↑

Properties

Label 1665.2
Level 1665
Weight 2
Dimension 70428
Nonzero newspaces 80
Sturm bound 393984
Trace bound 25

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 1665 = 3^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(393984\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1665))\).

Total New Old
Modular forms 100800 72320 28480
Cusp forms 96193 70428 25765
Eisenstein series 4607 1892 2715

Trace form

\( 70428 q - 94 q^{2} - 128 q^{3} - 86 q^{4} - 144 q^{5} - 400 q^{6} - 84 q^{7} - 102 q^{8} - 136 q^{9} + O(q^{10}) \) \( 70428 q - 94 q^{2} - 128 q^{3} - 86 q^{4} - 144 q^{5} - 400 q^{6} - 84 q^{7} - 102 q^{8} - 136 q^{9} - 456 q^{10} - 316 q^{11} - 160 q^{12} - 104 q^{13} - 132 q^{14} - 224 q^{15} - 310 q^{16} - 112 q^{17} - 176 q^{18} - 284 q^{19} - 212 q^{20} - 432 q^{21} - 124 q^{22} - 132 q^{23} - 216 q^{24} - 168 q^{25} - 334 q^{26} - 176 q^{27} - 220 q^{28} - 116 q^{29} - 280 q^{30} - 200 q^{31} + 10 q^{32} - 160 q^{33} + 8 q^{34} - 92 q^{35} - 368 q^{36} - 242 q^{37} - 112 q^{38} - 80 q^{39} + 19 q^{40} - 116 q^{41} - 72 q^{42} + 28 q^{43} + 172 q^{44} - 160 q^{45} - 748 q^{46} + 8 q^{47} - 64 q^{48} - 66 q^{49} - 91 q^{50} - 400 q^{51} - 112 q^{52} - 112 q^{53} - 136 q^{54} - 510 q^{55} - 372 q^{56} - 176 q^{57} - 124 q^{58} - 124 q^{59} - 256 q^{60} - 286 q^{61} - 96 q^{62} - 264 q^{63} - 170 q^{64} - 205 q^{65} - 608 q^{66} - 84 q^{67} - 32 q^{68} - 264 q^{69} - 84 q^{70} - 308 q^{71} - 336 q^{72} - 140 q^{73} + 182 q^{74} - 416 q^{75} - 36 q^{76} + 60 q^{77} - 64 q^{78} + 60 q^{79} + 106 q^{80} - 352 q^{81} - 48 q^{82} + 108 q^{83} - 69 q^{85} + 128 q^{86} - 56 q^{87} + 72 q^{88} + 114 q^{89} - 8 q^{90} - 840 q^{91} - 312 q^{92} - 240 q^{93} - 532 q^{94} - 298 q^{95} - 1040 q^{96} - 544 q^{97} - 806 q^{98} - 464 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1665))\)

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
1665.2.a \(\chi_{1665}(1, \cdot)\) 1665.2.a.a 1 1
1665.2.a.b 1
1665.2.a.c 1
1665.2.a.d 1
1665.2.a.e 1
1665.2.a.f 1
1665.2.a.g 1
1665.2.a.h 2
1665.2.a.i 2
1665.2.a.j 2
1665.2.a.k 2
1665.2.a.l 2
1665.2.a.m 3
1665.2.a.n 3
1665.2.a.o 5
1665.2.a.p 5
1665.2.a.q 5
1665.2.a.r 5
1665.2.a.s 5
1665.2.a.t 6
1665.2.a.u 6
1665.2.c \(\chi_{1665}(334, \cdot)\) 1665.2.c.a 2 1
1665.2.c.b 2
1665.2.c.c 2
1665.2.c.d 8
1665.2.c.e 18
1665.2.c.f 26
1665.2.c.g 32
1665.2.e \(\chi_{1665}(406, \cdot)\) 1665.2.e.a 2 1
1665.2.e.b 2
1665.2.e.c 10
1665.2.e.d 12
1665.2.e.e 12
1665.2.e.f 24
1665.2.g \(\chi_{1665}(739, \cdot)\) 1665.2.g.a 4 1
1665.2.g.b 16
1665.2.g.c 16
1665.2.g.d 16
1665.2.g.e 40
1665.2.i \(\chi_{1665}(556, \cdot)\) n/a 288 2
1665.2.j \(\chi_{1665}(676, \cdot)\) n/a 124 2
1665.2.k \(\chi_{1665}(211, \cdot)\) n/a 304 2
1665.2.l \(\chi_{1665}(121, \cdot)\) n/a 304 2
1665.2.m \(\chi_{1665}(1153, \cdot)\) n/a 186 2
1665.2.p \(\chi_{1665}(179, \cdot)\) n/a 152 2
1665.2.q \(\chi_{1665}(332, \cdot)\) n/a 152 2
1665.2.r \(\chi_{1665}(593, \cdot)\) n/a 144 2
1665.2.v \(\chi_{1665}(746, \cdot)\) 1665.2.v.a 48 2
1665.2.v.b 48
1665.2.w \(\chi_{1665}(253, \cdot)\) n/a 186 2
1665.2.y \(\chi_{1665}(196, \cdot)\) n/a 304 2
1665.2.ba \(\chi_{1665}(454, \cdot)\) n/a 448 2
1665.2.bc \(\chi_{1665}(619, \cdot)\) n/a 448 2
1665.2.bh \(\chi_{1665}(184, \cdot)\) n/a 448 2
1665.2.bj \(\chi_{1665}(64, \cdot)\) n/a 184 2
1665.2.bl \(\chi_{1665}(544, \cdot)\) n/a 448 2
1665.2.bo \(\chi_{1665}(961, \cdot)\) n/a 304 2
1665.2.bq \(\chi_{1665}(1306, \cdot)\) n/a 124 2
1665.2.bs \(\chi_{1665}(889, \cdot)\) n/a 432 2
1665.2.bu \(\chi_{1665}(1009, \cdot)\) n/a 188 2
1665.2.bv \(\chi_{1665}(286, \cdot)\) n/a 304 2
1665.2.by \(\chi_{1665}(529, \cdot)\) n/a 448 2
1665.2.ca \(\chi_{1665}(571, \cdot)\) n/a 912 6
1665.2.cb \(\chi_{1665}(46, \cdot)\) n/a 384 6
1665.2.cc \(\chi_{1665}(16, \cdot)\) n/a 912 6
1665.2.ce \(\chi_{1665}(547, \cdot)\) n/a 896 4
1665.2.cf \(\chi_{1665}(82, \cdot)\) n/a 372 4
1665.2.ci \(\chi_{1665}(808, \cdot)\) n/a 896 4
1665.2.cj \(\chi_{1665}(88, \cdot)\) n/a 896 4
1665.2.cl \(\chi_{1665}(356, \cdot)\) n/a 608 4
1665.2.cp \(\chi_{1665}(137, \cdot)\) n/a 896 4
1665.2.cq \(\chi_{1665}(212, \cdot)\) n/a 896 4
1665.2.cr \(\chi_{1665}(14, \cdot)\) n/a 896 4
1665.2.ct \(\chi_{1665}(569, \cdot)\) n/a 896 4
1665.2.cw \(\chi_{1665}(191, \cdot)\) n/a 608 4
1665.2.cy \(\chi_{1665}(251, \cdot)\) n/a 192 4
1665.2.cz \(\chi_{1665}(233, \cdot)\) n/a 304 4
1665.2.da \(\chi_{1665}(602, \cdot)\) n/a 304 4
1665.2.df \(\chi_{1665}(38, \cdot)\) n/a 864 4
1665.2.dg \(\chi_{1665}(47, \cdot)\) n/a 896 4
1665.2.dh \(\chi_{1665}(122, \cdot)\) n/a 896 4
1665.2.di \(\chi_{1665}(443, \cdot)\) n/a 896 4
1665.2.dm \(\chi_{1665}(524, \cdot)\) n/a 896 4
1665.2.do \(\chi_{1665}(134, \cdot)\) n/a 304 4
1665.2.dp \(\chi_{1665}(236, \cdot)\) n/a 608 4
1665.2.dr \(\chi_{1665}(208, \cdot)\) n/a 372 4
1665.2.du \(\chi_{1665}(193, \cdot)\) n/a 896 4
1665.2.dv \(\chi_{1665}(43, \cdot)\) n/a 896 4
1665.2.dy \(\chi_{1665}(637, \cdot)\) n/a 896 4
1665.2.eb \(\chi_{1665}(289, \cdot)\) n/a 552 6
1665.2.ec \(\chi_{1665}(139, \cdot)\) n/a 1344 6
1665.2.eh \(\chi_{1665}(4, \cdot)\) n/a 1344 6
1665.2.ek \(\chi_{1665}(34, \cdot)\) n/a 1344 6
1665.2.el \(\chi_{1665}(379, \cdot)\) n/a 564 6
1665.2.em \(\chi_{1665}(136, \cdot)\) n/a 384 6
1665.2.en \(\chi_{1665}(151, \cdot)\) n/a 912 6
1665.2.es \(\chi_{1665}(691, \cdot)\) n/a 912 6
1665.2.et \(\chi_{1665}(229, \cdot)\) n/a 1344 6
1665.2.eu \(\chi_{1665}(283, \cdot)\) n/a 2688 12
1665.2.ex \(\chi_{1665}(22, \cdot)\) n/a 2688 12
1665.2.ey \(\chi_{1665}(163, \cdot)\) n/a 1116 12
1665.2.fa \(\chi_{1665}(77, \cdot)\) n/a 2688 12
1665.2.fd \(\chi_{1665}(83, \cdot)\) n/a 2688 12
1665.2.fg \(\chi_{1665}(116, \cdot)\) n/a 624 12
1665.2.fh \(\chi_{1665}(59, \cdot)\) n/a 2688 12
1665.2.fi \(\chi_{1665}(56, \cdot)\) n/a 1824 12
1665.2.fj \(\chi_{1665}(89, \cdot)\) n/a 912 12
1665.2.fm \(\chi_{1665}(182, \cdot)\) n/a 2688 12
1665.2.fn \(\chi_{1665}(53, \cdot)\) n/a 912 12
1665.2.fs \(\chi_{1665}(62, \cdot)\) n/a 912 12
1665.2.ft \(\chi_{1665}(263, \cdot)\) n/a 2688 12
1665.2.fv \(\chi_{1665}(479, \cdot)\) n/a 2688 12
1665.2.fw \(\chi_{1665}(146, \cdot)\) n/a 1824 12
1665.2.fy \(\chi_{1665}(13, \cdot)\) n/a 2688 12
1665.2.gb \(\chi_{1665}(172, \cdot)\) n/a 1116 12
1665.2.gc \(\chi_{1665}(277, \cdot)\) n/a 2688 12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1665))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1665)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(333))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(555))\)\(^{\oplus 2}\)