Properties

Label 7400.2
Level 7400
Weight 2
Dimension 846953
Nonzero newspaces 96
Sturm bound 6566400

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Defining parameters

Level: \( N \) = \( 7400 = 2^{3} \cdot 5^{2} \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 96 \)
Sturm bound: \(6566400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7400))\).

Total New Old
Modular forms 1653696 852693 801003
Cusp forms 1629505 846953 782552
Eisenstein series 24191 5740 18451

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7400))\)

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
7400.2.a \(\chi_{7400}(1, \cdot)\) 7400.2.a.a 1 1
7400.2.a.b 1
7400.2.a.c 1
7400.2.a.d 1
7400.2.a.e 1
7400.2.a.f 1
7400.2.a.g 1
7400.2.a.h 1
7400.2.a.i 1
7400.2.a.j 1
7400.2.a.k 3
7400.2.a.l 3
7400.2.a.m 3
7400.2.a.n 4
7400.2.a.o 5
7400.2.a.p 5
7400.2.a.q 5
7400.2.a.r 5
7400.2.a.s 6
7400.2.a.t 8
7400.2.a.u 8
7400.2.a.v 8
7400.2.a.w 8
7400.2.a.x 9
7400.2.a.y 9
7400.2.a.z 10
7400.2.a.ba 10
7400.2.a.bb 10
7400.2.a.bc 10
7400.2.a.bd 16
7400.2.a.be 16
7400.2.d \(\chi_{7400}(3849, \cdot)\) n/a 162 1
7400.2.e \(\chi_{7400}(1849, \cdot)\) n/a 172 1
7400.2.f \(\chi_{7400}(3701, \cdot)\) n/a 684 1
7400.2.g \(\chi_{7400}(1701, \cdot)\) n/a 716 1
7400.2.j \(\chi_{7400}(5549, \cdot)\) n/a 680 1
7400.2.k \(\chi_{7400}(149, \cdot)\) n/a 648 1
7400.2.p \(\chi_{7400}(5401, \cdot)\) n/a 180 1
7400.2.q \(\chi_{7400}(1601, \cdot)\) n/a 362 2
7400.2.r \(\chi_{7400}(2251, \cdot)\) n/a 1432 2
7400.2.u \(\chi_{7400}(2399, \cdot)\) None 0 2
7400.2.w \(\chi_{7400}(3657, \cdot)\) n/a 342 2
7400.2.y \(\chi_{7400}(4143, \cdot)\) None 0 2
7400.2.ba \(\chi_{7400}(1407, \cdot)\) None 0 2
7400.2.bb \(\chi_{7400}(857, \cdot)\) n/a 342 2
7400.2.bd \(\chi_{7400}(4557, \cdot)\) n/a 1360 2
7400.2.bf \(\chi_{7400}(2443, \cdot)\) n/a 1296 2
7400.2.bh \(\chi_{7400}(443, \cdot)\) n/a 1360 2
7400.2.bk \(\chi_{7400}(1893, \cdot)\) n/a 1360 2
7400.2.bm \(\chi_{7400}(3151, \cdot)\) None 0 2
7400.2.bn \(\chi_{7400}(3299, \cdot)\) n/a 1360 2
7400.2.bp \(\chi_{7400}(1481, \cdot)\) n/a 1080 4
7400.2.bs \(\chi_{7400}(2601, \cdot)\) n/a 360 2
7400.2.bt \(\chi_{7400}(1749, \cdot)\) n/a 1360 2
7400.2.bu \(\chi_{7400}(2749, \cdot)\) n/a 1360 2
7400.2.bx \(\chi_{7400}(101, \cdot)\) n/a 1432 2
7400.2.by \(\chi_{7400}(5301, \cdot)\) n/a 1432 2
7400.2.cd \(\chi_{7400}(249, \cdot)\) n/a 344 2
7400.2.ce \(\chi_{7400}(5449, \cdot)\) n/a 340 2
7400.2.cf \(\chi_{7400}(201, \cdot)\) n/a 1086 6
7400.2.ci \(\chi_{7400}(1629, \cdot)\) n/a 4320 4
7400.2.cj \(\chi_{7400}(1109, \cdot)\) n/a 4544 4
7400.2.ck \(\chi_{7400}(961, \cdot)\) n/a 1144 4
7400.2.cn \(\chi_{7400}(369, \cdot)\) n/a 1136 4
7400.2.co \(\chi_{7400}(889, \cdot)\) n/a 1080 4
7400.2.ct \(\chi_{7400}(221, \cdot)\) n/a 4544 4
7400.2.cu \(\chi_{7400}(741, \cdot)\) n/a 4320 4
7400.2.cv \(\chi_{7400}(3899, \cdot)\) n/a 2720 4
7400.2.cy \(\chi_{7400}(3751, \cdot)\) None 0 4
7400.2.da \(\chi_{7400}(2857, \cdot)\) n/a 684 4
7400.2.db \(\chi_{7400}(343, \cdot)\) None 0 4
7400.2.dd \(\chi_{7400}(1343, \cdot)\) None 0 4
7400.2.df \(\chi_{7400}(193, \cdot)\) n/a 684 4
7400.2.dh \(\chi_{7400}(3893, \cdot)\) n/a 2720 4
7400.2.dk \(\chi_{7400}(307, \cdot)\) n/a 2720 4
7400.2.dm \(\chi_{7400}(507, \cdot)\) n/a 2720 4
7400.2.do \(\chi_{7400}(2493, \cdot)\) n/a 2720 4
7400.2.dq \(\chi_{7400}(199, \cdot)\) None 0 4
7400.2.dr \(\chi_{7400}(51, \cdot)\) n/a 2864 4
7400.2.dt \(\chi_{7400}(121, \cdot)\) n/a 2272 8
7400.2.dw \(\chi_{7400}(1249, \cdot)\) n/a 1032 6
7400.2.dx \(\chi_{7400}(1801, \cdot)\) n/a 1080 6
7400.2.dz \(\chi_{7400}(49, \cdot)\) n/a 1020 6
7400.2.eb \(\chi_{7400}(1949, \cdot)\) n/a 4080 6
7400.2.ed \(\chi_{7400}(2301, \cdot)\) n/a 4296 6
7400.2.eg \(\chi_{7400}(349, \cdot)\) n/a 4080 6
7400.2.ei \(\chi_{7400}(1101, \cdot)\) n/a 4296 6
7400.2.ej \(\chi_{7400}(31, \cdot)\) None 0 8
7400.2.em \(\chi_{7400}(179, \cdot)\) n/a 9088 8
7400.2.en \(\chi_{7400}(413, \cdot)\) n/a 9088 8
7400.2.eq \(\chi_{7400}(147, \cdot)\) n/a 9088 8
7400.2.es \(\chi_{7400}(667, \cdot)\) n/a 8640 8
7400.2.eu \(\chi_{7400}(117, \cdot)\) n/a 9088 8
7400.2.ew \(\chi_{7400}(2337, \cdot)\) n/a 2280 8
7400.2.ex \(\chi_{7400}(223, \cdot)\) None 0 8
7400.2.ez \(\chi_{7400}(887, \cdot)\) None 0 8
7400.2.fb \(\chi_{7400}(697, \cdot)\) n/a 2280 8
7400.2.fe \(\chi_{7400}(771, \cdot)\) n/a 9088 8
7400.2.ff \(\chi_{7400}(919, \cdot)\) None 0 8
7400.2.fj \(\chi_{7400}(581, \cdot)\) n/a 9088 8
7400.2.fk \(\chi_{7400}(381, \cdot)\) n/a 9088 8
7400.2.fl \(\chi_{7400}(729, \cdot)\) n/a 2288 8
7400.2.fm \(\chi_{7400}(529, \cdot)\) n/a 2272 8
7400.2.fp \(\chi_{7400}(841, \cdot)\) n/a 2288 8
7400.2.fu \(\chi_{7400}(989, \cdot)\) n/a 9088 8
7400.2.fv \(\chi_{7400}(269, \cdot)\) n/a 9088 8
7400.2.fw \(\chi_{7400}(757, \cdot)\) n/a 8160 12
7400.2.fz \(\chi_{7400}(351, \cdot)\) None 0 12
7400.2.ga \(\chi_{7400}(107, \cdot)\) n/a 8160 12
7400.2.gd \(\chi_{7400}(243, \cdot)\) n/a 8160 12
7400.2.ge \(\chi_{7400}(799, \cdot)\) None 0 12
7400.2.gh \(\chi_{7400}(93, \cdot)\) n/a 8160 12
7400.2.gj \(\chi_{7400}(257, \cdot)\) n/a 2052 12
7400.2.gk \(\chi_{7400}(499, \cdot)\) n/a 8160 12
7400.2.gm \(\chi_{7400}(543, \cdot)\) None 0 12
7400.2.gp \(\chi_{7400}(7, \cdot)\) None 0 12
7400.2.gr \(\chi_{7400}(651, \cdot)\) n/a 8592 12
7400.2.gs \(\chi_{7400}(57, \cdot)\) n/a 2052 12
7400.2.gu \(\chi_{7400}(81, \cdot)\) n/a 6816 24
7400.2.gv \(\chi_{7400}(119, \cdot)\) None 0 16
7400.2.gy \(\chi_{7400}(171, \cdot)\) n/a 18176 16
7400.2.gz \(\chi_{7400}(637, \cdot)\) n/a 18176 16
7400.2.hb \(\chi_{7400}(787, \cdot)\) n/a 18176 16
7400.2.hd \(\chi_{7400}(27, \cdot)\) n/a 18176 16
7400.2.hg \(\chi_{7400}(717, \cdot)\) n/a 18176 16
7400.2.hi \(\chi_{7400}(177, \cdot)\) n/a 4560 16
7400.2.hk \(\chi_{7400}(767, \cdot)\) None 0 16
7400.2.hm \(\chi_{7400}(47, \cdot)\) None 0 16
7400.2.hn \(\chi_{7400}(97, \cdot)\) n/a 4560 16
7400.2.hq \(\chi_{7400}(859, \cdot)\) n/a 18176 16
7400.2.hr \(\chi_{7400}(711, \cdot)\) None 0 16
7400.2.hu \(\chi_{7400}(21, \cdot)\) n/a 27264 24
7400.2.hw \(\chi_{7400}(229, \cdot)\) n/a 27264 24
7400.2.hx \(\chi_{7400}(181, \cdot)\) n/a 27264 24
7400.2.hz \(\chi_{7400}(189, \cdot)\) n/a 27264 24
7400.2.ib \(\chi_{7400}(9, \cdot)\) n/a 6864 24
7400.2.id \(\chi_{7400}(41, \cdot)\) n/a 6864 24
7400.2.ig \(\chi_{7400}(169, \cdot)\) n/a 6816 24
7400.2.ii \(\chi_{7400}(153, \cdot)\) n/a 13680 48
7400.2.ik \(\chi_{7400}(91, \cdot)\) n/a 54528 48
7400.2.in \(\chi_{7400}(127, \cdot)\) None 0 48
7400.2.io \(\chi_{7400}(247, \cdot)\) None 0 48
7400.2.ir \(\chi_{7400}(19, \cdot)\) n/a 54528 48
7400.2.it \(\chi_{7400}(17, \cdot)\) n/a 13680 48
7400.2.iv \(\chi_{7400}(13, \cdot)\) n/a 54528 48
7400.2.ix \(\chi_{7400}(39, \cdot)\) None 0 48
7400.2.iz \(\chi_{7400}(3, \cdot)\) n/a 54528 48
7400.2.ja \(\chi_{7400}(83, \cdot)\) n/a 54528 48
7400.2.jc \(\chi_{7400}(311, \cdot)\) None 0 48
7400.2.je \(\chi_{7400}(533, \cdot)\) n/a 54528 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7400))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7400)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(370))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(740))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(925))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1850))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3700))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7400))\)\(^{\oplus 1}\)