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Properties

Label 1575.2
Level 1575
Weight 2
Dimension 59493
Nonzero newspaces 60
Sturm bound 345600
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(345600\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1575))\).

Total New Old
Modular forms 89088 61337 27751
Cusp forms 83713 59493 24220
Eisenstein series 5375 1844 3531

Trace form

\( 59493 q - 85 q^{2} - 108 q^{3} - 105 q^{4} - 102 q^{5} - 172 q^{6} - 115 q^{7} - 195 q^{8} - 92 q^{9} + O(q^{10}) \) \( 59493 q - 85 q^{2} - 108 q^{3} - 105 q^{4} - 102 q^{5} - 172 q^{6} - 115 q^{7} - 195 q^{8} - 92 q^{9} - 282 q^{10} - 106 q^{11} - 32 q^{12} - 72 q^{13} - 57 q^{14} - 296 q^{15} - 65 q^{16} - 8 q^{17} + 12 q^{18} - 200 q^{19} + 36 q^{20} - 162 q^{21} - 44 q^{22} + 46 q^{23} + 104 q^{24} - 6 q^{25} - 24 q^{26} + 6 q^{27} - 95 q^{28} + 2 q^{29} - 48 q^{30} - 26 q^{31} + 257 q^{32} - 20 q^{33} + 190 q^{34} - 76 q^{35} - 428 q^{36} - 68 q^{37} + 98 q^{38} - 168 q^{39} + 42 q^{40} - 124 q^{41} - 122 q^{42} - 164 q^{43} - 18 q^{44} - 168 q^{45} - 184 q^{46} - 86 q^{47} - 328 q^{48} - 35 q^{49} - 110 q^{50} - 332 q^{51} + 284 q^{52} + 8 q^{53} - 122 q^{54} - 124 q^{55} - 105 q^{56} - 216 q^{57} + 352 q^{58} + 148 q^{59} - 232 q^{60} + 74 q^{61} + 88 q^{62} - 180 q^{63} - 531 q^{64} - 178 q^{65} - 38 q^{66} - 12 q^{67} - 488 q^{68} - 140 q^{69} - 114 q^{70} - 152 q^{71} - 594 q^{72} - 186 q^{73} - 440 q^{74} - 448 q^{75} - 138 q^{76} - 162 q^{77} - 756 q^{78} - 108 q^{79} - 1030 q^{80} - 344 q^{81} - 406 q^{82} - 514 q^{83} - 644 q^{84} - 282 q^{85} - 634 q^{86} - 506 q^{87} - 450 q^{88} - 690 q^{89} - 752 q^{90} - 704 q^{91} - 1312 q^{92} - 578 q^{93} - 230 q^{94} - 292 q^{95} - 1016 q^{96} - 136 q^{97} - 975 q^{98} - 600 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1575))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1575.2.a \(\chi_{1575}(1, \cdot)\) 1575.2.a.a 1 1
1575.2.a.b 1
1575.2.a.c 1
1575.2.a.d 1
1575.2.a.e 1
1575.2.a.f 1
1575.2.a.g 1
1575.2.a.h 1
1575.2.a.i 1
1575.2.a.j 1
1575.2.a.k 1
1575.2.a.l 2
1575.2.a.m 2
1575.2.a.n 2
1575.2.a.o 2
1575.2.a.p 2
1575.2.a.q 2
1575.2.a.r 2
1575.2.a.s 2
1575.2.a.t 2
1575.2.a.u 2
1575.2.a.v 2
1575.2.a.w 3
1575.2.a.x 3
1575.2.a.y 4
1575.2.a.z 4
1575.2.b \(\chi_{1575}(251, \cdot)\) 1575.2.b.a 4 1
1575.2.b.b 4
1575.2.b.c 4
1575.2.b.d 4
1575.2.b.e 4
1575.2.b.f 8
1575.2.b.g 8
1575.2.b.h 16
1575.2.d \(\chi_{1575}(1324, \cdot)\) 1575.2.d.a 2 1
1575.2.d.b 2
1575.2.d.c 2
1575.2.d.d 4
1575.2.d.e 4
1575.2.d.f 4
1575.2.d.g 4
1575.2.d.h 4
1575.2.d.i 4
1575.2.d.j 4
1575.2.d.k 4
1575.2.d.l 8
1575.2.g \(\chi_{1575}(1574, \cdot)\) 1575.2.g.a 8 1
1575.2.g.b 8
1575.2.g.c 8
1575.2.g.d 8
1575.2.g.e 16
1575.2.i \(\chi_{1575}(526, \cdot)\) n/a 228 2
1575.2.j \(\chi_{1575}(226, \cdot)\) n/a 120 2
1575.2.k \(\chi_{1575}(1201, \cdot)\) n/a 292 2
1575.2.l \(\chi_{1575}(151, \cdot)\) n/a 292 2
1575.2.m \(\chi_{1575}(1268, \cdot)\) 1575.2.m.a 8 2
1575.2.m.b 8
1575.2.m.c 12
1575.2.m.d 12
1575.2.m.e 16
1575.2.m.f 16
1575.2.p \(\chi_{1575}(118, \cdot)\) n/a 116 2
1575.2.q \(\chi_{1575}(316, \cdot)\) n/a 304 4
1575.2.s \(\chi_{1575}(499, \cdot)\) n/a 280 2
1575.2.u \(\chi_{1575}(101, \cdot)\) n/a 292 2
1575.2.v \(\chi_{1575}(299, \cdot)\) n/a 280 2
1575.2.ba \(\chi_{1575}(524, \cdot)\) n/a 280 2
1575.2.bc \(\chi_{1575}(899, \cdot)\) 1575.2.bc.a 8 2
1575.2.bc.b 8
1575.2.bc.c 24
1575.2.bc.d 24
1575.2.bc.e 32
1575.2.bf \(\chi_{1575}(551, \cdot)\) n/a 292 2
1575.2.bg \(\chi_{1575}(424, \cdot)\) n/a 116 2
1575.2.bi \(\chi_{1575}(274, \cdot)\) n/a 216 2
1575.2.bk \(\chi_{1575}(26, \cdot)\) 1575.2.bk.a 4 2
1575.2.bk.b 4
1575.2.bk.c 4
1575.2.bk.d 8
1575.2.bk.e 12
1575.2.bk.f 12
1575.2.bk.g 16
1575.2.bk.h 16
1575.2.bk.i 24
1575.2.bm \(\chi_{1575}(776, \cdot)\) n/a 292 2
1575.2.bp \(\chi_{1575}(949, \cdot)\) n/a 280 2
1575.2.br \(\chi_{1575}(824, \cdot)\) n/a 280 2
1575.2.bu \(\chi_{1575}(314, \cdot)\) n/a 320 4
1575.2.bx \(\chi_{1575}(64, \cdot)\) n/a 296 4
1575.2.bz \(\chi_{1575}(566, \cdot)\) n/a 320 4
1575.2.ca \(\chi_{1575}(418, \cdot)\) n/a 560 4
1575.2.cd \(\chi_{1575}(893, \cdot)\) n/a 560 4
1575.2.cf \(\chi_{1575}(32, \cdot)\) n/a 560 4
1575.2.ch \(\chi_{1575}(82, \cdot)\) n/a 232 4
1575.2.cj \(\chi_{1575}(643, \cdot)\) n/a 560 4
1575.2.ck \(\chi_{1575}(218, \cdot)\) n/a 432 4
1575.2.cm \(\chi_{1575}(107, \cdot)\) n/a 192 4
1575.2.co \(\chi_{1575}(157, \cdot)\) n/a 560 4
1575.2.cq \(\chi_{1575}(121, \cdot)\) n/a 1888 8
1575.2.cr \(\chi_{1575}(16, \cdot)\) n/a 1888 8
1575.2.cs \(\chi_{1575}(46, \cdot)\) n/a 784 8
1575.2.ct \(\chi_{1575}(106, \cdot)\) n/a 1440 8
1575.2.cu \(\chi_{1575}(433, \cdot)\) n/a 784 8
1575.2.cx \(\chi_{1575}(8, \cdot)\) n/a 480 8
1575.2.cz \(\chi_{1575}(164, \cdot)\) n/a 1888 8
1575.2.db \(\chi_{1575}(4, \cdot)\) n/a 1888 8
1575.2.de \(\chi_{1575}(41, \cdot)\) n/a 1888 8
1575.2.dg \(\chi_{1575}(206, \cdot)\) n/a 640 8
1575.2.di \(\chi_{1575}(169, \cdot)\) n/a 1440 8
1575.2.dk \(\chi_{1575}(109, \cdot)\) n/a 784 8
1575.2.dl \(\chi_{1575}(236, \cdot)\) n/a 1888 8
1575.2.do \(\chi_{1575}(89, \cdot)\) n/a 640 8
1575.2.dq \(\chi_{1575}(104, \cdot)\) n/a 1888 8
1575.2.dv \(\chi_{1575}(59, \cdot)\) n/a 1888 8
1575.2.dw \(\chi_{1575}(131, \cdot)\) n/a 1888 8
1575.2.dy \(\chi_{1575}(184, \cdot)\) n/a 1888 8
1575.2.eb \(\chi_{1575}(187, \cdot)\) n/a 3776 16
1575.2.ed \(\chi_{1575}(53, \cdot)\) n/a 1280 16
1575.2.ef \(\chi_{1575}(92, \cdot)\) n/a 2880 16
1575.2.eg \(\chi_{1575}(13, \cdot)\) n/a 3776 16
1575.2.ei \(\chi_{1575}(73, \cdot)\) n/a 1568 16
1575.2.ek \(\chi_{1575}(2, \cdot)\) n/a 3776 16
1575.2.em \(\chi_{1575}(23, \cdot)\) n/a 3776 16
1575.2.ep \(\chi_{1575}(52, \cdot)\) n/a 3776 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1575))\) into lower level spaces

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