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Properties

Label 3465.2
Level 3465
Weight 2
Dimension 281184
Nonzero newspaces 120
Sturm bound 1658880
Trace bound 16

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Defining parameters

Level: \( N \) = \( 3465 = 3^{2} \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 120 \)
Sturm bound: \(1658880\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3465))\).

Total New Old
Modular forms 422400 286040 136360
Cusp forms 407041 281184 125857
Eisenstein series 15359 4856 10503

Trace form

\( 281184 q - 112 q^{2} - 144 q^{3} - 144 q^{4} - 168 q^{5} - 400 q^{6} - 164 q^{7} - 316 q^{8} - 128 q^{9} + O(q^{10}) \) \( 281184 q - 112 q^{2} - 144 q^{3} - 144 q^{4} - 168 q^{5} - 400 q^{6} - 164 q^{7} - 316 q^{8} - 128 q^{9} - 498 q^{10} - 352 q^{11} - 192 q^{12} - 140 q^{13} - 96 q^{14} - 416 q^{15} - 352 q^{16} - 52 q^{17} + 48 q^{18} - 348 q^{19} + 74 q^{20} - 384 q^{21} - 332 q^{22} - 76 q^{23} + 296 q^{24} - 100 q^{25} + 124 q^{26} + 144 q^{27} - 124 q^{28} + 48 q^{29} + 164 q^{30} - 160 q^{31} + 744 q^{32} + 128 q^{33} + 216 q^{34} + 6 q^{35} - 520 q^{36} - 80 q^{37} + 460 q^{38} + 24 q^{39} + 270 q^{40} - 68 q^{41} + 160 q^{42} - 208 q^{43} + 80 q^{44} - 404 q^{45} - 764 q^{46} - 132 q^{47} - 160 q^{48} - 56 q^{49} - 368 q^{50} - 360 q^{51} + 388 q^{52} + 12 q^{53} + 72 q^{54} - 232 q^{55} - 620 q^{56} - 112 q^{57} + 724 q^{58} + 320 q^{59} - 12 q^{60} + 304 q^{61} + 940 q^{62} - 208 q^{63} + 668 q^{64} + 560 q^{65} + 204 q^{66} + 692 q^{67} + 1092 q^{68} + 352 q^{69} + 700 q^{70} + 292 q^{71} + 368 q^{72} + 336 q^{73} + 1156 q^{74} - 136 q^{75} + 1128 q^{76} + 348 q^{77} - 320 q^{78} + 400 q^{79} - 158 q^{80} - 160 q^{81} + 428 q^{82} - 176 q^{83} - 188 q^{84} - 196 q^{85} - 380 q^{86} - 472 q^{87} - 8 q^{88} - 604 q^{89} - 1044 q^{90} - 920 q^{91} - 1256 q^{92} - 632 q^{93} - 180 q^{94} - 816 q^{95} - 1672 q^{96} - 248 q^{97} - 776 q^{98} - 1032 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3465))\)

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
3465.2.a \(\chi_{3465}(1, \cdot)\) 3465.2.a.a 1 1
3465.2.a.b 1
3465.2.a.c 1
3465.2.a.d 1
3465.2.a.e 1
3465.2.a.f 1
3465.2.a.g 1
3465.2.a.h 1
3465.2.a.i 1
3465.2.a.j 1
3465.2.a.k 1
3465.2.a.l 1
3465.2.a.m 1
3465.2.a.n 1
3465.2.a.o 1
3465.2.a.p 1
3465.2.a.q 1
3465.2.a.r 1
3465.2.a.s 1
3465.2.a.t 1
3465.2.a.u 2
3465.2.a.v 2
3465.2.a.w 2
3465.2.a.x 2
3465.2.a.y 2
3465.2.a.z 2
3465.2.a.ba 3
3465.2.a.bb 3
3465.2.a.bc 3
3465.2.a.bd 3
3465.2.a.be 3
3465.2.a.bf 3
3465.2.a.bg 3
3465.2.a.bh 3
3465.2.a.bi 3
3465.2.a.bj 4
3465.2.a.bk 4
3465.2.a.bl 4
3465.2.a.bm 5
3465.2.a.bn 6
3465.2.a.bo 6
3465.2.a.bp 6
3465.2.a.bq 6
3465.2.c \(\chi_{3465}(694, \cdot)\) n/a 152 1
3465.2.d \(\chi_{3465}(881, \cdot)\) n/a 112 1
3465.2.f \(\chi_{3465}(2969, \cdot)\) n/a 144 1
3465.2.i \(\chi_{3465}(2386, \cdot)\) n/a 160 1
3465.2.k \(\chi_{3465}(3079, \cdot)\) n/a 236 1
3465.2.l \(\chi_{3465}(2276, \cdot)\) 3465.2.l.a 48 1
3465.2.l.b 48
3465.2.n \(\chi_{3465}(1574, \cdot)\) n/a 160 1
3465.2.q \(\chi_{3465}(331, \cdot)\) n/a 640 2
3465.2.r \(\chi_{3465}(1156, \cdot)\) n/a 480 2
3465.2.s \(\chi_{3465}(991, \cdot)\) n/a 264 2
3465.2.t \(\chi_{3465}(2641, \cdot)\) n/a 640 2
3465.2.v \(\chi_{3465}(1772, \cdot)\) n/a 240 2
3465.2.w \(\chi_{3465}(692, \cdot)\) n/a 384 2
3465.2.y \(\chi_{3465}(1882, \cdot)\) n/a 400 2
3465.2.bb \(\chi_{3465}(1198, \cdot)\) n/a 360 2
3465.2.bc \(\chi_{3465}(631, \cdot)\) n/a 480 4
3465.2.bd \(\chi_{3465}(241, \cdot)\) n/a 768 2
3465.2.bg \(\chi_{3465}(1649, \cdot)\) n/a 1136 2
3465.2.bi \(\chi_{3465}(1046, \cdot)\) n/a 640 2
3465.2.bj \(\chi_{3465}(529, \cdot)\) n/a 960 2
3465.2.bm \(\chi_{3465}(296, \cdot)\) n/a 256 2
3465.2.bn \(\chi_{3465}(1594, \cdot)\) n/a 472 2
3465.2.bp \(\chi_{3465}(419, \cdot)\) n/a 960 2
3465.2.bt \(\chi_{3465}(1244, \cdot)\) n/a 960 2
3465.2.bw \(\chi_{3465}(769, \cdot)\) n/a 1136 2
3465.2.by \(\chi_{3465}(1451, \cdot)\) n/a 768 2
3465.2.bz \(\chi_{3465}(439, \cdot)\) n/a 1136 2
3465.2.cb \(\chi_{3465}(1121, \cdot)\) n/a 576 2
3465.2.cf \(\chi_{3465}(89, \cdot)\) n/a 320 2
3465.2.ch \(\chi_{3465}(2861, \cdot)\) n/a 208 2
3465.2.ci \(\chi_{3465}(1684, \cdot)\) n/a 400 2
3465.2.ck \(\chi_{3465}(659, \cdot)\) n/a 864 2
3465.2.cm \(\chi_{3465}(2551, \cdot)\) n/a 768 2
3465.2.cp \(\chi_{3465}(2144, \cdot)\) n/a 1136 2
3465.2.cr \(\chi_{3465}(76, \cdot)\) n/a 768 2
3465.2.ct \(\chi_{3465}(1849, \cdot)\) n/a 720 2
3465.2.cv \(\chi_{3465}(551, \cdot)\) n/a 640 2
3465.2.cw \(\chi_{3465}(1024, \cdot)\) n/a 960 2
3465.2.cy \(\chi_{3465}(2036, \cdot)\) n/a 640 2
3465.2.da \(\chi_{3465}(901, \cdot)\) n/a 320 2
3465.2.dd \(\chi_{3465}(494, \cdot)\) n/a 384 2
3465.2.dg \(\chi_{3465}(1739, \cdot)\) n/a 960 2
3465.2.di \(\chi_{3465}(956, \cdot)\) n/a 768 2
3465.2.dj \(\chi_{3465}(934, \cdot)\) n/a 1136 2
3465.2.dn \(\chi_{3465}(944, \cdot)\) n/a 768 4
3465.2.dp \(\chi_{3465}(701, \cdot)\) n/a 384 4
3465.2.dq \(\chi_{3465}(244, \cdot)\) n/a 944 4
3465.2.ds \(\chi_{3465}(811, \cdot)\) n/a 640 4
3465.2.dv \(\chi_{3465}(134, \cdot)\) n/a 576 4
3465.2.dx \(\chi_{3465}(251, \cdot)\) n/a 512 4
3465.2.dy \(\chi_{3465}(64, \cdot)\) n/a 720 4
3465.2.eb \(\chi_{3465}(373, \cdot)\) n/a 2272 4
3465.2.ec \(\chi_{3465}(1123, \cdot)\) n/a 1920 4
3465.2.ee \(\chi_{3465}(857, \cdot)\) n/a 2272 4
3465.2.eh \(\chi_{3465}(23, \cdot)\) n/a 1920 4
3465.2.ei \(\chi_{3465}(617, \cdot)\) n/a 1440 4
3465.2.el \(\chi_{3465}(923, \cdot)\) n/a 2272 4
3465.2.em \(\chi_{3465}(142, \cdot)\) n/a 2272 4
3465.2.eo \(\chi_{3465}(802, \cdot)\) n/a 944 4
3465.2.er \(\chi_{3465}(397, \cdot)\) n/a 800 4
3465.2.et \(\chi_{3465}(628, \cdot)\) n/a 1920 4
3465.2.ev \(\chi_{3465}(593, \cdot)\) n/a 768 4
3465.2.ex \(\chi_{3465}(362, \cdot)\) n/a 2272 4
3465.2.ey \(\chi_{3465}(947, \cdot)\) n/a 1920 4
3465.2.fa \(\chi_{3465}(683, \cdot)\) n/a 640 4
3465.2.fd \(\chi_{3465}(727, \cdot)\) n/a 1920 4
3465.2.fe \(\chi_{3465}(43, \cdot)\) n/a 1728 4
3465.2.fg \(\chi_{3465}(466, \cdot)\) n/a 3072 8
3465.2.fh \(\chi_{3465}(361, \cdot)\) n/a 1280 8
3465.2.fi \(\chi_{3465}(421, \cdot)\) n/a 2304 8
3465.2.fj \(\chi_{3465}(16, \cdot)\) n/a 3072 8
3465.2.fk \(\chi_{3465}(127, \cdot)\) n/a 1440 8
3465.2.fn \(\chi_{3465}(433, \cdot)\) n/a 1888 8
3465.2.fp \(\chi_{3465}(62, \cdot)\) n/a 1536 8
3465.2.fq \(\chi_{3465}(323, \cdot)\) n/a 1152 8
3465.2.ft \(\chi_{3465}(304, \cdot)\) n/a 4544 8
3465.2.fu \(\chi_{3465}(326, \cdot)\) n/a 3072 8
3465.2.fw \(\chi_{3465}(509, \cdot)\) n/a 4544 8
3465.2.fz \(\chi_{3465}(359, \cdot)\) n/a 1536 8
3465.2.gc \(\chi_{3465}(271, \cdot)\) n/a 1280 8
3465.2.ge \(\chi_{3465}(146, \cdot)\) n/a 3072 8
3465.2.gg \(\chi_{3465}(4, \cdot)\) n/a 4544 8
3465.2.gh \(\chi_{3465}(236, \cdot)\) n/a 3072 8
3465.2.gj \(\chi_{3465}(169, \cdot)\) n/a 3456 8
3465.2.gl \(\chi_{3465}(391, \cdot)\) n/a 3072 8
3465.2.gn \(\chi_{3465}(569, \cdot)\) n/a 4544 8
3465.2.gq \(\chi_{3465}(61, \cdot)\) n/a 3072 8
3465.2.gs \(\chi_{3465}(29, \cdot)\) n/a 3456 8
3465.2.gu \(\chi_{3465}(289, \cdot)\) n/a 1888 8
3465.2.gv \(\chi_{3465}(26, \cdot)\) n/a 1024 8
3465.2.gx \(\chi_{3465}(269, \cdot)\) n/a 1536 8
3465.2.hb \(\chi_{3465}(281, \cdot)\) n/a 2304 8
3465.2.hd \(\chi_{3465}(94, \cdot)\) n/a 4544 8
3465.2.he \(\chi_{3465}(536, \cdot)\) n/a 3072 8
3465.2.hg \(\chi_{3465}(139, \cdot)\) n/a 4544 8
3465.2.hj \(\chi_{3465}(59, \cdot)\) n/a 4544 8
3465.2.hn \(\chi_{3465}(104, \cdot)\) n/a 4544 8
3465.2.hp \(\chi_{3465}(19, \cdot)\) n/a 1888 8
3465.2.hq \(\chi_{3465}(116, \cdot)\) n/a 1024 8
3465.2.ht \(\chi_{3465}(214, \cdot)\) n/a 4544 8
3465.2.hu \(\chi_{3465}(416, \cdot)\) n/a 3072 8
3465.2.hw \(\chi_{3465}(74, \cdot)\) n/a 4544 8
3465.2.hz \(\chi_{3465}(481, \cdot)\) n/a 3072 8
3465.2.ib \(\chi_{3465}(337, \cdot)\) n/a 6912 16
3465.2.ic \(\chi_{3465}(97, \cdot)\) n/a 9088 16
3465.2.if \(\chi_{3465}(53, \cdot)\) n/a 3072 16
3465.2.ih \(\chi_{3465}(158, \cdot)\) n/a 9088 16
3465.2.ii \(\chi_{3465}(173, \cdot)\) n/a 9088 16
3465.2.ik \(\chi_{3465}(17, \cdot)\) n/a 3072 16
3465.2.im \(\chi_{3465}(157, \cdot)\) n/a 9088 16
3465.2.io \(\chi_{3465}(82, \cdot)\) n/a 3776 16
3465.2.ir \(\chi_{3465}(172, \cdot)\) n/a 3776 16
3465.2.it \(\chi_{3465}(193, \cdot)\) n/a 9088 16
3465.2.iu \(\chi_{3465}(83, \cdot)\) n/a 9088 16
3465.2.ix \(\chi_{3465}(92, \cdot)\) n/a 6912 16
3465.2.iy \(\chi_{3465}(137, \cdot)\) n/a 9088 16
3465.2.jb \(\chi_{3465}(68, \cdot)\) n/a 9088 16
3465.2.jd \(\chi_{3465}(103, \cdot)\) n/a 9088 16
3465.2.je \(\chi_{3465}(277, \cdot)\) n/a 9088 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3465))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3465)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(385))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(495))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(693))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1155))\)\(^{\oplus 2}\)