↑

Properties

Label 5160.2
Level 5160
Weight 2
Dimension 273148
Nonzero newspaces 72
Sturm bound 2838528

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 5160 = 2^{3} \cdot 3 \cdot 5 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(2838528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5160))\).

Total New Old
Modular forms 717696 275116 442580
Cusp forms 701569 273148 428421
Eisenstein series 16127 1968 14159

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5160))\)

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
5160.2.a \(\chi_{5160}(1, \cdot)\) 5160.2.a.a 1 1
5160.2.a.b 1
5160.2.a.c 1
5160.2.a.d 1
5160.2.a.e 1
5160.2.a.f 1
5160.2.a.g 1
5160.2.a.h 1
5160.2.a.i 1
5160.2.a.j 1
5160.2.a.k 1
5160.2.a.l 1
5160.2.a.m 1
5160.2.a.n 1
5160.2.a.o 2
5160.2.a.p 2
5160.2.a.q 2
5160.2.a.r 3
5160.2.a.s 3
5160.2.a.t 4
5160.2.a.u 4
5160.2.a.v 4
5160.2.a.w 4
5160.2.a.x 5
5160.2.a.y 5
5160.2.a.z 6
5160.2.a.ba 6
5160.2.a.bb 6
5160.2.a.bc 7
5160.2.a.bd 7
5160.2.b \(\chi_{5160}(3439, \cdot)\) None 0 1
5160.2.c \(\chi_{5160}(3011, \cdot)\) n/a 672 1
5160.2.f \(\chi_{5160}(1549, \cdot)\) n/a 504 1
5160.2.g \(\chi_{5160}(2321, \cdot)\) n/a 176 1
5160.2.j \(\chi_{5160}(4901, \cdot)\) n/a 704 1
5160.2.k \(\chi_{5160}(4129, \cdot)\) n/a 128 1
5160.2.n \(\chi_{5160}(431, \cdot)\) None 0 1
5160.2.o \(\chi_{5160}(859, \cdot)\) n/a 528 1
5160.2.t \(\chi_{5160}(2581, \cdot)\) n/a 336 1
5160.2.u \(\chi_{5160}(1289, \cdot)\) n/a 264 1
5160.2.x \(\chi_{5160}(4471, \cdot)\) None 0 1
5160.2.y \(\chi_{5160}(1979, \cdot)\) n/a 1008 1
5160.2.bb \(\chi_{5160}(4559, \cdot)\) None 0 1
5160.2.bc \(\chi_{5160}(1891, \cdot)\) n/a 352 1
5160.2.bf \(\chi_{5160}(3869, \cdot)\) n/a 1048 1
5160.2.bg \(\chi_{5160}(1081, \cdot)\) n/a 176 2
5160.2.bi \(\chi_{5160}(1117, \cdot)\) n/a 1056 2
5160.2.bk \(\chi_{5160}(2753, \cdot)\) n/a 504 2
5160.2.bl \(\chi_{5160}(1807, \cdot)\) None 0 2
5160.2.bn \(\chi_{5160}(1547, \cdot)\) n/a 2096 2
5160.2.bp \(\chi_{5160}(2063, \cdot)\) None 0 2
5160.2.br \(\chi_{5160}(2323, \cdot)\) n/a 1008 2
5160.2.bu \(\chi_{5160}(173, \cdot)\) n/a 2016 2
5160.2.bw \(\chi_{5160}(1633, \cdot)\) n/a 264 2
5160.2.bx \(\chi_{5160}(3059, \cdot)\) n/a 2096 2
5160.2.by \(\chi_{5160}(2071, \cdot)\) None 0 2
5160.2.cb \(\chi_{5160}(209, \cdot)\) n/a 528 2
5160.2.cc \(\chi_{5160}(3661, \cdot)\) n/a 704 2
5160.2.cf \(\chi_{5160}(1469, \cdot)\) n/a 2096 2
5160.2.ci \(\chi_{5160}(811, \cdot)\) n/a 704 2
5160.2.cj \(\chi_{5160}(479, \cdot)\) None 0 2
5160.2.co \(\chi_{5160}(1241, \cdot)\) n/a 352 2
5160.2.cp \(\chi_{5160}(2629, \cdot)\) n/a 1056 2
5160.2.cs \(\chi_{5160}(251, \cdot)\) n/a 1408 2
5160.2.ct \(\chi_{5160}(1039, \cdot)\) None 0 2
5160.2.cw \(\chi_{5160}(3619, \cdot)\) n/a 1056 2
5160.2.cx \(\chi_{5160}(1511, \cdot)\) None 0 2
5160.2.da \(\chi_{5160}(49, \cdot)\) n/a 264 2
5160.2.db \(\chi_{5160}(2501, \cdot)\) n/a 1408 2
5160.2.dc \(\chi_{5160}(121, \cdot)\) n/a 528 6
5160.2.de \(\chi_{5160}(467, \cdot)\) n/a 4192 4
5160.2.dg \(\chi_{5160}(823, \cdot)\) None 0 4
5160.2.dh \(\chi_{5160}(737, \cdot)\) n/a 1056 4
5160.2.dj \(\chi_{5160}(37, \cdot)\) n/a 2112 4
5160.2.dl \(\chi_{5160}(553, \cdot)\) n/a 528 4
5160.2.dn \(\chi_{5160}(1253, \cdot)\) n/a 4192 4
5160.2.dq \(\chi_{5160}(307, \cdot)\) n/a 2112 4
5160.2.ds \(\chi_{5160}(983, \cdot)\) None 0 4
5160.2.dv \(\chi_{5160}(739, \cdot)\) n/a 3168 6
5160.2.dw \(\chi_{5160}(551, \cdot)\) None 0 6
5160.2.dz \(\chi_{5160}(649, \cdot)\) n/a 792 6
5160.2.ea \(\chi_{5160}(581, \cdot)\) n/a 4224 6
5160.2.ed \(\chi_{5160}(161, \cdot)\) n/a 1056 6
5160.2.ee \(\chi_{5160}(709, \cdot)\) n/a 3168 6
5160.2.eh \(\chi_{5160}(11, \cdot)\) n/a 4224 6
5160.2.ei \(\chi_{5160}(199, \cdot)\) None 0 6
5160.2.ej \(\chi_{5160}(389, \cdot)\) n/a 6288 6
5160.2.em \(\chi_{5160}(211, \cdot)\) n/a 2112 6
5160.2.en \(\chi_{5160}(1079, \cdot)\) None 0 6
5160.2.eq \(\chi_{5160}(59, \cdot)\) n/a 6288 6
5160.2.er \(\chi_{5160}(151, \cdot)\) None 0 6
5160.2.eu \(\chi_{5160}(1169, \cdot)\) n/a 1584 6
5160.2.ev \(\chi_{5160}(661, \cdot)\) n/a 2112 6
5160.2.ey \(\chi_{5160}(361, \cdot)\) n/a 1056 12
5160.2.ez \(\chi_{5160}(217, \cdot)\) n/a 1584 12
5160.2.fb \(\chi_{5160}(293, \cdot)\) n/a 12576 12
5160.2.fe \(\chi_{5160}(403, \cdot)\) n/a 6336 12
5160.2.fg \(\chi_{5160}(383, \cdot)\) None 0 12
5160.2.fi \(\chi_{5160}(323, \cdot)\) n/a 12576 12
5160.2.fk \(\chi_{5160}(127, \cdot)\) None 0 12
5160.2.fl \(\chi_{5160}(833, \cdot)\) n/a 3168 12
5160.2.fn \(\chi_{5160}(733, \cdot)\) n/a 6336 12
5160.2.fr \(\chi_{5160}(239, \cdot)\) None 0 12
5160.2.fs \(\chi_{5160}(91, \cdot)\) n/a 4224 12
5160.2.fv \(\chi_{5160}(29, \cdot)\) n/a 12576 12
5160.2.fy \(\chi_{5160}(181, \cdot)\) n/a 4224 12
5160.2.fz \(\chi_{5160}(89, \cdot)\) n/a 3168 12
5160.2.gc \(\chi_{5160}(631, \cdot)\) None 0 12
5160.2.gd \(\chi_{5160}(539, \cdot)\) n/a 12576 12
5160.2.ge \(\chi_{5160}(1061, \cdot)\) n/a 8448 12
5160.2.gf \(\chi_{5160}(169, \cdot)\) n/a 1584 12
5160.2.gi \(\chi_{5160}(311, \cdot)\) None 0 12
5160.2.gj \(\chi_{5160}(19, \cdot)\) n/a 6336 12
5160.2.gm \(\chi_{5160}(319, \cdot)\) None 0 12
5160.2.gn \(\chi_{5160}(611, \cdot)\) n/a 8448 12
5160.2.gq \(\chi_{5160}(109, \cdot)\) n/a 6336 12
5160.2.gr \(\chi_{5160}(521, \cdot)\) n/a 2112 12
5160.2.gu \(\chi_{5160}(263, \cdot)\) None 0 24
5160.2.gw \(\chi_{5160}(67, \cdot)\) n/a 12672 24
5160.2.gz \(\chi_{5160}(53, \cdot)\) n/a 25152 24
5160.2.hb \(\chi_{5160}(73, \cdot)\) n/a 3168 24
5160.2.hd \(\chi_{5160}(157, \cdot)\) n/a 12672 24
5160.2.hf \(\chi_{5160}(17, \cdot)\) n/a 6336 24
5160.2.hg \(\chi_{5160}(103, \cdot)\) None 0 24
5160.2.hi \(\chi_{5160}(227, \cdot)\) n/a 25152 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5160))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5160)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(86))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(129))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(172))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(215))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(258))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(344))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(430))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(516))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(645))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(860))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1032))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1290))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2580))\)\(^{\oplus 2}\)