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Properties

Label 6192.2
Level 6192
Weight 2
Dimension 471839
Nonzero newspaces 80
Sturm bound 4257792

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Defining parameters

Level: \( N \) = \( 6192 = 2^{4} \cdot 3^{2} \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(4257792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6192))\).

Total New Old
Modular forms 1073856 475159 598697
Cusp forms 1055041 471839 583202
Eisenstein series 18815 3320 15495

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6192))\)

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
6192.2.a \(\chi_{6192}(1, \cdot)\) 6192.2.a.a 1 1
6192.2.a.b 1
6192.2.a.c 1
6192.2.a.d 1
6192.2.a.e 1
6192.2.a.f 1
6192.2.a.g 1
6192.2.a.h 1
6192.2.a.i 1
6192.2.a.j 1
6192.2.a.k 1
6192.2.a.l 1
6192.2.a.m 1
6192.2.a.n 1
6192.2.a.o 1
6192.2.a.p 1
6192.2.a.q 1
6192.2.a.r 1
6192.2.a.s 1
6192.2.a.t 1
6192.2.a.u 1
6192.2.a.v 1
6192.2.a.w 1
6192.2.a.x 1
6192.2.a.y 1
6192.2.a.z 1
6192.2.a.ba 1
6192.2.a.bb 2
6192.2.a.bc 2
6192.2.a.bd 2
6192.2.a.be 2
6192.2.a.bf 2
6192.2.a.bg 2
6192.2.a.bh 2
6192.2.a.bi 2
6192.2.a.bj 2
6192.2.a.bk 2
6192.2.a.bl 2
6192.2.a.bm 2
6192.2.a.bn 2
6192.2.a.bo 2
6192.2.a.bp 2
6192.2.a.bq 2
6192.2.a.br 3
6192.2.a.bs 3
6192.2.a.bt 3
6192.2.a.bu 3
6192.2.a.bv 3
6192.2.a.bw 3
6192.2.a.bx 3
6192.2.a.by 4
6192.2.a.bz 4
6192.2.a.ca 5
6192.2.a.cb 6
6192.2.a.cc 6
6192.2.b \(\chi_{6192}(5417, \cdot)\) None 0 1
6192.2.d \(\chi_{6192}(431, \cdot)\) 6192.2.d.a 4 1
6192.2.d.b 4
6192.2.d.c 4
6192.2.d.d 16
6192.2.d.e 56
6192.2.g \(\chi_{6192}(3097, \cdot)\) None 0 1
6192.2.i \(\chi_{6192}(3439, \cdot)\) n/a 110 1
6192.2.j \(\chi_{6192}(3527, \cdot)\) None 0 1
6192.2.l \(\chi_{6192}(2321, \cdot)\) 6192.2.l.a 2 1
6192.2.l.b 2
6192.2.l.c 2
6192.2.l.d 2
6192.2.l.e 4
6192.2.l.f 6
6192.2.l.g 6
6192.2.l.h 8
6192.2.l.i 8
6192.2.l.j 12
6192.2.l.k 18
6192.2.l.l 18
6192.2.o \(\chi_{6192}(343, \cdot)\) None 0 1
6192.2.q \(\chi_{6192}(2065, \cdot)\) n/a 504 2
6192.2.r \(\chi_{6192}(49, \cdot)\) n/a 524 2
6192.2.s \(\chi_{6192}(4177, \cdot)\) n/a 218 2
6192.2.t \(\chi_{6192}(337, \cdot)\) n/a 524 2
6192.2.w \(\chi_{6192}(1549, \cdot)\) n/a 840 2
6192.2.x \(\chi_{6192}(1891, \cdot)\) n/a 876 2
6192.2.y \(\chi_{6192}(1979, \cdot)\) n/a 672 2
6192.2.z \(\chi_{6192}(773, \cdot)\) n/a 704 2
6192.2.bd \(\chi_{6192}(479, \cdot)\) n/a 528 2
6192.2.bf \(\chi_{6192}(3305, \cdot)\) None 0 2
6192.2.bg \(\chi_{6192}(1039, \cdot)\) n/a 528 2
6192.2.bi \(\chi_{6192}(3433, \cdot)\) None 0 2
6192.2.bk \(\chi_{6192}(7, \cdot)\) None 0 2
6192.2.bo \(\chi_{6192}(2407, \cdot)\) None 0 2
6192.2.br \(\chi_{6192}(2071, \cdot)\) None 0 2
6192.2.bu \(\chi_{6192}(4049, \cdot)\) n/a 176 2
6192.2.bw \(\chi_{6192}(1511, \cdot)\) None 0 2
6192.2.by \(\chi_{6192}(3863, \cdot)\) None 0 2
6192.2.bz \(\chi_{6192}(257, \cdot)\) n/a 524 2
6192.2.cb \(\chi_{6192}(1463, \cdot)\) None 0 2
6192.2.ce \(\chi_{6192}(2273, \cdot)\) n/a 524 2
6192.2.cf \(\chi_{6192}(5167, \cdot)\) n/a 220 2
6192.2.ch \(\chi_{6192}(1081, \cdot)\) None 0 2
6192.2.cj \(\chi_{6192}(3145, \cdot)\) None 0 2
6192.2.cm \(\chi_{6192}(1375, \cdot)\) n/a 528 2
6192.2.co \(\chi_{6192}(1033, \cdot)\) None 0 2
6192.2.cp \(\chi_{6192}(1327, \cdot)\) n/a 528 2
6192.2.cs \(\chi_{6192}(3017, \cdot)\) None 0 2
6192.2.ct \(\chi_{6192}(2495, \cdot)\) n/a 504 2
6192.2.cv \(\chi_{6192}(1289, \cdot)\) None 0 2
6192.2.cy \(\chi_{6192}(767, \cdot)\) n/a 528 2
6192.2.da \(\chi_{6192}(4607, \cdot)\) n/a 176 2
6192.2.dc \(\chi_{6192}(953, \cdot)\) None 0 2
6192.2.de \(\chi_{6192}(209, \cdot)\) n/a 524 2
6192.2.dg \(\chi_{6192}(3575, \cdot)\) None 0 2
6192.2.di \(\chi_{6192}(295, \cdot)\) None 0 2
6192.2.dk \(\chi_{6192}(145, \cdot)\) n/a 654 6
6192.2.dl \(\chi_{6192}(565, \cdot)\) n/a 4208 4
6192.2.dm \(\chi_{6192}(1843, \cdot)\) n/a 4208 4
6192.2.dp \(\chi_{6192}(1805, \cdot)\) n/a 4208 4
6192.2.dq \(\chi_{6192}(947, \cdot)\) n/a 4032 4
6192.2.dv \(\chi_{6192}(725, \cdot)\) n/a 4208 4
6192.2.dw \(\chi_{6192}(2501, \cdot)\) n/a 1408 4
6192.2.dx \(\chi_{6192}(995, \cdot)\) n/a 4208 4
6192.2.dy \(\chi_{6192}(251, \cdot)\) n/a 1408 4
6192.2.ed \(\chi_{6192}(523, \cdot)\) n/a 1752 4
6192.2.ee \(\chi_{6192}(1555, \cdot)\) n/a 4208 4
6192.2.ef \(\chi_{6192}(2629, \cdot)\) n/a 1752 4
6192.2.eg \(\chi_{6192}(853, \cdot)\) n/a 4208 4
6192.2.el \(\chi_{6192}(859, \cdot)\) n/a 4208 4
6192.2.em \(\chi_{6192}(517, \cdot)\) n/a 4032 4
6192.2.ep \(\chi_{6192}(1283, \cdot)\) n/a 4208 4
6192.2.eq \(\chi_{6192}(437, \cdot)\) n/a 4208 4
6192.2.es \(\chi_{6192}(161, \cdot)\) n/a 528 6
6192.2.eu \(\chi_{6192}(1079, \cdot)\) None 0 6
6192.2.ew \(\chi_{6192}(199, \cdot)\) None 0 6
6192.2.ez \(\chi_{6192}(575, \cdot)\) n/a 528 6
6192.2.fb \(\chi_{6192}(1097, \cdot)\) None 0 6
6192.2.fc \(\chi_{6192}(991, \cdot)\) n/a 660 6
6192.2.fe \(\chi_{6192}(649, \cdot)\) None 0 6
6192.2.fg \(\chi_{6192}(1057, \cdot)\) n/a 3144 12
6192.2.fh \(\chi_{6192}(289, \cdot)\) n/a 1308 12
6192.2.fi \(\chi_{6192}(529, \cdot)\) n/a 3144 12
6192.2.fj \(\chi_{6192}(97, \cdot)\) n/a 3144 12
6192.2.fk \(\chi_{6192}(667, \cdot)\) n/a 5256 12
6192.2.fl \(\chi_{6192}(613, \cdot)\) n/a 5256 12
6192.2.fq \(\chi_{6192}(125, \cdot)\) n/a 4224 12
6192.2.fr \(\chi_{6192}(35, \cdot)\) n/a 4224 12
6192.2.fs \(\chi_{6192}(455, \cdot)\) None 0 12
6192.2.fu \(\chi_{6192}(545, \cdot)\) n/a 3144 12
6192.2.fx \(\chi_{6192}(679, \cdot)\) None 0 12
6192.2.ga \(\chi_{6192}(175, \cdot)\) n/a 3168 12
6192.2.gb \(\chi_{6192}(121, \cdot)\) None 0 12
6192.2.gd \(\chi_{6192}(223, \cdot)\) n/a 3168 12
6192.2.gg \(\chi_{6192}(25, \cdot)\) None 0 12
6192.2.gi \(\chi_{6192}(361, \cdot)\) None 0 12
6192.2.gk \(\chi_{6192}(415, \cdot)\) n/a 1320 12
6192.2.gl \(\chi_{6192}(89, \cdot)\) None 0 12
6192.2.gn \(\chi_{6192}(143, \cdot)\) n/a 1056 12
6192.2.gp \(\chi_{6192}(239, \cdot)\) n/a 3168 12
6192.2.gs \(\chi_{6192}(137, \cdot)\) None 0 12
6192.2.gu \(\chi_{6192}(47, \cdot)\) n/a 3168 12
6192.2.gv \(\chi_{6192}(1481, \cdot)\) None 0 12
6192.2.gy \(\chi_{6192}(55, \cdot)\) None 0 12
6192.2.hb \(\chi_{6192}(151, \cdot)\) None 0 12
6192.2.hf \(\chi_{6192}(535, \cdot)\) None 0 12
6192.2.hg \(\chi_{6192}(929, \cdot)\) n/a 3144 12
6192.2.hj \(\chi_{6192}(551, \cdot)\) None 0 12
6192.2.hl \(\chi_{6192}(65, \cdot)\) n/a 3144 12
6192.2.hm \(\chi_{6192}(23, \cdot)\) None 0 12
6192.2.ho \(\chi_{6192}(359, \cdot)\) None 0 12
6192.2.hq \(\chi_{6192}(449, \cdot)\) n/a 1056 12
6192.2.hs \(\chi_{6192}(329, \cdot)\) None 0 12
6192.2.hu \(\chi_{6192}(95, \cdot)\) n/a 3168 12
6192.2.hx \(\chi_{6192}(169, \cdot)\) None 0 12
6192.2.hz \(\chi_{6192}(319, \cdot)\) n/a 3168 12
6192.2.ic \(\chi_{6192}(499, \cdot)\) n/a 25248 24
6192.2.id \(\chi_{6192}(13, \cdot)\) n/a 25248 24
6192.2.ig \(\chi_{6192}(539, \cdot)\) n/a 8448 24
6192.2.ih \(\chi_{6192}(203, \cdot)\) n/a 25248 24
6192.2.ii \(\chi_{6192}(413, \cdot)\) n/a 8448 24
6192.2.ij \(\chi_{6192}(5, \cdot)\) n/a 25248 24
6192.2.io \(\chi_{6192}(11, \cdot)\) n/a 25248 24
6192.2.ip \(\chi_{6192}(389, \cdot)\) n/a 25248 24
6192.2.iq \(\chi_{6192}(133, \cdot)\) n/a 25248 24
6192.2.ir \(\chi_{6192}(211, \cdot)\) n/a 25248 24
6192.2.iw \(\chi_{6192}(805, \cdot)\) n/a 25248 24
6192.2.ix \(\chi_{6192}(109, \cdot)\) n/a 10512 24
6192.2.iy \(\chi_{6192}(115, \cdot)\) n/a 25248 24
6192.2.iz \(\chi_{6192}(19, \cdot)\) n/a 10512 24
6192.2.jc \(\chi_{6192}(77, \cdot)\) n/a 25248 24
6192.2.jd \(\chi_{6192}(83, \cdot)\) n/a 25248 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6192))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6192)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(86))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(129))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(172))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(258))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(344))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(387))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(516))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(688))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(774))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1032))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1548))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2064))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3096))\)\(^{\oplus 2}\)