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

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

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 the 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

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