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Properties

Label 2080.2
Level 2080
Weight 2
Dimension 65076
Nonzero newspaces 72
Sturm bound 516096
Trace bound 25

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Defining parameters

Level: \( N \) = \( 2080 = 2^{5} \cdot 5 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(516096\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2080))\).

Total New Old
Modular forms 132096 66396 65700
Cusp forms 125953 65076 60877
Eisenstein series 6143 1320 4823

Trace form

\( 65076 q - 80 q^{2} - 64 q^{3} - 80 q^{4} - 124 q^{5} - 240 q^{6} - 64 q^{7} - 80 q^{8} - 124 q^{9} + O(q^{10}) \) \( 65076 q - 80 q^{2} - 64 q^{3} - 80 q^{4} - 124 q^{5} - 240 q^{6} - 64 q^{7} - 80 q^{8} - 124 q^{9} - 104 q^{10} - 184 q^{11} - 16 q^{12} - 76 q^{13} - 112 q^{14} - 84 q^{15} - 160 q^{16} - 24 q^{17} - 56 q^{19} - 88 q^{20} - 240 q^{21} - 32 q^{22} - 32 q^{23} - 128 q^{24} - 188 q^{25} - 304 q^{26} - 16 q^{27} - 160 q^{28} - 104 q^{29} - 184 q^{30} - 72 q^{31} - 160 q^{32} - 128 q^{33} - 128 q^{34} + 4 q^{35} - 352 q^{36} - 8 q^{37} - 48 q^{38} + 8 q^{39} - 240 q^{40} - 248 q^{41} + 32 q^{43} + 80 q^{44} - 4 q^{45} - 112 q^{46} + 128 q^{48} + 4 q^{49} - 40 q^{50} - 144 q^{51} - 72 q^{52} - 40 q^{53} - 32 q^{54} - 116 q^{55} - 192 q^{56} - 160 q^{57} - 96 q^{58} - 184 q^{59} - 256 q^{60} - 152 q^{61} - 160 q^{62} - 272 q^{63} - 320 q^{64} - 372 q^{65} - 880 q^{66} - 272 q^{67} - 224 q^{68} - 144 q^{69} - 432 q^{70} - 376 q^{71} - 464 q^{72} - 264 q^{73} - 368 q^{74} - 232 q^{75} - 496 q^{76} - 208 q^{77} - 312 q^{78} - 240 q^{79} - 448 q^{80} - 332 q^{81} - 400 q^{82} + 16 q^{83} - 608 q^{84} - 256 q^{85} - 576 q^{86} + 216 q^{87} - 416 q^{88} - 8 q^{89} - 576 q^{90} + 56 q^{91} - 608 q^{92} + 64 q^{93} - 256 q^{94} + 140 q^{95} - 480 q^{96} + 8 q^{97} - 256 q^{98} + 536 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2080))\)

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
2080.2.a \(\chi_{2080}(1, \cdot)\) 2080.2.a.a 1 1
2080.2.a.b 1
2080.2.a.c 1
2080.2.a.d 1
2080.2.a.e 1
2080.2.a.f 1
2080.2.a.g 2
2080.2.a.h 2
2080.2.a.i 2
2080.2.a.j 2
2080.2.a.k 2
2080.2.a.l 2
2080.2.a.m 3
2080.2.a.n 3
2080.2.a.o 4
2080.2.a.p 4
2080.2.a.q 4
2080.2.a.r 4
2080.2.a.s 4
2080.2.a.t 4
2080.2.d \(\chi_{2080}(1249, \cdot)\) 2080.2.d.a 2 1
2080.2.d.b 2
2080.2.d.c 2
2080.2.d.d 2
2080.2.d.e 12
2080.2.d.f 16
2080.2.d.g 16
2080.2.d.h 20
2080.2.e \(\chi_{2080}(2001, \cdot)\) 2080.2.e.a 28 1
2080.2.e.b 28
2080.2.f \(\chi_{2080}(129, \cdot)\) 2080.2.f.a 2 1
2080.2.f.b 2
2080.2.f.c 4
2080.2.f.d 4
2080.2.f.e 8
2080.2.f.f 8
2080.2.f.g 8
2080.2.f.h 8
2080.2.f.i 20
2080.2.f.j 20
2080.2.g \(\chi_{2080}(1041, \cdot)\) 2080.2.g.a 24 1
2080.2.g.b 24
2080.2.j \(\chi_{2080}(209, \cdot)\) 2080.2.j.a 36 1
2080.2.j.b 36
2080.2.k \(\chi_{2080}(961, \cdot)\) 2080.2.k.a 2 1
2080.2.k.b 2
2080.2.k.c 2
2080.2.k.d 2
2080.2.k.e 12
2080.2.k.f 12
2080.2.k.g 12
2080.2.k.h 12
2080.2.p \(\chi_{2080}(1169, \cdot)\) 2080.2.p.a 8 1
2080.2.p.b 72
2080.2.q \(\chi_{2080}(321, \cdot)\) n/a 112 2
2080.2.s \(\chi_{2080}(697, \cdot)\) None 0 2
2080.2.u \(\chi_{2080}(31, \cdot)\) n/a 112 2
2080.2.v \(\chi_{2080}(1223, \cdot)\) None 0 2
2080.2.y \(\chi_{2080}(103, \cdot)\) None 0 2
2080.2.z \(\chi_{2080}(239, \cdot)\) n/a 160 2
2080.2.bb \(\chi_{2080}(57, \cdot)\) None 0 2
2080.2.be \(\chi_{2080}(649, \cdot)\) None 0 2
2080.2.bg \(\chi_{2080}(577, \cdot)\) n/a 168 2
2080.2.bi \(\chi_{2080}(593, \cdot)\) n/a 160 2
2080.2.bj \(\chi_{2080}(521, \cdot)\) None 0 2
2080.2.bm \(\chi_{2080}(1191, \cdot)\) None 0 2
2080.2.bp \(\chi_{2080}(287, \cdot)\) n/a 144 2
2080.2.bq \(\chi_{2080}(207, \cdot)\) n/a 160 2
2080.2.bs \(\chi_{2080}(359, \cdot)\) None 0 2
2080.2.bt \(\chi_{2080}(151, \cdot)\) None 0 2
2080.2.bv \(\chi_{2080}(1247, \cdot)\) n/a 168 2
2080.2.bw \(\chi_{2080}(1327, \cdot)\) n/a 144 2
2080.2.bz \(\chi_{2080}(1399, \cdot)\) None 0 2
2080.2.cc \(\chi_{2080}(729, \cdot)\) None 0 2
2080.2.cd \(\chi_{2080}(993, \cdot)\) n/a 168 2
2080.2.cf \(\chi_{2080}(177, \cdot)\) n/a 160 2
2080.2.ch \(\chi_{2080}(441, \cdot)\) None 0 2
2080.2.cj \(\chi_{2080}(473, \cdot)\) None 0 2
2080.2.cm \(\chi_{2080}(1071, \cdot)\) n/a 112 2
2080.2.cn \(\chi_{2080}(183, \cdot)\) None 0 2
2080.2.cq \(\chi_{2080}(1143, \cdot)\) None 0 2
2080.2.cr \(\chi_{2080}(1279, \cdot)\) n/a 168 2
2080.2.cu \(\chi_{2080}(1097, \cdot)\) None 0 2
2080.2.cv \(\chi_{2080}(49, \cdot)\) n/a 160 2
2080.2.da \(\chi_{2080}(641, \cdot)\) n/a 112 2
2080.2.db \(\chi_{2080}(529, \cdot)\) n/a 160 2
2080.2.de \(\chi_{2080}(81, \cdot)\) n/a 112 2
2080.2.df \(\chi_{2080}(1089, \cdot)\) n/a 168 2
2080.2.dg \(\chi_{2080}(881, \cdot)\) n/a 112 2
2080.2.dh \(\chi_{2080}(289, \cdot)\) n/a 168 2
2080.2.dk \(\chi_{2080}(99, \cdot)\) n/a 1328 4
2080.2.dm \(\chi_{2080}(443, \cdot)\) n/a 1152 4
2080.2.dp \(\chi_{2080}(883, \cdot)\) n/a 1328 4
2080.2.dr \(\chi_{2080}(291, \cdot)\) n/a 896 4
2080.2.ds \(\chi_{2080}(181, \cdot)\) n/a 896 4
2080.2.dv \(\chi_{2080}(261, \cdot)\) n/a 768 4
2080.2.dw \(\chi_{2080}(213, \cdot)\) n/a 1328 4
2080.2.dz \(\chi_{2080}(317, \cdot)\) n/a 1328 4
2080.2.eb \(\chi_{2080}(437, \cdot)\) n/a 1328 4
2080.2.ec \(\chi_{2080}(333, \cdot)\) n/a 1328 4
2080.2.ef \(\chi_{2080}(389, \cdot)\) n/a 1328 4
2080.2.eg \(\chi_{2080}(469, \cdot)\) n/a 1152 4
2080.2.ej \(\chi_{2080}(499, \cdot)\) n/a 1328 4
2080.2.el \(\chi_{2080}(363, \cdot)\) n/a 1328 4
2080.2.em \(\chi_{2080}(27, \cdot)\) n/a 1152 4
2080.2.eo \(\chi_{2080}(811, \cdot)\) n/a 896 4
2080.2.eq \(\chi_{2080}(457, \cdot)\) None 0 4
2080.2.et \(\chi_{2080}(319, \cdot)\) n/a 336 4
2080.2.ev \(\chi_{2080}(503, \cdot)\) None 0 4
2080.2.ew \(\chi_{2080}(23, \cdot)\) None 0 4
2080.2.ey \(\chi_{2080}(111, \cdot)\) n/a 224 4
2080.2.fb \(\chi_{2080}(137, \cdot)\) None 0 4
2080.2.fd \(\chi_{2080}(121, \cdot)\) None 0 4
2080.2.ff \(\chi_{2080}(657, \cdot)\) n/a 320 4
2080.2.fh \(\chi_{2080}(353, \cdot)\) n/a 336 4
2080.2.fi \(\chi_{2080}(9, \cdot)\) None 0 4
2080.2.fk \(\chi_{2080}(1159, \cdot)\) None 0 4
2080.2.fm \(\chi_{2080}(367, \cdot)\) n/a 320 4
2080.2.fn \(\chi_{2080}(127, \cdot)\) n/a 336 4
2080.2.fq \(\chi_{2080}(71, \cdot)\) None 0 4
2080.2.ft \(\chi_{2080}(119, \cdot)\) None 0 4
2080.2.fw \(\chi_{2080}(303, \cdot)\) n/a 320 4
2080.2.fx \(\chi_{2080}(607, \cdot)\) n/a 336 4
2080.2.fz \(\chi_{2080}(951, \cdot)\) None 0 4
2080.2.gb \(\chi_{2080}(601, \cdot)\) None 0 4
2080.2.gc \(\chi_{2080}(977, \cdot)\) n/a 320 4
2080.2.ge \(\chi_{2080}(33, \cdot)\) n/a 336 4
2080.2.gg \(\chi_{2080}(329, \cdot)\) None 0 4
2080.2.gj \(\chi_{2080}(553, \cdot)\) None 0 4
2080.2.gl \(\chi_{2080}(1359, \cdot)\) n/a 320 4
2080.2.gn \(\chi_{2080}(87, \cdot)\) None 0 4
2080.2.go \(\chi_{2080}(407, \cdot)\) None 0 4
2080.2.gq \(\chi_{2080}(1151, \cdot)\) n/a 224 4
2080.2.gs \(\chi_{2080}(873, \cdot)\) None 0 4
2080.2.gv \(\chi_{2080}(171, \cdot)\) n/a 1792 8
2080.2.gw \(\chi_{2080}(3, \cdot)\) n/a 2656 8
2080.2.gz \(\chi_{2080}(43, \cdot)\) n/a 2656 8
2080.2.ha \(\chi_{2080}(19, \cdot)\) n/a 2656 8
2080.2.hc \(\chi_{2080}(69, \cdot)\) n/a 2656 8
2080.2.hf \(\chi_{2080}(29, \cdot)\) n/a 2656 8
2080.2.hh \(\chi_{2080}(197, \cdot)\) n/a 2656 8
2080.2.hi \(\chi_{2080}(37, \cdot)\) n/a 2656 8
2080.2.hk \(\chi_{2080}(293, \cdot)\) n/a 2656 8
2080.2.hn \(\chi_{2080}(397, \cdot)\) n/a 2656 8
2080.2.hp \(\chi_{2080}(101, \cdot)\) n/a 1792 8
2080.2.hq \(\chi_{2080}(61, \cdot)\) n/a 1792 8
2080.2.hs \(\chi_{2080}(11, \cdot)\) n/a 1792 8
2080.2.hv \(\chi_{2080}(563, \cdot)\) n/a 2656 8
2080.2.hw \(\chi_{2080}(523, \cdot)\) n/a 2656 8
2080.2.hz \(\chi_{2080}(379, \cdot)\) n/a 2656 8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2080))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2080)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(520))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1040))\)\(^{\oplus 2}\)