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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

\( 219470 q - 84 q^{2} - 84 q^{3} - 104 q^{4} - 106 q^{5} - 112 q^{6} - 90 q^{7} + 12 q^{9} + O(q^{10}) \) \( 219470 q - 84 q^{2} - 84 q^{3} - 104 q^{4} - 106 q^{5} - 112 q^{6} - 90 q^{7} + 12 q^{9} - 120 q^{10} + 78 q^{11} - 112 q^{12} - 6 q^{13} - 336 q^{14} - 42 q^{15} + 408 q^{16} - 100 q^{17} + 40 q^{18} - 460 q^{19} - 928 q^{20} - 738 q^{21} - 928 q^{22} - 710 q^{23} - 1584 q^{24} - 1374 q^{25} - 1736 q^{26} + 672 q^{27} - 1104 q^{28} + 454 q^{29} + 888 q^{30} - 294 q^{31} + 1896 q^{32} - 162 q^{33} + 864 q^{34} + 972 q^{35} - 1640 q^{36} + 1560 q^{37} - 2440 q^{38} + 366 q^{39} + 1432 q^{40} + 210 q^{41} + 1248 q^{42} - 3026 q^{43} + 4336 q^{44} + 386 q^{45} + 3368 q^{46} - 7698 q^{47} + 4776 q^{48} - 3170 q^{49} + 7116 q^{50} - 2050 q^{51} + 3744 q^{52} - 1156 q^{53} + 328 q^{54} - 476 q^{55} - 5856 q^{56} - 2328 q^{57} - 4616 q^{58} + 8378 q^{59} - 15976 q^{60} + 3802 q^{61} - 9552 q^{62} + 4998 q^{63} - 3440 q^{64} + 7486 q^{65} + 9728 q^{66} - 2534 q^{67} + 3344 q^{68} + 5406 q^{69} - 7032 q^{70} - 1000 q^{71} + 15792 q^{72} - 9428 q^{73} + 8096 q^{74} + 964 q^{75} - 2528 q^{76} + 9054 q^{77} + 920 q^{78} - 874 q^{79} - 13472 q^{80} + 700 q^{81} - 7152 q^{82} - 5334 q^{83} - 19216 q^{84} + 1386 q^{85} - 17792 q^{86} + 402 q^{87} + 9528 q^{88} - 1632 q^{89} - 2416 q^{90} + 10524 q^{91} + 24904 q^{92} - 1882 q^{93} + 24136 q^{94} + 2672 q^{95} + 12808 q^{96} - 5306 q^{97} + 28852 q^{98} + 3054 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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