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Properties

Label 6162.2
Level 6162
Weight 2
Dimension 258873
Nonzero newspaces 60
Sturm bound 4193280

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Defining parameters

Level: \( N \) = \( 6162 = 2 \cdot 3 \cdot 13 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(4193280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6162))\).

Total New Old
Modular forms 1055808 258873 796935
Cusp forms 1040833 258873 781960
Eisenstein series 14975 0 14975

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6162))\)

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
6162.2.a \(\chi_{6162}(1, \cdot)\) 6162.2.a.a 1 1
6162.2.a.b 1
6162.2.a.c 1
6162.2.a.d 1
6162.2.a.e 1
6162.2.a.f 1
6162.2.a.g 1
6162.2.a.h 1
6162.2.a.i 1
6162.2.a.j 1
6162.2.a.k 1
6162.2.a.l 1
6162.2.a.m 1
6162.2.a.n 1
6162.2.a.o 1
6162.2.a.p 1
6162.2.a.q 1
6162.2.a.r 2
6162.2.a.s 2
6162.2.a.t 2
6162.2.a.u 2
6162.2.a.v 2
6162.2.a.w 2
6162.2.a.x 3
6162.2.a.y 4
6162.2.a.z 4
6162.2.a.ba 5
6162.2.a.bb 5
6162.2.a.bc 5
6162.2.a.bd 5
6162.2.a.be 6
6162.2.a.bf 7
6162.2.a.bg 8
6162.2.a.bh 8
6162.2.a.bi 9
6162.2.a.bj 10
6162.2.a.bk 11
6162.2.a.bl 12
6162.2.a.bm 13
6162.2.a.bn 13
6162.2.b \(\chi_{6162}(1897, \cdot)\) n/a 180 1
6162.2.c \(\chi_{6162}(4265, \cdot)\) n/a 320 1
6162.2.h \(\chi_{6162}(6161, \cdot)\) n/a 376 1
6162.2.i \(\chi_{6162}(1951, \cdot)\) n/a 320 2
6162.2.j \(\chi_{6162}(529, \cdot)\) n/a 372 2
6162.2.k \(\chi_{6162}(55, \cdot)\) n/a 372 2
6162.2.l \(\chi_{6162}(4267, \cdot)\) n/a 368 2
6162.2.o \(\chi_{6162}(2527, \cdot)\) n/a 368 2
6162.2.p \(\chi_{6162}(317, \cdot)\) n/a 728 2
6162.2.s \(\chi_{6162}(2369, \cdot)\) n/a 744 2
6162.2.t \(\chi_{6162}(3319, \cdot)\) n/a 360 2
6162.2.w \(\chi_{6162}(1715, \cdot)\) n/a 744 2
6162.2.x \(\chi_{6162}(3611, \cdot)\) n/a 748 2
6162.2.bc \(\chi_{6162}(3137, \cdot)\) n/a 748 2
6162.2.bd \(\chi_{6162}(1603, \cdot)\) n/a 372 2
6162.2.be \(\chi_{6162}(419, \cdot)\) n/a 748 2
6162.2.bj \(\chi_{6162}(893, \cdot)\) n/a 748 2
6162.2.bk \(\chi_{6162}(2077, \cdot)\) n/a 372 2
6162.2.bl \(\chi_{6162}(2315, \cdot)\) n/a 640 2
6162.2.bm \(\chi_{6162}(181, \cdot)\) n/a 376 2
6162.2.bp \(\chi_{6162}(1421, \cdot)\) n/a 744 2
6162.2.bu \(\chi_{6162}(925, \cdot)\) n/a 744 4
6162.2.bv \(\chi_{6162}(791, \cdot)\) n/a 1456 4
6162.2.bw \(\chi_{6162}(2741, \cdot)\) n/a 1496 4
6162.2.bx \(\chi_{6162}(631, \cdot)\) n/a 752 4
6162.2.by \(\chi_{6162}(1051, \cdot)\) n/a 744 4
6162.2.bz \(\chi_{6162}(371, \cdot)\) n/a 1496 4
6162.2.cg \(\chi_{6162}(1919, \cdot)\) n/a 1488 4
6162.2.ch \(\chi_{6162}(577, \cdot)\) n/a 752 4
6162.2.ci \(\chi_{6162}(1015, \cdot)\) n/a 1920 12
6162.2.cj \(\chi_{6162}(545, \cdot)\) n/a 4512 12
6162.2.co \(\chi_{6162}(989, \cdot)\) n/a 3840 12
6162.2.cp \(\chi_{6162}(259, \cdot)\) n/a 2208 12
6162.2.cq \(\chi_{6162}(289, \cdot)\) n/a 4512 24
6162.2.cr \(\chi_{6162}(367, \cdot)\) n/a 4464 24
6162.2.cs \(\chi_{6162}(445, \cdot)\) n/a 4464 24
6162.2.ct \(\chi_{6162}(313, \cdot)\) n/a 3840 24
6162.2.cu \(\chi_{6162}(229, \cdot)\) n/a 4416 24
6162.2.cv \(\chi_{6162}(125, \cdot)\) n/a 9024 24
6162.2.da \(\chi_{6162}(17, \cdot)\) n/a 8928 24
6162.2.dd \(\chi_{6162}(25, \cdot)\) n/a 4512 24
6162.2.de \(\chi_{6162}(53, \cdot)\) n/a 7680 24
6162.2.df \(\chi_{6162}(121, \cdot)\) n/a 4464 24
6162.2.dg \(\chi_{6162}(29, \cdot)\) n/a 8976 24
6162.2.dl \(\chi_{6162}(107, \cdot)\) n/a 8976 24
6162.2.dm \(\chi_{6162}(49, \cdot)\) n/a 4464 24
6162.2.dn \(\chi_{6162}(797, \cdot)\) n/a 8976 24
6162.2.ds \(\chi_{6162}(1109, \cdot)\) n/a 8976 24
6162.2.dt \(\chi_{6162}(77, \cdot)\) n/a 8928 24
6162.2.dw \(\chi_{6162}(283, \cdot)\) n/a 4512 24
6162.2.dx \(\chi_{6162}(185, \cdot)\) n/a 8928 24
6162.2.ea \(\chi_{6162}(5, \cdot)\) n/a 17856 48
6162.2.eb \(\chi_{6162}(109, \cdot)\) n/a 9024 48
6162.2.ei \(\chi_{6162}(319, \cdot)\) n/a 8928 48
6162.2.ej \(\chi_{6162}(431, \cdot)\) n/a 17952 48
6162.2.ek \(\chi_{6162}(89, \cdot)\) n/a 17856 48
6162.2.el \(\chi_{6162}(7, \cdot)\) n/a 8928 48
6162.2.em \(\chi_{6162}(175, \cdot)\) n/a 9024 48
6162.2.en \(\chi_{6162}(11, \cdot)\) n/a 17952 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6162))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6162)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(158))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(237))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(474))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1027))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2054))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3081))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6162))\)\(^{\oplus 1}\)