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Properties

Label 5952.2
Level 5952
Weight 2
Dimension 412580
Nonzero newspaces 64
Sturm bound 3932160

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Defining parameters

Level: \( N \) = \( 5952 = 2^{6} \cdot 3 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(3932160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5952))\).

Total New Old
Modular forms 991680 415132 576548
Cusp forms 974401 412580 561821
Eisenstein series 17279 2552 14727

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5952))\)

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
5952.2.a \(\chi_{5952}(1, \cdot)\) 5952.2.a.a 1 1
5952.2.a.b 1
5952.2.a.c 1
5952.2.a.d 1
5952.2.a.e 1
5952.2.a.f 1
5952.2.a.g 1
5952.2.a.h 1
5952.2.a.i 1
5952.2.a.j 1
5952.2.a.k 1
5952.2.a.l 1
5952.2.a.m 1
5952.2.a.n 1
5952.2.a.o 1
5952.2.a.p 1
5952.2.a.q 1
5952.2.a.r 1
5952.2.a.s 1
5952.2.a.t 1
5952.2.a.u 1
5952.2.a.v 1
5952.2.a.w 1
5952.2.a.x 1
5952.2.a.y 1
5952.2.a.z 1
5952.2.a.ba 1
5952.2.a.bb 1
5952.2.a.bc 1
5952.2.a.bd 1
5952.2.a.be 1
5952.2.a.bf 1
5952.2.a.bg 1
5952.2.a.bh 1
5952.2.a.bi 2
5952.2.a.bj 2
5952.2.a.bk 2
5952.2.a.bl 2
5952.2.a.bm 2
5952.2.a.bn 2
5952.2.a.bo 2
5952.2.a.bp 2
5952.2.a.bq 2
5952.2.a.br 2
5952.2.a.bs 2
5952.2.a.bt 2
5952.2.a.bu 2
5952.2.a.bv 2
5952.2.a.bw 3
5952.2.a.bx 3
5952.2.a.by 3
5952.2.a.bz 3
5952.2.a.ca 3
5952.2.a.cb 3
5952.2.a.cc 3
5952.2.a.cd 3
5952.2.a.ce 3
5952.2.a.cf 3
5952.2.a.cg 3
5952.2.a.ch 3
5952.2.a.ci 5
5952.2.a.cj 5
5952.2.a.ck 6
5952.2.a.cl 6
5952.2.c \(\chi_{5952}(991, \cdot)\) n/a 128 1
5952.2.e \(\chi_{5952}(4031, \cdot)\) n/a 240 1
5952.2.f \(\chi_{5952}(2977, \cdot)\) n/a 120 1
5952.2.h \(\chi_{5952}(3905, \cdot)\) n/a 252 1
5952.2.j \(\chi_{5952}(1055, \cdot)\) n/a 240 1
5952.2.l \(\chi_{5952}(3967, \cdot)\) n/a 128 1
5952.2.o \(\chi_{5952}(929, \cdot)\) n/a 256 1
5952.2.q \(\chi_{5952}(769, \cdot)\) n/a 256 2
5952.2.t \(\chi_{5952}(1489, \cdot)\) n/a 240 2
5952.2.u \(\chi_{5952}(2417, \cdot)\) n/a 504 2
5952.2.v \(\chi_{5952}(2479, \cdot)\) n/a 256 2
5952.2.w \(\chi_{5952}(2543, \cdot)\) n/a 480 2
5952.2.z \(\chi_{5952}(3073, \cdot)\) n/a 512 4
5952.2.bb \(\chi_{5952}(161, \cdot)\) n/a 512 2
5952.2.be \(\chi_{5952}(1855, \cdot)\) n/a 256 2
5952.2.bg \(\chi_{5952}(1823, \cdot)\) n/a 512 2
5952.2.bi \(\chi_{5952}(1793, \cdot)\) n/a 504 2
5952.2.bk \(\chi_{5952}(3745, \cdot)\) n/a 256 2
5952.2.bl \(\chi_{5952}(191, \cdot)\) n/a 504 2
5952.2.bn \(\chi_{5952}(223, \cdot)\) n/a 256 2
5952.2.bp \(\chi_{5952}(745, \cdot)\) None 0 4
5952.2.bs \(\chi_{5952}(185, \cdot)\) None 0 4
5952.2.bu \(\chi_{5952}(311, \cdot)\) None 0 4
5952.2.bv \(\chi_{5952}(247, \cdot)\) None 0 4
5952.2.by \(\chi_{5952}(449, \cdot)\) n/a 1008 4
5952.2.ca \(\chi_{5952}(97, \cdot)\) n/a 512 4
5952.2.cb \(\chi_{5952}(1151, \cdot)\) n/a 1008 4
5952.2.cd \(\chi_{5952}(1759, \cdot)\) n/a 512 4
5952.2.cg \(\chi_{5952}(1697, \cdot)\) n/a 1024 4
5952.2.cj \(\chi_{5952}(511, \cdot)\) n/a 512 4
5952.2.cl \(\chi_{5952}(95, \cdot)\) n/a 1024 4
5952.2.co \(\chi_{5952}(335, \cdot)\) n/a 1008 4
5952.2.cp \(\chi_{5952}(367, \cdot)\) n/a 512 4
5952.2.cq \(\chi_{5952}(305, \cdot)\) n/a 1008 4
5952.2.cr \(\chi_{5952}(625, \cdot)\) n/a 512 4
5952.2.cu \(\chi_{5952}(193, \cdot)\) n/a 1024 8
5952.2.cv \(\chi_{5952}(683, \cdot)\) n/a 7680 8
5952.2.cy \(\chi_{5952}(619, \cdot)\) n/a 4096 8
5952.2.da \(\chi_{5952}(373, \cdot)\) n/a 3840 8
5952.2.db \(\chi_{5952}(557, \cdot)\) n/a 8160 8
5952.2.df \(\chi_{5952}(47, \cdot)\) n/a 2016 8
5952.2.dg \(\chi_{5952}(271, \cdot)\) n/a 1024 8
5952.2.dh \(\chi_{5952}(209, \cdot)\) n/a 2016 8
5952.2.di \(\chi_{5952}(529, \cdot)\) n/a 1024 8
5952.2.dl \(\chi_{5952}(935, \cdot)\) None 0 8
5952.2.do \(\chi_{5952}(967, \cdot)\) None 0 8
5952.2.dq \(\chi_{5952}(25, \cdot)\) None 0 8
5952.2.dr \(\chi_{5952}(905, \cdot)\) None 0 8
5952.2.dt \(\chi_{5952}(479, \cdot)\) n/a 2048 8
5952.2.dv \(\chi_{5952}(127, \cdot)\) n/a 1024 8
5952.2.dy \(\chi_{5952}(353, \cdot)\) n/a 2048 8
5952.2.eb \(\chi_{5952}(415, \cdot)\) n/a 1024 8
5952.2.ed \(\chi_{5952}(1343, \cdot)\) n/a 2016 8
5952.2.ee \(\chi_{5952}(289, \cdot)\) n/a 1024 8
5952.2.eg \(\chi_{5952}(65, \cdot)\) n/a 2016 8
5952.2.ej \(\chi_{5952}(151, \cdot)\) None 0 16
5952.2.ek \(\chi_{5952}(407, \cdot)\) None 0 16
5952.2.em \(\chi_{5952}(89, \cdot)\) None 0 16
5952.2.ep \(\chi_{5952}(841, \cdot)\) None 0 16
5952.2.eq \(\chi_{5952}(253, \cdot)\) n/a 8192 16
5952.2.et \(\chi_{5952}(533, \cdot)\) n/a 16320 16
5952.2.ev \(\chi_{5952}(563, \cdot)\) n/a 16320 16
5952.2.ew \(\chi_{5952}(595, \cdot)\) n/a 8192 16
5952.2.fa \(\chi_{5952}(49, \cdot)\) n/a 2048 16
5952.2.fb \(\chi_{5952}(17, \cdot)\) n/a 4032 16
5952.2.fc \(\chi_{5952}(79, \cdot)\) n/a 2048 16
5952.2.fd \(\chi_{5952}(143, \cdot)\) n/a 4032 16
5952.2.fh \(\chi_{5952}(29, \cdot)\) n/a 32640 32
5952.2.fi \(\chi_{5952}(109, \cdot)\) n/a 16384 32
5952.2.fk \(\chi_{5952}(91, \cdot)\) n/a 16384 32
5952.2.fn \(\chi_{5952}(35, \cdot)\) n/a 32640 32
5952.2.fp \(\chi_{5952}(137, \cdot)\) None 0 32
5952.2.fq \(\chi_{5952}(121, \cdot)\) None 0 32
5952.2.fs \(\chi_{5952}(55, \cdot)\) None 0 32
5952.2.fv \(\chi_{5952}(71, \cdot)\) None 0 32
5952.2.fx \(\chi_{5952}(43, \cdot)\) n/a 32768 64
5952.2.fy \(\chi_{5952}(59, \cdot)\) n/a 65280 64
5952.2.ga \(\chi_{5952}(53, \cdot)\) n/a 65280 64
5952.2.gd \(\chi_{5952}(133, \cdot)\) n/a 32768 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5952))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5952)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(248))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(372))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(496))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(744))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(992))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1488))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1984))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2976))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5952))\)\(^{\oplus 1}\)