Properties

Label 7600.2
Level 7600
Weight 2
Dimension 887747
Nonzero newspaces 84
Sturm bound 6912000

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Defining parameters

Level: \( N \) = \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 84 \)
Sturm bound: \(6912000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7600))\).

Total New Old
Modular forms 1742112 894019 848093
Cusp forms 1713889 887747 826142
Eisenstein series 28223 6272 21951

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7600))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
7600.2.a \(\chi_{7600}(1, \cdot)\) 7600.2.a.a 1 1
7600.2.a.b 1
7600.2.a.c 1
7600.2.a.d 1
7600.2.a.e 1
7600.2.a.f 1
7600.2.a.g 1
7600.2.a.h 1
7600.2.a.i 1
7600.2.a.j 1
7600.2.a.k 1
7600.2.a.l 1
7600.2.a.m 1
7600.2.a.n 1
7600.2.a.o 1
7600.2.a.p 1
7600.2.a.q 1
7600.2.a.r 1
7600.2.a.s 1
7600.2.a.t 1
7600.2.a.u 2
7600.2.a.v 2
7600.2.a.w 2
7600.2.a.x 2
7600.2.a.y 2
7600.2.a.z 2
7600.2.a.ba 2
7600.2.a.bb 2
7600.2.a.bc 2
7600.2.a.bd 2
7600.2.a.be 2
7600.2.a.bf 2
7600.2.a.bg 2
7600.2.a.bh 3
7600.2.a.bi 3
7600.2.a.bj 3
7600.2.a.bk 3
7600.2.a.bl 3
7600.2.a.bm 3
7600.2.a.bn 3
7600.2.a.bo 3
7600.2.a.bp 3
7600.2.a.bq 3
7600.2.a.br 3
7600.2.a.bs 3
7600.2.a.bt 3
7600.2.a.bu 3
7600.2.a.bv 3
7600.2.a.bw 3
7600.2.a.bx 3
7600.2.a.by 3
7600.2.a.bz 3
7600.2.a.ca 3
7600.2.a.cb 3
7600.2.a.cc 3
7600.2.a.cd 3
7600.2.a.ce 4
7600.2.a.cf 4
7600.2.a.cg 6
7600.2.a.ch 6
7600.2.a.ci 6
7600.2.a.cj 6
7600.2.a.ck 6
7600.2.a.cl 6
7600.2.a.cm 6
7600.2.a.cn 6
7600.2.d \(\chi_{7600}(3649, \cdot)\) n/a 162 1
7600.2.e \(\chi_{7600}(151, \cdot)\) None 0 1
7600.2.f \(\chi_{7600}(3801, \cdot)\) None 0 1
7600.2.g \(\chi_{7600}(7599, \cdot)\) n/a 180 1
7600.2.j \(\chi_{7600}(3951, \cdot)\) n/a 190 1
7600.2.k \(\chi_{7600}(7449, \cdot)\) None 0 1
7600.2.p \(\chi_{7600}(3799, \cdot)\) None 0 1
7600.2.q \(\chi_{7600}(2401, \cdot)\) n/a 374 2
7600.2.r \(\chi_{7600}(4293, \cdot)\) n/a 1432 2
7600.2.t \(\chi_{7600}(6043, \cdot)\) n/a 1296 2
7600.2.w \(\chi_{7600}(1899, \cdot)\) n/a 1432 2
7600.2.y \(\chi_{7600}(1901, \cdot)\) n/a 1368 2
7600.2.bb \(\chi_{7600}(2393, \cdot)\) None 0 2
7600.2.bc \(\chi_{7600}(1407, \cdot)\) n/a 324 2
7600.2.bd \(\chi_{7600}(3457, \cdot)\) n/a 356 2
7600.2.be \(\chi_{7600}(343, \cdot)\) None 0 2
7600.2.bi \(\chi_{7600}(1749, \cdot)\) n/a 1296 2
7600.2.bk \(\chi_{7600}(2051, \cdot)\) n/a 1508 2
7600.2.bl \(\chi_{7600}(2243, \cdot)\) n/a 1296 2
7600.2.bn \(\chi_{7600}(493, \cdot)\) n/a 1432 2
7600.2.bp \(\chi_{7600}(1521, \cdot)\) n/a 1080 4
7600.2.bq \(\chi_{7600}(2249, \cdot)\) None 0 2
7600.2.br \(\chi_{7600}(1551, \cdot)\) n/a 380 2
7600.2.bw \(\chi_{7600}(1399, \cdot)\) None 0 2
7600.2.bz \(\chi_{7600}(3751, \cdot)\) None 0 2
7600.2.ca \(\chi_{7600}(49, \cdot)\) n/a 356 2
7600.2.cb \(\chi_{7600}(3599, \cdot)\) n/a 360 2
7600.2.cc \(\chi_{7600}(201, \cdot)\) None 0 2
7600.2.cf \(\chi_{7600}(1201, \cdot)\) n/a 1122 6
7600.2.ci \(\chi_{7600}(1369, \cdot)\) None 0 4
7600.2.cj \(\chi_{7600}(911, \cdot)\) n/a 1200 4
7600.2.ck \(\chi_{7600}(759, \cdot)\) None 0 4
7600.2.cn \(\chi_{7600}(1671, \cdot)\) None 0 4
7600.2.co \(\chi_{7600}(609, \cdot)\) n/a 1080 4
7600.2.ct \(\chi_{7600}(1519, \cdot)\) n/a 1200 4
7600.2.cu \(\chi_{7600}(761, \cdot)\) None 0 4
7600.2.cv \(\chi_{7600}(4093, \cdot)\) n/a 2864 4
7600.2.cx \(\chi_{7600}(4643, \cdot)\) n/a 2864 4
7600.2.da \(\chi_{7600}(501, \cdot)\) n/a 3016 4
7600.2.dc \(\chi_{7600}(1699, \cdot)\) n/a 2864 4
7600.2.dd \(\chi_{7600}(3257, \cdot)\) None 0 4
7600.2.de \(\chi_{7600}(543, \cdot)\) n/a 720 4
7600.2.dj \(\chi_{7600}(1057, \cdot)\) n/a 712 4
7600.2.dk \(\chi_{7600}(7, \cdot)\) None 0 4
7600.2.dm \(\chi_{7600}(1851, \cdot)\) n/a 3016 4
7600.2.do \(\chi_{7600}(349, \cdot)\) n/a 2864 4
7600.2.dp \(\chi_{7600}(843, \cdot)\) n/a 2864 4
7600.2.dr \(\chi_{7600}(293, \cdot)\) n/a 2864 4
7600.2.dt \(\chi_{7600}(881, \cdot)\) n/a 2384 8
7600.2.du \(\chi_{7600}(599, \cdot)\) None 0 6
7600.2.dz \(\chi_{7600}(2201, \cdot)\) None 0 6
7600.2.ea \(\chi_{7600}(1199, \cdot)\) n/a 1080 6
7600.2.ed \(\chi_{7600}(2049, \cdot)\) n/a 1068 6
7600.2.ee \(\chi_{7600}(1351, \cdot)\) None 0 6
7600.2.ef \(\chi_{7600}(751, \cdot)\) n/a 1140 6
7600.2.eg \(\chi_{7600}(1049, \cdot)\) None 0 6
7600.2.ek \(\chi_{7600}(37, \cdot)\) n/a 9568 8
7600.2.em \(\chi_{7600}(267, \cdot)\) n/a 8640 8
7600.2.en \(\chi_{7600}(381, \cdot)\) n/a 8640 8
7600.2.ep \(\chi_{7600}(379, \cdot)\) n/a 9568 8
7600.2.et \(\chi_{7600}(647, \cdot)\) None 0 8
7600.2.eu \(\chi_{7600}(113, \cdot)\) n/a 2384 8
7600.2.ev \(\chi_{7600}(1103, \cdot)\) n/a 2160 8
7600.2.ew \(\chi_{7600}(873, \cdot)\) None 0 8
7600.2.ez \(\chi_{7600}(531, \cdot)\) n/a 9568 8
7600.2.fb \(\chi_{7600}(229, \cdot)\) n/a 8640 8
7600.2.fe \(\chi_{7600}(1027, \cdot)\) n/a 8640 8
7600.2.fg \(\chi_{7600}(797, \cdot)\) n/a 9568 8
7600.2.fh \(\chi_{7600}(1489, \cdot)\) n/a 2384 8
7600.2.fi \(\chi_{7600}(711, \cdot)\) None 0 8
7600.2.fn \(\chi_{7600}(121, \cdot)\) None 0 8
7600.2.fo \(\chi_{7600}(559, \cdot)\) n/a 2400 8
7600.2.fr \(\chi_{7600}(31, \cdot)\) n/a 2400 8
7600.2.fs \(\chi_{7600}(729, \cdot)\) None 0 8
7600.2.ft \(\chi_{7600}(1319, \cdot)\) None 0 8
7600.2.fw \(\chi_{7600}(149, \cdot)\) n/a 8592 12
7600.2.fx \(\chi_{7600}(51, \cdot)\) n/a 9048 12
7600.2.gc \(\chi_{7600}(193, \cdot)\) n/a 2136 12
7600.2.gd \(\chi_{7600}(807, \cdot)\) None 0 12
7600.2.gg \(\chi_{7600}(643, \cdot)\) n/a 8592 12
7600.2.gh \(\chi_{7600}(357, \cdot)\) n/a 8592 12
7600.2.gk \(\chi_{7600}(1093, \cdot)\) n/a 8592 12
7600.2.gl \(\chi_{7600}(43, \cdot)\) n/a 8592 12
7600.2.go \(\chi_{7600}(393, \cdot)\) None 0 12
7600.2.gp \(\chi_{7600}(207, \cdot)\) n/a 2160 12
7600.2.gq \(\chi_{7600}(101, \cdot)\) n/a 9048 12
7600.2.gr \(\chi_{7600}(299, \cdot)\) n/a 8592 12
7600.2.gu \(\chi_{7600}(81, \cdot)\) n/a 7152 24
7600.2.gw \(\chi_{7600}(373, \cdot)\) n/a 19136 16
7600.2.gy \(\chi_{7600}(387, \cdot)\) n/a 19136 16
7600.2.gz \(\chi_{7600}(179, \cdot)\) n/a 19136 16
7600.2.hb \(\chi_{7600}(581, \cdot)\) n/a 19136 16
7600.2.hd \(\chi_{7600}(87, \cdot)\) None 0 16
7600.2.he \(\chi_{7600}(673, \cdot)\) n/a 4768 16
7600.2.hj \(\chi_{7600}(463, \cdot)\) n/a 4800 16
7600.2.hk \(\chi_{7600}(217, \cdot)\) None 0 16
7600.2.hl \(\chi_{7600}(429, \cdot)\) n/a 19136 16
7600.2.hn \(\chi_{7600}(331, \cdot)\) n/a 19136 16
7600.2.hq \(\chi_{7600}(83, \cdot)\) n/a 19136 16
7600.2.hs \(\chi_{7600}(597, \cdot)\) n/a 19136 16
7600.2.ht \(\chi_{7600}(79, \cdot)\) n/a 7200 24
7600.2.hu \(\chi_{7600}(441, \cdot)\) None 0 24
7600.2.hz \(\chi_{7600}(279, \cdot)\) None 0 24
7600.2.ic \(\chi_{7600}(9, \cdot)\) None 0 24
7600.2.id \(\chi_{7600}(431, \cdot)\) n/a 7200 24
7600.2.ie \(\chi_{7600}(71, \cdot)\) None 0 24
7600.2.if \(\chi_{7600}(289, \cdot)\) n/a 7152 24
7600.2.ik \(\chi_{7600}(91, \cdot)\) n/a 57408 48
7600.2.il \(\chi_{7600}(309, \cdot)\) n/a 57408 48
7600.2.im \(\chi_{7600}(47, \cdot)\) n/a 14400 48
7600.2.in \(\chi_{7600}(553, \cdot)\) None 0 48
7600.2.iq \(\chi_{7600}(123, \cdot)\) n/a 57408 48
7600.2.ir \(\chi_{7600}(53, \cdot)\) n/a 57408 48
7600.2.iu \(\chi_{7600}(13, \cdot)\) n/a 57408 48
7600.2.iv \(\chi_{7600}(187, \cdot)\) n/a 57408 48
7600.2.iy \(\chi_{7600}(23, \cdot)\) None 0 48
7600.2.iz \(\chi_{7600}(33, \cdot)\) n/a 14304 48
7600.2.je \(\chi_{7600}(59, \cdot)\) n/a 57408 48
7600.2.jf \(\chi_{7600}(61, \cdot)\) n/a 57408 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7600)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(380))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(475))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(760))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(950))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1900))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3800))\)\(^{\oplus 2}\)