Properties

Label 2448.4
Level 2448
Weight 4
Dimension 219470
Nonzero newspaces 52
Sturm bound 1327104
Trace bound 25

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Defining parameters

Level: \( N \) = \( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 52 \)
Sturm bound: \(1327104\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2448))\).

Total New Old
Modular forms 501248 220684 280564
Cusp forms 494080 219470 274610
Eisenstein series 7168 1214 5954

Trace form

\( 219470 q - 84 q^{2} - 84 q^{3} - 104 q^{4} - 106 q^{5} - 112 q^{6} - 90 q^{7} + 12 q^{9} - 120 q^{10} + 78 q^{11} - 112 q^{12} - 6 q^{13} - 336 q^{14} - 42 q^{15} + 408 q^{16} - 100 q^{17} + 40 q^{18} - 460 q^{19}+ \cdots + 3054 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2448))\)

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
2448.4.a \(\chi_{2448}(1, \cdot)\) 2448.4.a.a 1 1
2448.4.a.b 1
2448.4.a.c 1
2448.4.a.d 1
2448.4.a.e 1
2448.4.a.f 1
2448.4.a.g 1
2448.4.a.h 1
2448.4.a.i 1
2448.4.a.j 1
2448.4.a.k 1
2448.4.a.l 1
2448.4.a.m 1
2448.4.a.n 1
2448.4.a.o 1
2448.4.a.p 1
2448.4.a.q 1
2448.4.a.r 1
2448.4.a.s 2
2448.4.a.t 2
2448.4.a.u 2
2448.4.a.v 2
2448.4.a.w 2
2448.4.a.x 2
2448.4.a.y 2
2448.4.a.z 2
2448.4.a.ba 3
2448.4.a.bb 3
2448.4.a.bc 3
2448.4.a.bd 3
2448.4.a.be 3
2448.4.a.bf 3
2448.4.a.bg 3
2448.4.a.bh 3
2448.4.a.bi 3
2448.4.a.bj 3
2448.4.a.bk 3
2448.4.a.bl 3
2448.4.a.bm 3
2448.4.a.bn 3
2448.4.a.bo 4
2448.4.a.bp 4
2448.4.a.bq 4
2448.4.a.br 4
2448.4.a.bs 4
2448.4.a.bt 5
2448.4.a.bu 5
2448.4.a.bv 7
2448.4.a.bw 7
2448.4.c \(\chi_{2448}(577, \cdot)\) n/a 134 1
2448.4.e \(\chi_{2448}(1871, \cdot)\) 2448.4.e.a 32 1
2448.4.e.b 64
2448.4.f \(\chi_{2448}(1225, \cdot)\) None 0 1
2448.4.h \(\chi_{2448}(1223, \cdot)\) None 0 1
2448.4.j \(\chi_{2448}(647, \cdot)\) None 0 1
2448.4.l \(\chi_{2448}(1801, \cdot)\) None 0 1
2448.4.o \(\chi_{2448}(2447, \cdot)\) n/a 108 1
2448.4.q \(\chi_{2448}(817, \cdot)\) n/a 576 2
2448.4.s \(\chi_{2448}(395, \cdot)\) n/a 864 2
2448.4.t \(\chi_{2448}(973, \cdot)\) n/a 1076 2
2448.4.v \(\chi_{2448}(613, \cdot)\) n/a 960 2
2448.4.x \(\chi_{2448}(611, \cdot)\) n/a 864 2
2448.4.z \(\chi_{2448}(2087, \cdot)\) None 0 2
2448.4.bb \(\chi_{2448}(217, \cdot)\) None 0 2
2448.4.be \(\chi_{2448}(1441, \cdot)\) n/a 268 2
2448.4.bg \(\chi_{2448}(863, \cdot)\) n/a 216 2
2448.4.bi \(\chi_{2448}(35, \cdot)\) n/a 768 2
2448.4.bk \(\chi_{2448}(1189, \cdot)\) n/a 1076 2
2448.4.bm \(\chi_{2448}(829, \cdot)\) n/a 1076 2
2448.4.bn \(\chi_{2448}(251, \cdot)\) n/a 864 2
2448.4.bq \(\chi_{2448}(815, \cdot)\) n/a 648 2
2448.4.bt \(\chi_{2448}(169, \cdot)\) None 0 2
2448.4.bv \(\chi_{2448}(1463, \cdot)\) None 0 2
2448.4.bx \(\chi_{2448}(407, \cdot)\) None 0 2
2448.4.bz \(\chi_{2448}(409, \cdot)\) None 0 2
2448.4.ca \(\chi_{2448}(239, \cdot)\) n/a 576 2
2448.4.cc \(\chi_{2448}(1393, \cdot)\) n/a 644 2
2448.4.cg \(\chi_{2448}(145, \cdot)\) n/a 536 4
2448.4.ch \(\chi_{2448}(287, \cdot)\) n/a 432 4
2448.4.ci \(\chi_{2448}(179, \cdot)\) n/a 1728 4
2448.4.cj \(\chi_{2448}(253, \cdot)\) n/a 2152 4
2448.4.cm \(\chi_{2448}(899, \cdot)\) n/a 1728 4
2448.4.cn \(\chi_{2448}(325, \cdot)\) n/a 2152 4
2448.4.cq \(\chi_{2448}(937, \cdot)\) None 0 4
2448.4.cr \(\chi_{2448}(359, \cdot)\) None 0 4
2448.4.cu \(\chi_{2448}(803, \cdot)\) n/a 5168 4
2448.4.cx \(\chi_{2448}(13, \cdot)\) n/a 5168 4
2448.4.cy \(\chi_{2448}(373, \cdot)\) n/a 5168 4
2448.4.da \(\chi_{2448}(443, \cdot)\) n/a 4608 4
2448.4.dd \(\chi_{2448}(625, \cdot)\) n/a 1288 4
2448.4.df \(\chi_{2448}(47, \cdot)\) n/a 1296 4
2448.4.dg \(\chi_{2448}(455, \cdot)\) None 0 4
2448.4.di \(\chi_{2448}(1033, \cdot)\) None 0 4
2448.4.dl \(\chi_{2448}(203, \cdot)\) n/a 5168 4
2448.4.dn \(\chi_{2448}(205, \cdot)\) n/a 4608 4
2448.4.do \(\chi_{2448}(157, \cdot)\) n/a 5168 4
2448.4.dr \(\chi_{2448}(659, \cdot)\) n/a 5168 4
2448.4.dt \(\chi_{2448}(197, \cdot)\) n/a 3456 8
2448.4.du \(\chi_{2448}(91, \cdot)\) n/a 4304 8
2448.4.dx \(\chi_{2448}(449, \cdot)\) n/a 864 8
2448.4.dy \(\chi_{2448}(415, \cdot)\) n/a 1080 8
2448.4.eb \(\chi_{2448}(199, \cdot)\) None 0 8
2448.4.ec \(\chi_{2448}(233, \cdot)\) None 0 8
2448.4.ef \(\chi_{2448}(125, \cdot)\) n/a 3456 8
2448.4.eg \(\chi_{2448}(163, \cdot)\) n/a 4304 8
2448.4.ei \(\chi_{2448}(25, \cdot)\) None 0 8
2448.4.ej \(\chi_{2448}(263, \cdot)\) None 0 8
2448.4.eo \(\chi_{2448}(155, \cdot)\) n/a 10336 8
2448.4.ep \(\chi_{2448}(229, \cdot)\) n/a 10336 8
2448.4.es \(\chi_{2448}(59, \cdot)\) n/a 10336 8
2448.4.et \(\chi_{2448}(349, \cdot)\) n/a 10336 8
2448.4.ew \(\chi_{2448}(49, \cdot)\) n/a 2576 8
2448.4.ex \(\chi_{2448}(383, \cdot)\) n/a 2592 8
2448.4.ez \(\chi_{2448}(139, \cdot)\) n/a 20672 16
2448.4.fa \(\chi_{2448}(5, \cdot)\) n/a 20672 16
2448.4.fd \(\chi_{2448}(31, \cdot)\) n/a 5184 16
2448.4.fe \(\chi_{2448}(65, \cdot)\) n/a 5152 16
2448.4.fh \(\chi_{2448}(41, \cdot)\) None 0 16
2448.4.fi \(\chi_{2448}(7, \cdot)\) None 0 16
2448.4.fl \(\chi_{2448}(283, \cdot)\) n/a 20672 16
2448.4.fm \(\chi_{2448}(29, \cdot)\) n/a 20672 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2448))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2448)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(306))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(408))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(612))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(816))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1224))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2448))\)\(^{\oplus 1}\)