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Properties

Label 2448.2
Level 2448
Weight 2
Dimension 72752
Nonzero newspaces 52
Sturm bound 663552
Trace bound 25

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Defining parameters

Level: \( N \) = \( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 52 \)
Sturm bound: \(663552\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2448))\).

Total New Old
Modular forms 169472 73966 95506
Cusp forms 162305 72752 89553
Eisenstein series 7167 1214 5953

Trace form

\( 72752 q - 84 q^{2} - 84 q^{3} - 88 q^{4} - 110 q^{5} - 112 q^{6} - 74 q^{7} - 96 q^{8} - 36 q^{9} + O(q^{10}) \) \( 72752 q - 84 q^{2} - 84 q^{3} - 88 q^{4} - 110 q^{5} - 112 q^{6} - 74 q^{7} - 96 q^{8} - 36 q^{9} - 256 q^{10} - 90 q^{11} - 112 q^{12} - 122 q^{13} - 48 q^{14} - 90 q^{15} - 40 q^{16} - 194 q^{17} - 200 q^{18} - 196 q^{19} + 16 q^{20} - 114 q^{21} + 8 q^{22} - 22 q^{23} - 48 q^{24} + 32 q^{25} + 32 q^{26} - 48 q^{27} - 176 q^{28} - 46 q^{29} - 72 q^{30} - 38 q^{31} - 24 q^{32} - 210 q^{33} - 80 q^{34} + 12 q^{35} - 104 q^{36} - 332 q^{37} - 176 q^{38} + 30 q^{39} - 200 q^{40} + 6 q^{41} - 192 q^{42} + 54 q^{43} - 256 q^{44} - 94 q^{45} - 376 q^{46} + 78 q^{47} - 216 q^{48} - 256 q^{49} - 252 q^{50} - 58 q^{51} - 304 q^{52} - 104 q^{53} - 200 q^{54} - 108 q^{55} - 288 q^{56} - 72 q^{57} - 160 q^{58} - 62 q^{59} - 328 q^{60} - 122 q^{61} - 288 q^{62} - 90 q^{63} - 112 q^{64} - 442 q^{65} - 352 q^{66} - 126 q^{67} - 176 q^{68} - 450 q^{69} - 8 q^{70} - 248 q^{71} - 336 q^{72} - 96 q^{73} - 200 q^{74} - 188 q^{75} - 16 q^{76} - 258 q^{77} - 328 q^{78} - 202 q^{79} - 352 q^{80} - 404 q^{81} - 272 q^{82} - 318 q^{83} - 400 q^{84} - 98 q^{85} - 472 q^{86} - 222 q^{87} - 232 q^{88} - 60 q^{89} - 400 q^{90} - 356 q^{91} - 280 q^{92} - 58 q^{93} - 280 q^{94} - 272 q^{95} - 248 q^{96} - 166 q^{97} - 268 q^{98} - 114 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2448))\)

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
2448.2.a \(\chi_{2448}(1, \cdot)\) 2448.2.a.a 1 1
2448.2.a.b 1
2448.2.a.c 1
2448.2.a.d 1
2448.2.a.e 1
2448.2.a.f 1
2448.2.a.g 1
2448.2.a.h 1
2448.2.a.i 1
2448.2.a.j 1
2448.2.a.k 1
2448.2.a.l 1
2448.2.a.m 1
2448.2.a.n 1
2448.2.a.o 1
2448.2.a.p 1
2448.2.a.q 1
2448.2.a.r 1
2448.2.a.s 1
2448.2.a.t 1
2448.2.a.u 2
2448.2.a.v 2
2448.2.a.w 2
2448.2.a.x 2
2448.2.a.y 2
2448.2.a.z 2
2448.2.a.ba 2
2448.2.a.bb 3
2448.2.a.bc 3
2448.2.c \(\chi_{2448}(577, \cdot)\) 2448.2.c.a 2 1
2448.2.c.b 2
2448.2.c.c 2
2448.2.c.d 2
2448.2.c.e 2
2448.2.c.f 2
2448.2.c.g 2
2448.2.c.h 2
2448.2.c.i 2
2448.2.c.j 2
2448.2.c.k 2
2448.2.c.l 2
2448.2.c.m 2
2448.2.c.n 2
2448.2.c.o 2
2448.2.c.p 4
2448.2.c.q 4
2448.2.c.r 6
2448.2.e \(\chi_{2448}(1871, \cdot)\) 2448.2.e.a 8 1
2448.2.e.b 24
2448.2.f \(\chi_{2448}(1225, \cdot)\) None 0 1
2448.2.h \(\chi_{2448}(1223, \cdot)\) None 0 1
2448.2.j \(\chi_{2448}(647, \cdot)\) None 0 1
2448.2.l \(\chi_{2448}(1801, \cdot)\) None 0 1
2448.2.o \(\chi_{2448}(2447, \cdot)\) 2448.2.o.a 4 1
2448.2.o.b 4
2448.2.o.c 4
2448.2.o.d 24
2448.2.q \(\chi_{2448}(817, \cdot)\) n/a 192 2
2448.2.s \(\chi_{2448}(395, \cdot)\) n/a 288 2
2448.2.t \(\chi_{2448}(973, \cdot)\) n/a 356 2
2448.2.v \(\chi_{2448}(613, \cdot)\) n/a 320 2
2448.2.x \(\chi_{2448}(611, \cdot)\) n/a 288 2
2448.2.z \(\chi_{2448}(2087, \cdot)\) None 0 2
2448.2.bb \(\chi_{2448}(217, \cdot)\) None 0 2
2448.2.be \(\chi_{2448}(1441, \cdot)\) 2448.2.be.a 2 2
2448.2.be.b 2
2448.2.be.c 2
2448.2.be.d 2
2448.2.be.e 2
2448.2.be.f 2
2448.2.be.g 2
2448.2.be.h 2
2448.2.be.i 2
2448.2.be.j 2
2448.2.be.k 2
2448.2.be.l 2
2448.2.be.m 2
2448.2.be.n 2
2448.2.be.o 4
2448.2.be.p 4
2448.2.be.q 4
2448.2.be.r 4
2448.2.be.s 4
2448.2.be.t 4
2448.2.be.u 4
2448.2.be.v 6
2448.2.be.w 6
2448.2.be.x 8
2448.2.be.y 12
2448.2.bg \(\chi_{2448}(863, \cdot)\) 2448.2.bg.a 4 2
2448.2.bg.b 4
2448.2.bg.c 8
2448.2.bg.d 8
2448.2.bg.e 8
2448.2.bg.f 40
2448.2.bi \(\chi_{2448}(35, \cdot)\) n/a 256 2
2448.2.bk \(\chi_{2448}(1189, \cdot)\) n/a 356 2
2448.2.bm \(\chi_{2448}(829, \cdot)\) n/a 356 2
2448.2.bn \(\chi_{2448}(251, \cdot)\) n/a 288 2
2448.2.bq \(\chi_{2448}(815, \cdot)\) n/a 216 2
2448.2.bt \(\chi_{2448}(169, \cdot)\) None 0 2
2448.2.bv \(\chi_{2448}(1463, \cdot)\) None 0 2
2448.2.bx \(\chi_{2448}(407, \cdot)\) None 0 2
2448.2.bz \(\chi_{2448}(409, \cdot)\) None 0 2
2448.2.ca \(\chi_{2448}(239, \cdot)\) n/a 192 2
2448.2.cc \(\chi_{2448}(1393, \cdot)\) n/a 212 2
2448.2.cg \(\chi_{2448}(145, \cdot)\) n/a 176 4
2448.2.ch \(\chi_{2448}(287, \cdot)\) n/a 144 4
2448.2.ci \(\chi_{2448}(179, \cdot)\) n/a 576 4
2448.2.cj \(\chi_{2448}(253, \cdot)\) n/a 712 4
2448.2.cm \(\chi_{2448}(899, \cdot)\) n/a 576 4
2448.2.cn \(\chi_{2448}(325, \cdot)\) n/a 712 4
2448.2.cq \(\chi_{2448}(937, \cdot)\) None 0 4
2448.2.cr \(\chi_{2448}(359, \cdot)\) None 0 4
2448.2.cu \(\chi_{2448}(803, \cdot)\) n/a 1712 4
2448.2.cx \(\chi_{2448}(13, \cdot)\) n/a 1712 4
2448.2.cy \(\chi_{2448}(373, \cdot)\) n/a 1712 4
2448.2.da \(\chi_{2448}(443, \cdot)\) n/a 1536 4
2448.2.dd \(\chi_{2448}(625, \cdot)\) n/a 424 4
2448.2.df \(\chi_{2448}(47, \cdot)\) n/a 432 4
2448.2.dg \(\chi_{2448}(455, \cdot)\) None 0 4
2448.2.di \(\chi_{2448}(1033, \cdot)\) None 0 4
2448.2.dl \(\chi_{2448}(203, \cdot)\) n/a 1712 4
2448.2.dn \(\chi_{2448}(205, \cdot)\) n/a 1536 4
2448.2.do \(\chi_{2448}(157, \cdot)\) n/a 1712 4
2448.2.dr \(\chi_{2448}(659, \cdot)\) n/a 1712 4
2448.2.dt \(\chi_{2448}(197, \cdot)\) n/a 1152 8
2448.2.du \(\chi_{2448}(91, \cdot)\) n/a 1424 8
2448.2.dx \(\chi_{2448}(449, \cdot)\) n/a 288 8
2448.2.dy \(\chi_{2448}(415, \cdot)\) n/a 360 8
2448.2.eb \(\chi_{2448}(199, \cdot)\) None 0 8
2448.2.ec \(\chi_{2448}(233, \cdot)\) None 0 8
2448.2.ef \(\chi_{2448}(125, \cdot)\) n/a 1152 8
2448.2.eg \(\chi_{2448}(163, \cdot)\) n/a 1424 8
2448.2.ei \(\chi_{2448}(25, \cdot)\) None 0 8
2448.2.ej \(\chi_{2448}(263, \cdot)\) None 0 8
2448.2.eo \(\chi_{2448}(155, \cdot)\) n/a 3424 8
2448.2.ep \(\chi_{2448}(229, \cdot)\) n/a 3424 8
2448.2.es \(\chi_{2448}(59, \cdot)\) n/a 3424 8
2448.2.et \(\chi_{2448}(349, \cdot)\) n/a 3424 8
2448.2.ew \(\chi_{2448}(49, \cdot)\) n/a 848 8
2448.2.ex \(\chi_{2448}(383, \cdot)\) n/a 864 8
2448.2.ez \(\chi_{2448}(139, \cdot)\) n/a 6848 16
2448.2.fa \(\chi_{2448}(5, \cdot)\) n/a 6848 16
2448.2.fd \(\chi_{2448}(31, \cdot)\) n/a 1728 16
2448.2.fe \(\chi_{2448}(65, \cdot)\) n/a 1696 16
2448.2.fh \(\chi_{2448}(41, \cdot)\) None 0 16
2448.2.fi \(\chi_{2448}(7, \cdot)\) None 0 16
2448.2.fl \(\chi_{2448}(283, \cdot)\) n/a 6848 16
2448.2.fm \(\chi_{2448}(29, \cdot)\) n/a 6848 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2448))\) into lower level spaces

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