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Properties

Label 7632.2
Level 7632
Weight 2
Dimension 717674
Nonzero newspaces 56
Sturm bound 6469632

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Defining parameters

Level: \( N \) = \( 7632 = 2^{4} \cdot 3^{2} \cdot 53 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(6469632\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7632))\).

Total New Old
Modular forms 1629056 721804 907252
Cusp forms 1605761 717674 888087
Eisenstein series 23295 4130 19165

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7632))\)

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
7632.2.a \(\chi_{7632}(1, \cdot)\) 7632.2.a.a 1 1
7632.2.a.b 1
7632.2.a.c 1
7632.2.a.d 1
7632.2.a.e 1
7632.2.a.f 1
7632.2.a.g 1
7632.2.a.h 1
7632.2.a.i 1
7632.2.a.j 1
7632.2.a.k 1
7632.2.a.l 1
7632.2.a.m 1
7632.2.a.n 1
7632.2.a.o 1
7632.2.a.p 1
7632.2.a.q 1
7632.2.a.r 1
7632.2.a.s 2
7632.2.a.t 2
7632.2.a.u 2
7632.2.a.v 2
7632.2.a.w 2
7632.2.a.x 2
7632.2.a.y 2
7632.2.a.z 2
7632.2.a.ba 2
7632.2.a.bb 2
7632.2.a.bc 2
7632.2.a.bd 2
7632.2.a.be 2
7632.2.a.bf 3
7632.2.a.bg 3
7632.2.a.bh 3
7632.2.a.bi 3
7632.2.a.bj 3
7632.2.a.bk 3
7632.2.a.bl 3
7632.2.a.bm 3
7632.2.a.bn 3
7632.2.a.bo 3
7632.2.a.bp 3
7632.2.a.bq 4
7632.2.a.br 4
7632.2.a.bs 4
7632.2.a.bt 5
7632.2.a.bu 5
7632.2.a.bv 5
7632.2.a.bw 5
7632.2.a.bx 5
7632.2.a.by 8
7632.2.a.bz 8
7632.2.b \(\chi_{7632}(3815, \cdot)\) None 0 1
7632.2.e \(\chi_{7632}(2015, \cdot)\) n/a 104 1
7632.2.f \(\chi_{7632}(3817, \cdot)\) None 0 1
7632.2.i \(\chi_{7632}(5617, \cdot)\) n/a 134 1
7632.2.j \(\chi_{7632}(5831, \cdot)\) None 0 1
7632.2.m \(\chi_{7632}(7631, \cdot)\) n/a 108 1
7632.2.n \(\chi_{7632}(1801, \cdot)\) None 0 1
7632.2.q \(\chi_{7632}(2545, \cdot)\) n/a 624 2
7632.2.r \(\chi_{7632}(235, \cdot)\) n/a 1076 2
7632.2.u \(\chi_{7632}(4157, \cdot)\) n/a 864 2
7632.2.v \(\chi_{7632}(1673, \cdot)\) None 0 2
7632.2.z \(\chi_{7632}(1909, \cdot)\) n/a 1040 2
7632.2.ba \(\chi_{7632}(3709, \cdot)\) n/a 1076 2
7632.2.bc \(\chi_{7632}(5489, \cdot)\) n/a 216 2
7632.2.bd \(\chi_{7632}(5383, \cdot)\) None 0 2
7632.2.bf \(\chi_{7632}(107, \cdot)\) n/a 832 2
7632.2.bg \(\chi_{7632}(1907, \cdot)\) n/a 864 2
7632.2.bk \(\chi_{7632}(1567, \cdot)\) n/a 270 2
7632.2.bl \(\chi_{7632}(4051, \cdot)\) n/a 1076 2
7632.2.bo \(\chi_{7632}(341, \cdot)\) n/a 864 2
7632.2.br \(\chi_{7632}(4345, \cdot)\) None 0 2
7632.2.bs \(\chi_{7632}(2543, \cdot)\) n/a 648 2
7632.2.bv \(\chi_{7632}(743, \cdot)\) None 0 2
7632.2.bw \(\chi_{7632}(529, \cdot)\) n/a 644 2
7632.2.bz \(\chi_{7632}(1273, \cdot)\) None 0 2
7632.2.ca \(\chi_{7632}(4559, \cdot)\) n/a 624 2
7632.2.cd \(\chi_{7632}(1271, \cdot)\) None 0 2
7632.2.cf \(\chi_{7632}(1037, \cdot)\) n/a 5168 4
7632.2.cg \(\chi_{7632}(1507, \cdot)\) n/a 5168 4
7632.2.ci \(\chi_{7632}(4111, \cdot)\) n/a 1296 4
7632.2.ck \(\chi_{7632}(635, \cdot)\) n/a 5168 4
7632.2.cl \(\chi_{7632}(1379, \cdot)\) n/a 4992 4
7632.2.cp \(\chi_{7632}(295, \cdot)\) None 0 4
7632.2.cq \(\chi_{7632}(401, \cdot)\) n/a 1288 4
7632.2.cu \(\chi_{7632}(1165, \cdot)\) n/a 5168 4
7632.2.cv \(\chi_{7632}(637, \cdot)\) n/a 4992 4
7632.2.cx \(\chi_{7632}(4217, \cdot)\) None 0 4
7632.2.cz \(\chi_{7632}(1613, \cdot)\) n/a 5168 4
7632.2.da \(\chi_{7632}(931, \cdot)\) n/a 5168 4
7632.2.dc \(\chi_{7632}(289, \cdot)\) n/a 1608 12
7632.2.df \(\chi_{7632}(361, \cdot)\) None 0 12
7632.2.dg \(\chi_{7632}(143, \cdot)\) n/a 1296 12
7632.2.dj \(\chi_{7632}(791, \cdot)\) None 0 12
7632.2.dk \(\chi_{7632}(433, \cdot)\) n/a 1608 12
7632.2.dn \(\chi_{7632}(505, \cdot)\) None 0 12
7632.2.do \(\chi_{7632}(863, \cdot)\) n/a 1296 12
7632.2.dr \(\chi_{7632}(647, \cdot)\) None 0 12
7632.2.ds \(\chi_{7632}(49, \cdot)\) n/a 7728 24
7632.2.dt \(\chi_{7632}(125, \cdot)\) n/a 10368 24
7632.2.dw \(\chi_{7632}(451, \cdot)\) n/a 12912 24
7632.2.dx \(\chi_{7632}(127, \cdot)\) n/a 3240 24
7632.2.eb \(\chi_{7632}(395, \cdot)\) n/a 10368 24
7632.2.ec \(\chi_{7632}(467, \cdot)\) n/a 10368 24
7632.2.ee \(\chi_{7632}(55, \cdot)\) None 0 24
7632.2.ef \(\chi_{7632}(161, \cdot)\) n/a 2592 24
7632.2.eh \(\chi_{7632}(685, \cdot)\) n/a 12912 24
7632.2.ei \(\chi_{7632}(37, \cdot)\) n/a 12912 24
7632.2.em \(\chi_{7632}(233, \cdot)\) None 0 24
7632.2.en \(\chi_{7632}(557, \cdot)\) n/a 10368 24
7632.2.eq \(\chi_{7632}(19, \cdot)\) n/a 12912 24
7632.2.er \(\chi_{7632}(695, \cdot)\) None 0 24
7632.2.eu \(\chi_{7632}(47, \cdot)\) n/a 7776 24
7632.2.ev \(\chi_{7632}(121, \cdot)\) None 0 24
7632.2.ey \(\chi_{7632}(241, \cdot)\) n/a 7728 24
7632.2.ez \(\chi_{7632}(119, \cdot)\) None 0 24
7632.2.fc \(\chi_{7632}(335, \cdot)\) n/a 7776 24
7632.2.fd \(\chi_{7632}(25, \cdot)\) None 0 24
7632.2.fh \(\chi_{7632}(139, \cdot)\) n/a 62016 48
7632.2.fi \(\chi_{7632}(101, \cdot)\) n/a 62016 48
7632.2.fk \(\chi_{7632}(41, \cdot)\) None 0 48
7632.2.fm \(\chi_{7632}(229, \cdot)\) n/a 62016 48
7632.2.fn \(\chi_{7632}(13, \cdot)\) n/a 62016 48
7632.2.fr \(\chi_{7632}(65, \cdot)\) n/a 15456 48
7632.2.fs \(\chi_{7632}(103, \cdot)\) None 0 48
7632.2.fw \(\chi_{7632}(11, \cdot)\) n/a 62016 48
7632.2.fx \(\chi_{7632}(155, \cdot)\) n/a 62016 48
7632.2.fz \(\chi_{7632}(31, \cdot)\) n/a 15552 48
7632.2.gb \(\chi_{7632}(67, \cdot)\) n/a 62016 48
7632.2.gc \(\chi_{7632}(5, \cdot)\) n/a 62016 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7632))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7632)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(106))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(159))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(212))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(318))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(424))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(477))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(636))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(848))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(954))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1272))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1908))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2544))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3816))\)\(^{\oplus 2}\)