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Properties

Label 2400.4
Level 2400
Weight 4
Dimension 178762
Nonzero newspaces 40
Sturm bound 1228800
Trace bound 25

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Defining parameters

Level: \( N \) = \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(1228800\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2400))\).

Total New Old
Modular forms 464384 179582 284802
Cusp forms 457216 178762 278454
Eisenstein series 7168 820 6348

Trace form

\( 178762 q - 38 q^{3} - 104 q^{4} - 84 q^{6} - 108 q^{7} - 98 q^{9} - 128 q^{10} - 4 q^{12} + 132 q^{13} + 416 q^{14} - 48 q^{15} + 432 q^{16} + 208 q^{17} + 20 q^{18} - 68 q^{19} - 68 q^{21} - 496 q^{22}+ \cdots + 2212 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2400))\)

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
2400.4.a \(\chi_{2400}(1, \cdot)\) 2400.4.a.a 1 1
2400.4.a.b 1
2400.4.a.c 1
2400.4.a.d 1
2400.4.a.e 1
2400.4.a.f 1
2400.4.a.g 1
2400.4.a.h 1
2400.4.a.i 1
2400.4.a.j 1
2400.4.a.k 1
2400.4.a.l 1
2400.4.a.m 1
2400.4.a.n 1
2400.4.a.o 1
2400.4.a.p 1
2400.4.a.q 1
2400.4.a.r 1
2400.4.a.s 1
2400.4.a.t 1
2400.4.a.u 1
2400.4.a.v 1
2400.4.a.w 2
2400.4.a.x 2
2400.4.a.y 2
2400.4.a.z 2
2400.4.a.ba 2
2400.4.a.bb 2
2400.4.a.bc 2
2400.4.a.bd 2
2400.4.a.be 3
2400.4.a.bf 3
2400.4.a.bg 3
2400.4.a.bh 3
2400.4.a.bi 3
2400.4.a.bj 3
2400.4.a.bk 3
2400.4.a.bl 3
2400.4.a.bm 3
2400.4.a.bn 3
2400.4.a.bo 3
2400.4.a.bp 3
2400.4.a.bq 3
2400.4.a.br 3
2400.4.a.bs 3
2400.4.a.bt 3
2400.4.a.bu 3
2400.4.a.bv 3
2400.4.a.bw 3
2400.4.a.bx 3
2400.4.a.by 4
2400.4.a.bz 4
2400.4.a.ca 4
2400.4.a.cb 4
2400.4.b \(\chi_{2400}(2351, \cdot)\) n/a 222 1
2400.4.d \(\chi_{2400}(49, \cdot)\) n/a 108 1
2400.4.f \(\chi_{2400}(1249, \cdot)\) n/a 108 1
2400.4.h \(\chi_{2400}(1151, \cdot)\) n/a 228 1
2400.4.k \(\chi_{2400}(1201, \cdot)\) n/a 114 1
2400.4.m \(\chi_{2400}(1199, \cdot)\) n/a 212 1
2400.4.o \(\chi_{2400}(2399, \cdot)\) n/a 216 1
2400.4.s \(\chi_{2400}(601, \cdot)\) None 0 2
2400.4.t \(\chi_{2400}(599, \cdot)\) None 0 2
2400.4.v \(\chi_{2400}(257, \cdot)\) n/a 432 2
2400.4.w \(\chi_{2400}(607, \cdot)\) n/a 216 2
2400.4.y \(\chi_{2400}(7, \cdot)\) None 0 2
2400.4.bb \(\chi_{2400}(857, \cdot)\) None 0 2
2400.4.bc \(\chi_{2400}(1207, \cdot)\) None 0 2
2400.4.bf \(\chi_{2400}(2057, \cdot)\) None 0 2
2400.4.bh \(\chi_{2400}(943, \cdot)\) n/a 216 2
2400.4.bi \(\chi_{2400}(593, \cdot)\) n/a 424 2
2400.4.bk \(\chi_{2400}(551, \cdot)\) None 0 2
2400.4.bl \(\chi_{2400}(649, \cdot)\) None 0 2
2400.4.bo \(\chi_{2400}(481, \cdot)\) n/a 720 4
2400.4.bp \(\chi_{2400}(43, \cdot)\) n/a 1728 4
2400.4.bs \(\chi_{2400}(893, \cdot)\) n/a 3440 4
2400.4.bt \(\chi_{2400}(299, \cdot)\) n/a 3440 4
2400.4.bw \(\chi_{2400}(301, \cdot)\) n/a 1824 4
2400.4.by \(\chi_{2400}(251, \cdot)\) n/a 3624 4
2400.4.bz \(\chi_{2400}(349, \cdot)\) n/a 1728 4
2400.4.cc \(\chi_{2400}(293, \cdot)\) n/a 3440 4
2400.4.cd \(\chi_{2400}(643, \cdot)\) n/a 1728 4
2400.4.cg \(\chi_{2400}(191, \cdot)\) n/a 1440 4
2400.4.ci \(\chi_{2400}(289, \cdot)\) n/a 720 4
2400.4.ck \(\chi_{2400}(529, \cdot)\) n/a 720 4
2400.4.cm \(\chi_{2400}(431, \cdot)\) n/a 1424 4
2400.4.co \(\chi_{2400}(479, \cdot)\) n/a 1440 4
2400.4.cq \(\chi_{2400}(239, \cdot)\) n/a 1424 4
2400.4.cs \(\chi_{2400}(241, \cdot)\) n/a 720 4
2400.4.cu \(\chi_{2400}(119, \cdot)\) None 0 8
2400.4.cv \(\chi_{2400}(121, \cdot)\) None 0 8
2400.4.cz \(\chi_{2400}(17, \cdot)\) n/a 2848 8
2400.4.da \(\chi_{2400}(367, \cdot)\) n/a 1440 8
2400.4.dc \(\chi_{2400}(137, \cdot)\) None 0 8
2400.4.df \(\chi_{2400}(103, \cdot)\) None 0 8
2400.4.dg \(\chi_{2400}(233, \cdot)\) None 0 8
2400.4.dj \(\chi_{2400}(487, \cdot)\) None 0 8
2400.4.dl \(\chi_{2400}(127, \cdot)\) n/a 1440 8
2400.4.dm \(\chi_{2400}(353, \cdot)\) n/a 2880 8
2400.4.dq \(\chi_{2400}(169, \cdot)\) None 0 8
2400.4.dr \(\chi_{2400}(71, \cdot)\) None 0 8
2400.4.ds \(\chi_{2400}(173, \cdot)\) n/a 22976 16
2400.4.dv \(\chi_{2400}(67, \cdot)\) n/a 11520 16
2400.4.dx \(\chi_{2400}(109, \cdot)\) n/a 11520 16
2400.4.dy \(\chi_{2400}(11, \cdot)\) n/a 22976 16
2400.4.ea \(\chi_{2400}(61, \cdot)\) n/a 11520 16
2400.4.ed \(\chi_{2400}(59, \cdot)\) n/a 22976 16
2400.4.ef \(\chi_{2400}(163, \cdot)\) n/a 11520 16
2400.4.eg \(\chi_{2400}(53, \cdot)\) n/a 22976 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2400))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2400)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 30}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(800))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2400))\)\(^{\oplus 1}\)