
19275.2.bb \(\chi_{19275}(5401, \cdot)\) n/a 3264 4
19275.2.bd \(\chi_{19275}(256, \cdot)\) n/a 5168 4
19275.2.bg \(\chi_{19275}(2314, \cdot)\) n/a 5120 4
19275.2.bi \(\chi_{19275}(2569, \cdot)\) n/a 5152 4
19275.2.bk \(\chi_{19275}(3349, \cdot)\) n/a 6208 8
19275.2.bn \(\chi_{19275}(1157, \cdot)\) n/a 12352 8
19275.2.bo \(\chi_{19275}(32, \cdot)\) n/a 12352 8
19275.2.br \(\chi_{19275}(1801, \cdot)\) n/a 6528 8
19275.2.bs \(\chi_{19275}(16, \cdot)\) n/a 10336 8
19275.2.bv \(\chi_{19275}(2297, \cdot)\) n/a 20608 8
19275.2.by \(\chi_{19275}(2828, \cdot)\) n/a 20480 8
19275.2.bz \(\chi_{19275}(2312, \cdot)\) n/a 20608 8
19275.2.cb \(\chi_{19275}(2072, \cdot)\) n/a 20608 8
19275.2.cc \(\chi_{19275}(2329, \cdot)\) n/a 10304 8
19275.2.cf \(\chi_{19275}(1576, \cdot)\) n/a 13056 16
19275.2.ch \(\chi_{19275}(68, \cdot)\) n/a 24704 16
19275.2.ci \(\chi_{19275}(6818, \cdot)\) n/a 24704 16
19275.2.ck \(\chi_{19275}(274, \cdot)\) n/a 12416 16
19275.2.cn \(\chi_{19275}(1546, \cdot)\) n/a 20672 16
19275.2.co \(\chi_{19275}(1538, \cdot)\) n/a 41216 16
19275.2.cp \(\chi_{19275}(578, \cdot)\) n/a 41216 16
19275.2.ct \(\chi_{19275}(4, \cdot)\) n/a 20608 16
19275.2.cv \(\chi_{19275}(368, \cdot)\) n/a 49408 32
19275.2.cw \(\chi_{19275}(301, \cdot)\) n/a 26112 32
19275.2.cz \(\chi_{19275}(349, \cdot)\) n/a 24832 32
19275.2.da \(\chi_{19275}(1682, \cdot)\) n/a 49408 32
19275.2.dd \(\chi_{19275}(1036, \cdot)\) n/a 41344 32
19275.2.df \(\chi_{19275}(2, \cdot)\) n/a 82432 32
19275.2.dg \(\chi_{19275}(773, \cdot)\) n/a 82432 32
19275.2.di \(\chi_{19275}(259, \cdot)\) n/a 41216 32
19275.2.dk \(\chi_{19275}(293, \cdot)\) n/a 98816 64
19275.2.dn \(\chi_{19275}(49, \cdot)\) n/a 49408 64
19275.2.dp \(\chi_{19275}(226, \cdot)\) n/a 52352 64
19275.2.dr \(\chi_{19275}(143, \cdot)\) n/a 98816 64
19275.2.ds \(\chi_{19275}(34, \cdot)\) n/a 82432 64
19275.2.dv \(\chi_{19275}(17, \cdot)\) n/a 164864 64
19275.2.dw \(\chi_{19275}(137, \cdot)\) n/a 164864 64
19275.2.dz \(\chi_{19275}(121, \cdot)\) n/a 82688 64
19275.2.ea \(\chi_{19275}(74, \cdot)\) n/a 197632 128
19275.2.ed \(\chi_{19275}(82, \cdot)\) n/a 99072 128
19275.2.ef \(\chi_{19275}(7, \cdot)\) n/a 99072 128
19275.2.eg \(\chi_{19275}(101, \cdot)\) n/a 208384 128
19275.2.ei \(\chi_{19275}(92, \cdot)\) n/a 329728 128
19275.2.ek \(\chi_{19275}(46, \cdot)\) n/a 165376 128
19275.2.en \(\chi_{19275}(169, \cdot)\) n/a 164864 128
19275.2.ep \(\chi_{19275}(23, \cdot)\) n/a 329728 128
19275.2.eq \(\chi_{19275}(98, \cdot)\) n/a 659456 256
19275.2.es \(\chi_{19275}(31, \cdot)\) n/a 329728 256
19275.2.eu \(\chi_{19275}(79, \cdot)\) n/a 330752 256
19275.2.ex \(\chi_{19275}(62, \cdot)\) n/a 659456 256
19275.2.ez \(\chi_{19275}(41, \cdot)\) n/a 1318912 512
19275.2.fa \(\chi_{19275}(112, \cdot)\) n/a 660480 512
19275.2.fc \(\chi_{19275}(28, \cdot)\) n/a 660480 512
19275.2.ff \(\chi_{19275}(14, \cdot)\) n/a 1318912 512

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(19275))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(19275)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(257))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(771))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3855))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6425))\)\(^{\oplus 2}\)