↑

Properties

Label 4312.2
Level 4312
Weight 2
Dimension 297871
Nonzero newspaces 48
Sturm bound 2257920

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 4312 = 2^{3} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(2257920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4312))\).

Total New Old
Modular forms 571680 301363 270317
Cusp forms 557281 297871 259410
Eisenstein series 14399 3492 10907

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4312))\)

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
4312.2.a \(\chi_{4312}(1, \cdot)\) 4312.2.a.a 1 1
4312.2.a.b 1
4312.2.a.c 1
4312.2.a.d 1
4312.2.a.e 1
4312.2.a.f 1
4312.2.a.g 1
4312.2.a.h 1
4312.2.a.i 1
4312.2.a.j 1
4312.2.a.k 1
4312.2.a.l 1
4312.2.a.m 2
4312.2.a.n 2
4312.2.a.o 2
4312.2.a.p 2
4312.2.a.q 2
4312.2.a.r 2
4312.2.a.s 2
4312.2.a.t 2
4312.2.a.u 2
4312.2.a.v 3
4312.2.a.w 3
4312.2.a.x 3
4312.2.a.y 4
4312.2.a.z 4
4312.2.a.ba 4
4312.2.a.bb 4
4312.2.a.bc 4
4312.2.a.bd 4
4312.2.a.be 5
4312.2.a.bf 5
4312.2.a.bg 5
4312.2.a.bh 5
4312.2.a.bi 8
4312.2.a.bj 12
4312.2.c \(\chi_{4312}(2157, \cdot)\) n/a 410 1
4312.2.e \(\chi_{4312}(3233, \cdot)\) n/a 120 1
4312.2.f \(\chi_{4312}(3431, \cdot)\) None 0 1
4312.2.h \(\chi_{4312}(4115, \cdot)\) n/a 400 1
4312.2.j \(\chi_{4312}(1959, \cdot)\) None 0 1
4312.2.l \(\chi_{4312}(1275, \cdot)\) n/a 482 1
4312.2.o \(\chi_{4312}(1077, \cdot)\) n/a 472 1
4312.2.q \(\chi_{4312}(177, \cdot)\) n/a 200 2
4312.2.r \(\chi_{4312}(785, \cdot)\) n/a 492 4
4312.2.s \(\chi_{4312}(901, \cdot)\) n/a 944 2
4312.2.w \(\chi_{4312}(815, \cdot)\) None 0 2
4312.2.y \(\chi_{4312}(1451, \cdot)\) n/a 944 2
4312.2.ba \(\chi_{4312}(263, \cdot)\) None 0 2
4312.2.bc \(\chi_{4312}(2971, \cdot)\) n/a 800 2
4312.2.bd \(\chi_{4312}(2333, \cdot)\) n/a 800 2
4312.2.bf \(\chi_{4312}(2089, \cdot)\) n/a 240 2
4312.2.bh \(\chi_{4312}(617, \cdot)\) n/a 840 6
4312.2.bj \(\chi_{4312}(293, \cdot)\) n/a 1888 4
4312.2.bm \(\chi_{4312}(491, \cdot)\) n/a 1928 4
4312.2.bo \(\chi_{4312}(1175, \cdot)\) None 0 4
4312.2.bq \(\chi_{4312}(587, \cdot)\) n/a 1888 4
4312.2.bs \(\chi_{4312}(1471, \cdot)\) None 0 4
4312.2.bt \(\chi_{4312}(1273, \cdot)\) n/a 480 4
4312.2.bv \(\chi_{4312}(1373, \cdot)\) n/a 1928 4
4312.2.by \(\chi_{4312}(461, \cdot)\) n/a 4008 6
4312.2.cb \(\chi_{4312}(43, \cdot)\) n/a 4008 6
4312.2.cd \(\chi_{4312}(111, \cdot)\) None 0 6
4312.2.cf \(\chi_{4312}(419, \cdot)\) n/a 3360 6
4312.2.ch \(\chi_{4312}(351, \cdot)\) None 0 6
4312.2.ci \(\chi_{4312}(153, \cdot)\) n/a 1008 6
4312.2.ck \(\chi_{4312}(309, \cdot)\) n/a 3360 6
4312.2.cm \(\chi_{4312}(361, \cdot)\) n/a 960 8
4312.2.cn \(\chi_{4312}(529, \cdot)\) n/a 1680 12
4312.2.cp \(\chi_{4312}(129, \cdot)\) n/a 960 8
4312.2.cr \(\chi_{4312}(949, \cdot)\) n/a 3776 8
4312.2.cs \(\chi_{4312}(411, \cdot)\) n/a 3776 8
4312.2.cu \(\chi_{4312}(79, \cdot)\) None 0 8
4312.2.cw \(\chi_{4312}(459, \cdot)\) n/a 3776 8
4312.2.cy \(\chi_{4312}(31, \cdot)\) None 0 8
4312.2.dc \(\chi_{4312}(117, \cdot)\) n/a 3776 8
4312.2.dd \(\chi_{4312}(113, \cdot)\) n/a 4032 24
4312.2.df \(\chi_{4312}(241, \cdot)\) n/a 2016 12
4312.2.dh \(\chi_{4312}(221, \cdot)\) n/a 6720 12
4312.2.di \(\chi_{4312}(243, \cdot)\) n/a 6720 12
4312.2.dk \(\chi_{4312}(527, \cdot)\) None 0 12
4312.2.dm \(\chi_{4312}(219, \cdot)\) n/a 8016 12
4312.2.do \(\chi_{4312}(199, \cdot)\) None 0 12
4312.2.ds \(\chi_{4312}(285, \cdot)\) n/a 8016 12
4312.2.du \(\chi_{4312}(141, \cdot)\) n/a 16032 24
4312.2.dw \(\chi_{4312}(41, \cdot)\) n/a 4032 24
4312.2.dx \(\chi_{4312}(127, \cdot)\) None 0 24
4312.2.dz \(\chi_{4312}(27, \cdot)\) n/a 16032 24
4312.2.eb \(\chi_{4312}(223, \cdot)\) None 0 24
4312.2.ed \(\chi_{4312}(211, \cdot)\) n/a 16032 24
4312.2.eg \(\chi_{4312}(13, \cdot)\) n/a 16032 24
4312.2.ei \(\chi_{4312}(9, \cdot)\) n/a 8064 48
4312.2.ej \(\chi_{4312}(61, \cdot)\) n/a 32064 48
4312.2.en \(\chi_{4312}(47, \cdot)\) None 0 48
4312.2.ep \(\chi_{4312}(51, \cdot)\) n/a 32064 48
4312.2.er \(\chi_{4312}(39, \cdot)\) None 0 48
4312.2.et \(\chi_{4312}(3, \cdot)\) n/a 32064 48
4312.2.eu \(\chi_{4312}(37, \cdot)\) n/a 32064 48
4312.2.ew \(\chi_{4312}(17, \cdot)\) n/a 8064 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4312))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4312)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(539))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(616))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1078))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2156))\)\(^{\oplus 2}\)