Properties

Label 1575.4
Level 1575
Weight 4
Dimension 180323
Nonzero newspaces 60
Sturm bound 691200
Trace bound 4

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Defining parameters

Level: N N = 1575=32527 1575 = 3^{2} \cdot 5^{2} \cdot 7
Weight: k k = 4 4
Nonzero newspaces: 60 60
Sturm bound: 691200691200
Trace bound: 44

Dimensions

The following table gives the dimensions of various subspaces of M4(Γ1(1575))M_{4}(\Gamma_1(1575)).

Total New Old
Modular forms 261888 182167 79721
Cusp forms 256512 180323 76189
Eisenstein series 5376 1844 3532

Trace form

180323q83q2102q315q4102q5190q672q793q8+58q952q10+19q11260q12728q13411q14656q151475q16703q17++33414q99+O(q100) 180323 q - 83 q^{2} - 102 q^{3} - 15 q^{4} - 102 q^{5} - 190 q^{6} - 72 q^{7} - 93 q^{8} + 58 q^{9} - 52 q^{10} + 19 q^{11} - 260 q^{12} - 728 q^{13} - 411 q^{14} - 656 q^{15} - 1475 q^{16} - 703 q^{17}+ \cdots + 33414 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S4new(Γ1(1575))S_{4}^{\mathrm{new}}(\Gamma_1(1575))

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space Sknew(N,χ) S_k^{\mathrm{new}}(N, \chi) we list available newforms together with their dimension.

Label χ\chi Newforms Dimension χ\chi degree
1575.4.a χ1575(1,)\chi_{1575}(1, \cdot) 1575.4.a.a 1 1
1575.4.a.b 1
1575.4.a.c 1
1575.4.a.d 1
1575.4.a.e 1
1575.4.a.f 1
1575.4.a.g 1
1575.4.a.h 1
1575.4.a.i 1
1575.4.a.j 1
1575.4.a.k 1
1575.4.a.l 1
1575.4.a.m 2
1575.4.a.n 2
1575.4.a.o 2
1575.4.a.p 2
1575.4.a.q 2
1575.4.a.r 2
1575.4.a.s 2
1575.4.a.t 2
1575.4.a.u 2
1575.4.a.v 2
1575.4.a.w 2
1575.4.a.x 2
1575.4.a.y 2
1575.4.a.z 2
1575.4.a.ba 3
1575.4.a.bb 3
1575.4.a.bc 3
1575.4.a.bd 3
1575.4.a.be 3
1575.4.a.bf 4
1575.4.a.bg 4
1575.4.a.bh 4
1575.4.a.bi 4
1575.4.a.bj 4
1575.4.a.bk 4
1575.4.a.bl 4
1575.4.a.bm 4
1575.4.a.bn 5
1575.4.a.bo 5
1575.4.a.bp 5
1575.4.a.bq 5
1575.4.a.br 8
1575.4.a.bs 8
1575.4.a.bt 10
1575.4.a.bu 10
1575.4.b χ1575(251,)\chi_{1575}(251, \cdot) n/a 152 1
1575.4.d χ1575(1324,)\chi_{1575}(1324, \cdot) n/a 134 1
1575.4.g χ1575(1574,)\chi_{1575}(1574, \cdot) n/a 144 1
1575.4.i χ1575(526,)\chi_{1575}(526, \cdot) n/a 684 2
1575.4.j χ1575(226,)\chi_{1575}(226, \cdot) n/a 374 2
1575.4.k χ1575(1201,)\chi_{1575}(1201, \cdot) n/a 900 2
1575.4.l χ1575(151,)\chi_{1575}(151, \cdot) n/a 900 2
1575.4.m χ1575(1268,)\chi_{1575}(1268, \cdot) n/a 216 2
1575.4.p χ1575(118,)\chi_{1575}(118, \cdot) n/a 356 2
1575.4.q χ1575(316,)\chi_{1575}(316, \cdot) n/a 896 4
1575.4.s χ1575(499,)\chi_{1575}(499, \cdot) n/a 856 2
1575.4.u χ1575(101,)\chi_{1575}(101, \cdot) n/a 900 2
1575.4.v χ1575(299,)\chi_{1575}(299, \cdot) n/a 856 2
1575.4.ba χ1575(524,)\chi_{1575}(524, \cdot) n/a 856 2
1575.4.bc χ1575(899,)\chi_{1575}(899, \cdot) n/a 288 2
1575.4.bf χ1575(551,)\chi_{1575}(551, \cdot) n/a 900 2
1575.4.bg χ1575(424,)\chi_{1575}(424, \cdot) n/a 356 2
1575.4.bi χ1575(274,)\chi_{1575}(274, \cdot) n/a 648 2
1575.4.bk χ1575(26,)\chi_{1575}(26, \cdot) n/a 304 2
1575.4.bm χ1575(776,)\chi_{1575}(776, \cdot) n/a 900 2
1575.4.bp χ1575(949,)\chi_{1575}(949, \cdot) n/a 856 2
1575.4.br χ1575(824,)\chi_{1575}(824, \cdot) n/a 856 2
1575.4.bu χ1575(314,)\chi_{1575}(314, \cdot) n/a 960 4
1575.4.bx χ1575(64,)\chi_{1575}(64, \cdot) n/a 904 4
1575.4.bz χ1575(566,)\chi_{1575}(566, \cdot) n/a 960 4
1575.4.ca χ1575(418,)\chi_{1575}(418, \cdot) n/a 1712 4
1575.4.cd χ1575(893,)\chi_{1575}(893, \cdot) n/a 1712 4
1575.4.cf χ1575(32,)\chi_{1575}(32, \cdot) n/a 1712 4
1575.4.ch χ1575(82,)\chi_{1575}(82, \cdot) n/a 712 4
1575.4.cj χ1575(643,)\chi_{1575}(643, \cdot) n/a 1712 4
1575.4.ck χ1575(218,)\chi_{1575}(218, \cdot) n/a 1296 4
1575.4.cm χ1575(107,)\chi_{1575}(107, \cdot) n/a 576 4
1575.4.co χ1575(157,)\chi_{1575}(157, \cdot) n/a 1712 4
1575.4.cq χ1575(121,)\chi_{1575}(121, \cdot) n/a 5728 8
1575.4.cr χ1575(16,)\chi_{1575}(16, \cdot) n/a 5728 8
1575.4.cs χ1575(46,)\chi_{1575}(46, \cdot) n/a 2384 8
1575.4.ct χ1575(106,)\chi_{1575}(106, \cdot) n/a 4320 8
1575.4.cu χ1575(433,)\chi_{1575}(433, \cdot) n/a 2384 8
1575.4.cx χ1575(8,)\chi_{1575}(8, \cdot) n/a 1440 8
1575.4.cz χ1575(164,)\chi_{1575}(164, \cdot) n/a 5728 8
1575.4.db χ1575(4,)\chi_{1575}(4, \cdot) n/a 5728 8
1575.4.de χ1575(41,)\chi_{1575}(41, \cdot) n/a 5728 8
1575.4.dg χ1575(206,)\chi_{1575}(206, \cdot) n/a 1920 8
1575.4.di χ1575(169,)\chi_{1575}(169, \cdot) n/a 4320 8
1575.4.dk χ1575(109,)\chi_{1575}(109, \cdot) n/a 2384 8
1575.4.dl χ1575(236,)\chi_{1575}(236, \cdot) n/a 5728 8
1575.4.do χ1575(89,)\chi_{1575}(89, \cdot) n/a 1920 8
1575.4.dq χ1575(104,)\chi_{1575}(104, \cdot) n/a 5728 8
1575.4.dv χ1575(59,)\chi_{1575}(59, \cdot) n/a 5728 8
1575.4.dw χ1575(131,)\chi_{1575}(131, \cdot) n/a 5728 8
1575.4.dy χ1575(184,)\chi_{1575}(184, \cdot) n/a 5728 8
1575.4.eb χ1575(187,)\chi_{1575}(187, \cdot) n/a 11456 16
1575.4.ed χ1575(53,)\chi_{1575}(53, \cdot) n/a 3840 16
1575.4.ef χ1575(92,)\chi_{1575}(92, \cdot) n/a 8640 16
1575.4.eg χ1575(13,)\chi_{1575}(13, \cdot) n/a 11456 16
1575.4.ei χ1575(73,)\chi_{1575}(73, \cdot) n/a 4768 16
1575.4.ek χ1575(2,)\chi_{1575}(2, \cdot) n/a 11456 16
1575.4.em χ1575(23,)\chi_{1575}(23, \cdot) n/a 11456 16
1575.4.ep χ1575(52,)\chi_{1575}(52, \cdot) n/a 11456 16

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

Decomposition of S4old(Γ1(1575))S_{4}^{\mathrm{old}}(\Gamma_1(1575)) into lower level spaces

S4old(Γ1(1575)) S_{4}^{\mathrm{old}}(\Gamma_1(1575)) \cong S4new(Γ1(1))S_{4}^{\mathrm{new}}(\Gamma_1(1))18^{\oplus 18}\oplusS4new(Γ1(3))S_{4}^{\mathrm{new}}(\Gamma_1(3))12^{\oplus 12}\oplusS4new(Γ1(5))S_{4}^{\mathrm{new}}(\Gamma_1(5))12^{\oplus 12}\oplusS4new(Γ1(7))S_{4}^{\mathrm{new}}(\Gamma_1(7))9^{\oplus 9}\oplusS4new(Γ1(9))S_{4}^{\mathrm{new}}(\Gamma_1(9))6^{\oplus 6}\oplusS4new(Γ1(15))S_{4}^{\mathrm{new}}(\Gamma_1(15))8^{\oplus 8}\oplusS4new(Γ1(21))S_{4}^{\mathrm{new}}(\Gamma_1(21))6^{\oplus 6}\oplusS4new(Γ1(25))S_{4}^{\mathrm{new}}(\Gamma_1(25))6^{\oplus 6}\oplusS4new(Γ1(35))S_{4}^{\mathrm{new}}(\Gamma_1(35))6^{\oplus 6}\oplusS4new(Γ1(45))S_{4}^{\mathrm{new}}(\Gamma_1(45))4^{\oplus 4}\oplusS4new(Γ1(63))S_{4}^{\mathrm{new}}(\Gamma_1(63))3^{\oplus 3}\oplusS4new(Γ1(75))S_{4}^{\mathrm{new}}(\Gamma_1(75))4^{\oplus 4}\oplusS4new(Γ1(105))S_{4}^{\mathrm{new}}(\Gamma_1(105))4^{\oplus 4}\oplusS4new(Γ1(175))S_{4}^{\mathrm{new}}(\Gamma_1(175))3^{\oplus 3}\oplusS4new(Γ1(225))S_{4}^{\mathrm{new}}(\Gamma_1(225))2^{\oplus 2}\oplusS4new(Γ1(315))S_{4}^{\mathrm{new}}(\Gamma_1(315))2^{\oplus 2}\oplusS4new(Γ1(525))S_{4}^{\mathrm{new}}(\Gamma_1(525))2^{\oplus 2}