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: \( N \) = \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(691200\)
Trace bound: \(4\)

Dimensions

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

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

Trace form

\( 180323q - 83q^{2} - 102q^{3} - 15q^{4} - 102q^{5} - 190q^{6} - 72q^{7} - 93q^{8} + 58q^{9} + O(q^{10}) \) \( 180323q - 83q^{2} - 102q^{3} - 15q^{4} - 102q^{5} - 190q^{6} - 72q^{7} - 93q^{8} + 58q^{9} - 52q^{10} + 19q^{11} - 260q^{12} - 728q^{13} - 411q^{14} - 656q^{15} - 1475q^{16} - 703q^{17} - 876q^{18} + 325q^{19} + 1596q^{20} + 543q^{21} + 3066q^{22} + 2027q^{23} + 938q^{24} - 1386q^{25} - 1398q^{26} - 1056q^{27} - 2017q^{28} - 5120q^{29} - 2448q^{30} - 2983q^{31} - 6425q^{32} - 4208q^{33} + 918q^{34} - 1016q^{35} - 4346q^{36} + 3001q^{37} + 6688q^{38} + 3258q^{39} + 7752q^{40} + 7144q^{41} + 4456q^{42} - 616q^{43} + 11226q^{44} + 4392q^{45} - 242q^{46} + 12623q^{47} + 16058q^{48} + 3410q^{49} - 3400q^{50} + 238q^{51} - 3162q^{52} - 8225q^{53} - 14624q^{54} - 564q^{55} + 645q^{56} - 17214q^{57} - 3816q^{58} - 16771q^{59} - 28072q^{60} - 14479q^{61} - 26320q^{62} - 3519q^{63} - 23411q^{64} - 10418q^{65} + 4354q^{66} - 5757q^{67} + 10634q^{68} + 16234q^{69} + 2166q^{70} + 8312q^{71} + 19968q^{72} + 26227q^{73} + 20438q^{74} + 12992q^{75} + 21554q^{76} - 1266q^{77} - 10704q^{78} + 7983q^{79} + 32680q^{80} - 1154q^{81} + 14842q^{82} + 24226q^{83} - 938q^{84} + 10298q^{85} + 16156q^{86} - 3518q^{87} - 66348q^{88} - 26289q^{89} - 18512q^{90} - 22236q^{91} - 30212q^{92} + 19294q^{93} - 30636q^{94} - 4772q^{95} + 42568q^{96} - 12520q^{97} + 47433q^{98} + 33414q^{99} + O(q^{100}) \)

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

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

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

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

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

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