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Properties

Label 1575.3
Level 1575
Weight 3
Dimension 119909
Nonzero newspaces 60
Sturm bound 518400
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(518400\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1575))\).

Total New Old
Modular forms 175488 121755 53733
Cusp forms 170112 119909 50203
Eisenstein series 5376 1846 3530

Trace form

\( 119909 q - 67 q^{2} - 102 q^{3} - 63 q^{4} - 92 q^{5} - 190 q^{6} - 97 q^{7} - 315 q^{8} - 170 q^{9} + O(q^{10}) \) \( 119909 q - 67 q^{2} - 102 q^{3} - 63 q^{4} - 92 q^{5} - 190 q^{6} - 97 q^{7} - 315 q^{8} - 170 q^{9} - 412 q^{10} - 302 q^{11} - 272 q^{12} - 170 q^{13} - 237 q^{14} - 296 q^{15} - 175 q^{16} - 30 q^{17} + 36 q^{18} - 184 q^{19} - 244 q^{20} - 204 q^{21} - 620 q^{22} - 368 q^{23} - 178 q^{24} - 396 q^{25} - 1062 q^{26} - 282 q^{27} - 537 q^{28} - 250 q^{29} - 48 q^{30} + 150 q^{31} + 1189 q^{32} + 418 q^{33} + 916 q^{34} + 424 q^{35} + 1726 q^{36} + 122 q^{37} + 1824 q^{38} + 1308 q^{39} - 48 q^{40} + 896 q^{41} + 406 q^{42} - 264 q^{43} + 620 q^{44} - 408 q^{45} - 246 q^{46} - 1094 q^{47} - 1594 q^{48} - 693 q^{49} - 1880 q^{50} - 1658 q^{51} - 922 q^{52} - 1510 q^{53} - 1964 q^{54} - 124 q^{55} - 1353 q^{56} - 1590 q^{57} - 908 q^{58} - 166 q^{59} + 1208 q^{60} - 308 q^{61} + 3308 q^{62} + 792 q^{63} + 3841 q^{64} + 2912 q^{65} + 1270 q^{66} + 2172 q^{67} + 4516 q^{68} + 1408 q^{69} + 1446 q^{70} + 1474 q^{71} + 2496 q^{72} + 1948 q^{73} + 4284 q^{74} + 1472 q^{75} + 176 q^{76} + 1178 q^{77} + 2604 q^{78} - 606 q^{79} - 800 q^{80} + 1870 q^{81} - 1884 q^{82} - 654 q^{83} + 1414 q^{84} - 3952 q^{85} + 3010 q^{86} + 910 q^{87} - 978 q^{88} - 546 q^{89} - 1712 q^{90} + 2290 q^{91} + 450 q^{92} + 382 q^{93} + 3586 q^{94} - 172 q^{95} - 224 q^{96} + 3340 q^{97} + 3457 q^{98} - 2952 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1575))\)

We only show spaces with odd 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
1575.3.c \(\chi_{1575}(701, \cdot)\) 1575.3.c.a 4 1
1575.3.c.b 16
1575.3.c.c 16
1575.3.c.d 16
1575.3.c.e 24
1575.3.e \(\chi_{1575}(874, \cdot)\) n/a 118 1
1575.3.f \(\chi_{1575}(449, \cdot)\) 1575.3.f.a 8 1
1575.3.f.b 32
1575.3.f.c 32
1575.3.h \(\chi_{1575}(1126, \cdot)\) n/a 123 1
1575.3.n \(\chi_{1575}(818, \cdot)\) n/a 192 2
1575.3.o \(\chi_{1575}(568, \cdot)\) n/a 180 2
1575.3.r \(\chi_{1575}(1174, \cdot)\) n/a 568 2
1575.3.t \(\chi_{1575}(326, \cdot)\) n/a 596 2
1575.3.w \(\chi_{1575}(599, \cdot)\) n/a 568 2
1575.3.x \(\chi_{1575}(451, \cdot)\) n/a 248 2
1575.3.y \(\chi_{1575}(76, \cdot)\) n/a 596 2
1575.3.z \(\chi_{1575}(674, \cdot)\) n/a 192 2
1575.3.bb \(\chi_{1575}(974, \cdot)\) n/a 432 2
1575.3.bd \(\chi_{1575}(376, \cdot)\) n/a 596 2
1575.3.be \(\chi_{1575}(851, \cdot)\) n/a 596 2
1575.3.bh \(\chi_{1575}(349, \cdot)\) n/a 568 2
1575.3.bj \(\chi_{1575}(199, \cdot)\) n/a 236 2
1575.3.bl \(\chi_{1575}(176, \cdot)\) n/a 456 2
1575.3.bn \(\chi_{1575}(926, \cdot)\) n/a 204 2
1575.3.bo \(\chi_{1575}(124, \cdot)\) n/a 568 2
1575.3.bq \(\chi_{1575}(1426, \cdot)\) n/a 596 2
1575.3.bs \(\chi_{1575}(74, \cdot)\) n/a 568 2
1575.3.bt \(\chi_{1575}(181, \cdot)\) n/a 792 4
1575.3.bv \(\chi_{1575}(134, \cdot)\) n/a 480 4
1575.3.bw \(\chi_{1575}(244, \cdot)\) n/a 792 4
1575.3.by \(\chi_{1575}(71, \cdot)\) n/a 480 4
1575.3.cb \(\chi_{1575}(718, \cdot)\) n/a 1136 4
1575.3.cc \(\chi_{1575}(68, \cdot)\) n/a 1136 4
1575.3.ce \(\chi_{1575}(1118, \cdot)\) n/a 1136 4
1575.3.cg \(\chi_{1575}(43, \cdot)\) n/a 864 4
1575.3.ci \(\chi_{1575}(793, \cdot)\) n/a 472 4
1575.3.cl \(\chi_{1575}(143, \cdot)\) n/a 384 4
1575.3.cn \(\chi_{1575}(293, \cdot)\) n/a 1136 4
1575.3.cp \(\chi_{1575}(193, \cdot)\) n/a 1136 4
1575.3.cv \(\chi_{1575}(127, \cdot)\) n/a 1200 8
1575.3.cw \(\chi_{1575}(62, \cdot)\) n/a 1280 8
1575.3.cy \(\chi_{1575}(389, \cdot)\) n/a 3808 8
1575.3.da \(\chi_{1575}(166, \cdot)\) n/a 3808 8
1575.3.dc \(\chi_{1575}(94, \cdot)\) n/a 3808 8
1575.3.dd \(\chi_{1575}(116, \cdot)\) n/a 1280 8
1575.3.df \(\chi_{1575}(281, \cdot)\) n/a 2880 8
1575.3.dh \(\chi_{1575}(19, \cdot)\) n/a 1584 8
1575.3.dj \(\chi_{1575}(34, \cdot)\) n/a 3808 8
1575.3.dm \(\chi_{1575}(191, \cdot)\) n/a 3808 8
1575.3.dn \(\chi_{1575}(31, \cdot)\) n/a 3808 8
1575.3.dp \(\chi_{1575}(29, \cdot)\) n/a 2880 8
1575.3.dr \(\chi_{1575}(44, \cdot)\) n/a 1280 8
1575.3.ds \(\chi_{1575}(286, \cdot)\) n/a 3808 8
1575.3.dt \(\chi_{1575}(136, \cdot)\) n/a 1584 8
1575.3.du \(\chi_{1575}(254, \cdot)\) n/a 3808 8
1575.3.dx \(\chi_{1575}(11, \cdot)\) n/a 3808 8
1575.3.dz \(\chi_{1575}(229, \cdot)\) n/a 3808 8
1575.3.ea \(\chi_{1575}(67, \cdot)\) n/a 7616 16
1575.3.ec \(\chi_{1575}(83, \cdot)\) n/a 7616 16
1575.3.ee \(\chi_{1575}(17, \cdot)\) n/a 2560 16
1575.3.eh \(\chi_{1575}(37, \cdot)\) n/a 3168 16
1575.3.ej \(\chi_{1575}(22, \cdot)\) n/a 5760 16
1575.3.el \(\chi_{1575}(47, \cdot)\) n/a 7616 16
1575.3.en \(\chi_{1575}(38, \cdot)\) n/a 7616 16
1575.3.eo \(\chi_{1575}(58, \cdot)\) n/a 7616 16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1575))\) into lower level spaces

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