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Properties

Label 7128.2
Level 7128
Weight 2
Dimension 609696
Nonzero newspaces 48
Sturm bound 5598720

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Defining parameters

Level: \( N \) = \( 7128 = 2^{3} \cdot 3^{4} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(5598720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7128))\).

Total New Old
Modular forms 1412640 613728 798912
Cusp forms 1386721 609696 777025
Eisenstein series 25919 4032 21887

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7128))\)

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
7128.2.a \(\chi_{7128}(1, \cdot)\) 7128.2.a.a 1 1
7128.2.a.b 1
7128.2.a.c 1
7128.2.a.d 1
7128.2.a.e 1
7128.2.a.f 1
7128.2.a.g 1
7128.2.a.h 1
7128.2.a.i 2
7128.2.a.j 2
7128.2.a.k 2
7128.2.a.l 2
7128.2.a.m 2
7128.2.a.n 2
7128.2.a.o 3
7128.2.a.p 3
7128.2.a.q 4
7128.2.a.r 4
7128.2.a.s 4
7128.2.a.t 4
7128.2.a.u 5
7128.2.a.v 5
7128.2.a.w 6
7128.2.a.x 6
7128.2.a.y 6
7128.2.a.z 6
7128.2.a.ba 6
7128.2.a.bb 6
7128.2.a.bc 8
7128.2.a.bd 8
7128.2.a.be 8
7128.2.a.bf 8
7128.2.b \(\chi_{7128}(5345, \cdot)\) n/a 144 1
7128.2.d \(\chi_{7128}(5831, \cdot)\) None 0 1
7128.2.f \(\chi_{7128}(3565, \cdot)\) n/a 480 1
7128.2.h \(\chi_{7128}(6643, \cdot)\) n/a 568 1
7128.2.k \(\chi_{7128}(2267, \cdot)\) n/a 480 1
7128.2.m \(\chi_{7128}(1781, \cdot)\) n/a 568 1
7128.2.o \(\chi_{7128}(3079, \cdot)\) None 0 1
7128.2.q \(\chi_{7128}(2377, \cdot)\) n/a 240 2
7128.2.r \(\chi_{7128}(1945, \cdot)\) n/a 576 4
7128.2.u \(\chi_{7128}(703, \cdot)\) None 0 2
7128.2.w \(\chi_{7128}(4157, \cdot)\) n/a 1144 2
7128.2.y \(\chi_{7128}(4643, \cdot)\) n/a 960 2
7128.2.z \(\chi_{7128}(1891, \cdot)\) n/a 1144 2
7128.2.bb \(\chi_{7128}(1189, \cdot)\) n/a 960 2
7128.2.bd \(\chi_{7128}(1079, \cdot)\) None 0 2
7128.2.bf \(\chi_{7128}(593, \cdot)\) n/a 288 2
7128.2.bh \(\chi_{7128}(793, \cdot)\) n/a 540 6
7128.2.bj \(\chi_{7128}(1135, \cdot)\) None 0 4
7128.2.bl \(\chi_{7128}(3077, \cdot)\) n/a 2272 4
7128.2.bn \(\chi_{7128}(323, \cdot)\) n/a 2272 4
7128.2.bq \(\chi_{7128}(811, \cdot)\) n/a 2272 4
7128.2.bs \(\chi_{7128}(973, \cdot)\) n/a 2272 4
7128.2.bu \(\chi_{7128}(647, \cdot)\) None 0 4
7128.2.bw \(\chi_{7128}(161, \cdot)\) n/a 576 4
7128.2.bx \(\chi_{7128}(433, \cdot)\) n/a 1152 8
7128.2.ca \(\chi_{7128}(197, \cdot)\) n/a 2568 6
7128.2.cb \(\chi_{7128}(1385, \cdot)\) n/a 648 6
7128.2.ce \(\chi_{7128}(397, \cdot)\) n/a 2160 6
7128.2.cf \(\chi_{7128}(1495, \cdot)\) None 0 6
7128.2.ci \(\chi_{7128}(683, \cdot)\) n/a 2160 6
7128.2.cj \(\chi_{7128}(287, \cdot)\) None 0 6
7128.2.cm \(\chi_{7128}(307, \cdot)\) n/a 2568 6
7128.2.cn \(\chi_{7128}(265, \cdot)\) n/a 4860 18
7128.2.cp \(\chi_{7128}(1025, \cdot)\) n/a 1152 8
7128.2.cr \(\chi_{7128}(863, \cdot)\) None 0 8
7128.2.ct \(\chi_{7128}(757, \cdot)\) n/a 4576 8
7128.2.cv \(\chi_{7128}(2323, \cdot)\) n/a 4576 8
7128.2.cw \(\chi_{7128}(1835, \cdot)\) n/a 4576 8
7128.2.cy \(\chi_{7128}(701, \cdot)\) n/a 4576 8
7128.2.da \(\chi_{7128}(271, \cdot)\) None 0 8
7128.2.dd \(\chi_{7128}(289, \cdot)\) n/a 2592 24
7128.2.df \(\chi_{7128}(175, \cdot)\) None 0 18
7128.2.dh \(\chi_{7128}(461, \cdot)\) n/a 23256 18
7128.2.dj \(\chi_{7128}(155, \cdot)\) n/a 19440 18
7128.2.dl \(\chi_{7128}(23, \cdot)\) None 0 18
7128.2.dn \(\chi_{7128}(65, \cdot)\) n/a 5832 18
7128.2.dp \(\chi_{7128}(43, \cdot)\) n/a 23256 18
7128.2.dr \(\chi_{7128}(133, \cdot)\) n/a 19440 18
7128.2.dt \(\chi_{7128}(19, \cdot)\) n/a 10272 24
7128.2.dw \(\chi_{7128}(71, \cdot)\) None 0 24
7128.2.dx \(\chi_{7128}(179, \cdot)\) n/a 10272 24
7128.2.ea \(\chi_{7128}(127, \cdot)\) None 0 24
7128.2.eb \(\chi_{7128}(37, \cdot)\) n/a 10272 24
7128.2.ee \(\chi_{7128}(17, \cdot)\) n/a 2592 24
7128.2.ef \(\chi_{7128}(413, \cdot)\) n/a 10272 24
7128.2.ei \(\chi_{7128}(25, \cdot)\) n/a 23328 72
7128.2.ek \(\chi_{7128}(139, \cdot)\) n/a 93024 72
7128.2.em \(\chi_{7128}(157, \cdot)\) n/a 93024 72
7128.2.eo \(\chi_{7128}(47, \cdot)\) None 0 72
7128.2.eq \(\chi_{7128}(41, \cdot)\) n/a 23328 72
7128.2.es \(\chi_{7128}(29, \cdot)\) n/a 93024 72
7128.2.eu \(\chi_{7128}(59, \cdot)\) n/a 93024 72
7128.2.ex \(\chi_{7128}(7, \cdot)\) None 0 72

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7128))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7128)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 40}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(297))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(594))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(648))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(792))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(891))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1188))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1782))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2376))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3564))\)\(^{\oplus 2}\)