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Properties

Label 6253.2
Level 6253
Weight 2
Dimension 1589755
Nonzero newspaces 96
Sturm bound 6473376

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Defining parameters

Level: \( N \) = \( 6253 = 13^{2} \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 96 \)
Sturm bound: \(6473376\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6253))\).

Total New Old
Modular forms 1626552 1604069 22483
Cusp forms 1610137 1589755 20382
Eisenstein series 16415 14314 2101

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6253))\)

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
6253.2.a \(\chi_{6253}(1, \cdot)\) 6253.2.a.a 1 1
6253.2.a.b 1
6253.2.a.c 1
6253.2.a.d 3
6253.2.a.e 3
6253.2.a.f 7
6253.2.a.g 7
6253.2.a.h 11
6253.2.a.i 11
6253.2.a.j 18
6253.2.a.k 18
6253.2.a.l 21
6253.2.a.m 21
6253.2.a.n 21
6253.2.a.o 21
6253.2.a.p 42
6253.2.a.q 42
6253.2.a.r 51
6253.2.a.s 51
6253.2.a.t 57
6253.2.a.u 57
6253.2.b \(\chi_{6253}(3886, \cdot)\) n/a 462 1
6253.2.c \(\chi_{6253}(2367, \cdot)\) n/a 480 1
6253.2.d \(\chi_{6253}(6252, \cdot)\) n/a 480 1
6253.2.e \(\chi_{6253}(1691, \cdot)\) n/a 962 2
6253.2.f \(\chi_{6253}(2850, \cdot)\) n/a 924 2
6253.2.g \(\chi_{6253}(1712, \cdot)\) n/a 956 2
6253.2.h \(\chi_{6253}(1543, \cdot)\) n/a 956 2
6253.2.i \(\chi_{6253}(746, \cdot)\) n/a 958 2
6253.2.n \(\chi_{6253}(2436, \cdot)\) n/a 958 2
6253.2.o \(\chi_{6253}(2896, \cdot)\) n/a 952 2
6253.2.p \(\chi_{6253}(529, \cdot)\) n/a 952 2
6253.2.q \(\chi_{6253}(4393, \cdot)\) n/a 960 2
6253.2.r \(\chi_{6253}(147, \cdot)\) n/a 956 2
6253.2.s \(\chi_{6253}(1713, \cdot)\) n/a 956 2
6253.2.t \(\chi_{6253}(2219, \cdot)\) n/a 952 2
6253.2.u \(\chi_{6253}(1037, \cdot)\) n/a 924 2
6253.2.v \(\chi_{6253}(508, \cdot)\) n/a 960 2
6253.2.w \(\chi_{6253}(5576, \cdot)\) n/a 956 2
6253.2.x \(\chi_{6253}(360, \cdot)\) n/a 952 2
6253.2.y \(\chi_{6253}(2727, \cdot)\) n/a 952 2
6253.2.z \(\chi_{6253}(1544, \cdot)\) n/a 956 2
6253.2.ba \(\chi_{6253}(867, \cdot)\) n/a 2874 6
6253.2.bb \(\chi_{6253}(2343, \cdot)\) n/a 2874 6
6253.2.bc \(\chi_{6253}(1015, \cdot)\) n/a 2880 6
6253.2.bd \(\chi_{6253}(526, \cdot)\) n/a 1908 4
6253.2.be \(\chi_{6253}(319, \cdot)\) n/a 1908 4
6253.2.bf \(\chi_{6253}(1671, \cdot)\) n/a 1908 4
6253.2.bg \(\chi_{6253}(1451, \cdot)\) n/a 1916 4
6253.2.bx \(\chi_{6253}(1540, \cdot)\) n/a 1908 4
6253.2.by \(\chi_{6253}(606, \cdot)\) n/a 1916 4
6253.2.bz \(\chi_{6253}(80, \cdot)\) n/a 1908 4
6253.2.ca \(\chi_{6253}(695, \cdot)\) n/a 1908 4
6253.2.cb \(\chi_{6253}(482, \cdot)\) n/a 6552 12
6253.2.cc \(\chi_{6253}(1353, \cdot)\) n/a 2874 6
6253.2.cd \(\chi_{6253}(675, \cdot)\) n/a 2856 6
6253.2.ce \(\chi_{6253}(654, \cdot)\) n/a 2874 6
6253.2.cf \(\chi_{6253}(361, \cdot)\) n/a 2874 6
6253.2.cg \(\chi_{6253}(192, \cdot)\) n/a 2862 6
6253.2.ch \(\chi_{6253}(484, \cdot)\) n/a 2862 6
6253.2.ci \(\chi_{6253}(2174, \cdot)\) n/a 2862 6
6253.2.cj \(\chi_{6253}(530, \cdot)\) n/a 2862 6
6253.2.ck \(\chi_{6253}(337, \cdot)\) n/a 2868 6
6253.2.cl \(\chi_{6253}(480, \cdot)\) n/a 6864 12
6253.2.cm \(\chi_{6253}(443, \cdot)\) n/a 6888 12
6253.2.cn \(\chi_{6253}(38, \cdot)\) n/a 6552 12
6253.2.co \(\chi_{6253}(775, \cdot)\) n/a 5724 12
6253.2.cp \(\chi_{6253}(19, \cdot)\) n/a 5736 12
6253.2.cq \(\chi_{6253}(150, \cdot)\) n/a 5736 12
6253.2.dd \(\chi_{6253}(357, \cdot)\) n/a 5736 12
6253.2.de \(\chi_{6253}(587, \cdot)\) n/a 5736 12
6253.2.df \(\chi_{6253}(239, \cdot)\) n/a 5724 12
6253.2.dg \(\chi_{6253}(100, \cdot)\) n/a 13776 24
6253.2.dh \(\chi_{6253}(211, \cdot)\) n/a 13776 24
6253.2.di \(\chi_{6253}(334, \cdot)\) n/a 13104 24
6253.2.dj \(\chi_{6253}(248, \cdot)\) n/a 13728 24
6253.2.dk \(\chi_{6253}(31, \cdot)\) n/a 13752 24
6253.2.dp \(\chi_{6253}(216, \cdot)\) n/a 13752 24
6253.2.dq \(\chi_{6253}(101, \cdot)\) n/a 13776 24
6253.2.dr \(\chi_{6253}(121, \cdot)\) n/a 13824 24
6253.2.ds \(\chi_{6253}(159, \cdot)\) n/a 13824 24
6253.2.dt \(\chi_{6253}(285, \cdot)\) n/a 13776 24
6253.2.du \(\chi_{6253}(27, \cdot)\) n/a 13776 24
6253.2.dv \(\chi_{6253}(75, \cdot)\) n/a 13104 24
6253.2.dw \(\chi_{6253}(295, \cdot)\) n/a 13824 24
6253.2.dx \(\chi_{6253}(212, \cdot)\) n/a 13776 24
6253.2.dy \(\chi_{6253}(36, \cdot)\) n/a 13776 24
6253.2.dz \(\chi_{6253}(64, \cdot)\) n/a 13728 24
6253.2.ea \(\chi_{6253}(48, \cdot)\) n/a 13824 24
6253.2.eb \(\chi_{6253}(10, \cdot)\) n/a 13824 24
6253.2.ec \(\chi_{6253}(53, \cdot)\) n/a 41328 72
6253.2.ed \(\chi_{6253}(16, \cdot)\) n/a 41256 72
6253.2.ee \(\chi_{6253}(9, \cdot)\) n/a 41256 72
6253.2.ef \(\chi_{6253}(214, \cdot)\) n/a 27600 48
6253.2.eg \(\chi_{6253}(6, \cdot)\) n/a 27600 48
6253.2.eh \(\chi_{6253}(125, \cdot)\) n/a 27504 48
6253.2.ei \(\chi_{6253}(97, \cdot)\) n/a 27600 48
6253.2.ez \(\chi_{6253}(8, \cdot)\) n/a 27504 48
6253.2.fa \(\chi_{6253}(154, \cdot)\) n/a 27600 48
6253.2.fb \(\chi_{6253}(162, \cdot)\) n/a 27600 48
6253.2.fc \(\chi_{6253}(45, \cdot)\) n/a 27600 48
6253.2.fd \(\chi_{6253}(25, \cdot)\) n/a 41328 72
6253.2.fe \(\chi_{6253}(49, \cdot)\) n/a 41400 72
6253.2.ff \(\chi_{6253}(152, \cdot)\) n/a 41400 72
6253.2.fg \(\chi_{6253}(3, \cdot)\) n/a 41400 72
6253.2.fh \(\chi_{6253}(160, \cdot)\) n/a 41400 72
6253.2.fi \(\chi_{6253}(4, \cdot)\) n/a 41256 72
6253.2.fj \(\chi_{6253}(95, \cdot)\) n/a 41256 72
6253.2.fk \(\chi_{6253}(12, \cdot)\) n/a 41472 72
6253.2.fl \(\chi_{6253}(40, \cdot)\) n/a 41472 72
6253.2.fm \(\chi_{6253}(5, \cdot)\) n/a 82800 144
6253.2.fn \(\chi_{6253}(50, \cdot)\) n/a 82656 144
6253.2.fo \(\chi_{6253}(2, \cdot)\) n/a 82656 144
6253.2.gb \(\chi_{6253}(20, \cdot)\) n/a 82656 144
6253.2.gc \(\chi_{6253}(54, \cdot)\) n/a 82656 144
6253.2.gd \(\chi_{6253}(18, \cdot)\) n/a 82800 144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6253))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6253)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(481))\)\(^{\oplus 2}\)