Properties

Label 1848.2
Level 1848
Weight 2
Dimension 36280
Nonzero newspaces 48
Sturm bound 368640
Trace bound 12

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Defining parameters

Level: \( N \) = \( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(368640\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1848))\).

Total New Old
Modular forms 95040 37000 58040
Cusp forms 89281 36280 53001
Eisenstein series 5759 720 5039

Trace form

\( 36280 q - 8 q^{2} - 40 q^{3} - 72 q^{4} - 8 q^{5} - 20 q^{6} - 84 q^{7} + 16 q^{8} - 80 q^{9} + O(q^{10}) \) \( 36280 q - 8 q^{2} - 40 q^{3} - 72 q^{4} - 8 q^{5} - 20 q^{6} - 84 q^{7} + 16 q^{8} - 80 q^{9} - 40 q^{10} - 4 q^{11} - 36 q^{12} - 32 q^{13} + 8 q^{14} - 96 q^{15} - 56 q^{16} - 72 q^{17} - 52 q^{18} - 116 q^{19} + 40 q^{20} - 20 q^{21} - 132 q^{22} + 32 q^{23} - 4 q^{24} - 156 q^{25} + 88 q^{26} + 32 q^{27} + 116 q^{28} - 16 q^{29} + 112 q^{30} + 48 q^{31} + 192 q^{32} + 248 q^{34} + 132 q^{35} + 124 q^{36} + 48 q^{37} + 304 q^{38} + 152 q^{39} + 376 q^{40} + 112 q^{41} + 8 q^{42} - 8 q^{43} + 232 q^{44} + 136 q^{45} + 72 q^{46} + 168 q^{47} + 40 q^{48} - 32 q^{49} + 104 q^{50} + 186 q^{51} - 8 q^{52} + 64 q^{53} - 36 q^{54} + 108 q^{55} - 104 q^{56} + 38 q^{57} - 184 q^{58} + 160 q^{59} - 132 q^{60} - 8 q^{61} - 232 q^{62} + 118 q^{63} - 384 q^{64} + 80 q^{65} - 114 q^{66} + 8 q^{67} - 120 q^{68} + 64 q^{69} - 328 q^{70} + 208 q^{71} - 248 q^{72} - 80 q^{73} - 136 q^{74} + 150 q^{75} - 472 q^{76} + 24 q^{77} - 552 q^{78} + 296 q^{79} - 440 q^{80} - 120 q^{81} - 600 q^{82} + 288 q^{83} - 390 q^{84} + 80 q^{85} - 352 q^{86} - 12 q^{87} - 676 q^{88} - 32 q^{89} - 312 q^{90} - 72 q^{91} - 344 q^{92} - 104 q^{93} - 584 q^{94} + 48 q^{95} - 480 q^{96} + 28 q^{97} - 348 q^{98} - 240 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1848))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1848.2.a \(\chi_{1848}(1, \cdot)\) 1848.2.a.a 1 1
1848.2.a.b 1
1848.2.a.c 1
1848.2.a.d 1
1848.2.a.e 1
1848.2.a.f 1
1848.2.a.g 1
1848.2.a.h 1
1848.2.a.i 1
1848.2.a.j 1
1848.2.a.k 1
1848.2.a.l 1
1848.2.a.m 2
1848.2.a.n 2
1848.2.a.o 2
1848.2.a.p 2
1848.2.a.q 2
1848.2.a.r 2
1848.2.a.s 2
1848.2.a.t 3
1848.2.a.u 3
1848.2.d \(\chi_{1848}(727, \cdot)\) None 0 1
1848.2.e \(\chi_{1848}(923, \cdot)\) n/a 376 1
1848.2.f \(\chi_{1848}(1121, \cdot)\) 1848.2.f.a 36 1
1848.2.f.b 36
1848.2.g \(\chi_{1848}(925, \cdot)\) n/a 120 1
1848.2.j \(\chi_{1848}(43, \cdot)\) n/a 144 1
1848.2.k \(\chi_{1848}(1079, \cdot)\) None 0 1
1848.2.p \(\chi_{1848}(1805, \cdot)\) n/a 320 1
1848.2.q \(\chi_{1848}(769, \cdot)\) 1848.2.q.a 24 1
1848.2.q.b 24
1848.2.t \(\chi_{1848}(967, \cdot)\) None 0 1
1848.2.u \(\chi_{1848}(155, \cdot)\) n/a 240 1
1848.2.v \(\chi_{1848}(881, \cdot)\) 1848.2.v.a 8 1
1848.2.v.b 8
1848.2.v.c 16
1848.2.v.d 16
1848.2.v.e 32
1848.2.w \(\chi_{1848}(1693, \cdot)\) n/a 192 1
1848.2.z \(\chi_{1848}(1651, \cdot)\) n/a 160 1
1848.2.ba \(\chi_{1848}(1847, \cdot)\) None 0 1
1848.2.bf \(\chi_{1848}(197, \cdot)\) n/a 288 1
1848.2.bg \(\chi_{1848}(529, \cdot)\) 1848.2.bg.a 2 2
1848.2.bg.b 2
1848.2.bg.c 4
1848.2.bg.d 6
1848.2.bg.e 6
1848.2.bg.f 8
1848.2.bg.g 8
1848.2.bg.h 10
1848.2.bg.i 10
1848.2.bg.j 12
1848.2.bg.k 12
1848.2.bh \(\chi_{1848}(169, \cdot)\) n/a 144 4
1848.2.bk \(\chi_{1848}(901, \cdot)\) n/a 384 2
1848.2.bl \(\chi_{1848}(89, \cdot)\) n/a 160 2
1848.2.bm \(\chi_{1848}(683, \cdot)\) n/a 640 2
1848.2.bn \(\chi_{1848}(1495, \cdot)\) None 0 2
1848.2.bq \(\chi_{1848}(725, \cdot)\) n/a 752 2
1848.2.bv \(\chi_{1848}(1055, \cdot)\) None 0 2
1848.2.bw \(\chi_{1848}(859, \cdot)\) n/a 320 2
1848.2.bz \(\chi_{1848}(1453, \cdot)\) n/a 320 2
1848.2.ca \(\chi_{1848}(65, \cdot)\) n/a 192 2
1848.2.cb \(\chi_{1848}(131, \cdot)\) n/a 752 2
1848.2.cc \(\chi_{1848}(199, \cdot)\) None 0 2
1848.2.cf \(\chi_{1848}(241, \cdot)\) 1848.2.cf.a 48 2
1848.2.cf.b 48
1848.2.cg \(\chi_{1848}(1013, \cdot)\) n/a 640 2
1848.2.cl \(\chi_{1848}(23, \cdot)\) None 0 2
1848.2.cm \(\chi_{1848}(571, \cdot)\) n/a 384 2
1848.2.cn \(\chi_{1848}(29, \cdot)\) n/a 1152 4
1848.2.cs \(\chi_{1848}(643, \cdot)\) n/a 768 4
1848.2.ct \(\chi_{1848}(167, \cdot)\) None 0 4
1848.2.cw \(\chi_{1848}(377, \cdot)\) n/a 384 4
1848.2.cx \(\chi_{1848}(13, \cdot)\) n/a 768 4
1848.2.cy \(\chi_{1848}(127, \cdot)\) None 0 4
1848.2.cz \(\chi_{1848}(323, \cdot)\) n/a 1152 4
1848.2.dc \(\chi_{1848}(125, \cdot)\) n/a 1504 4
1848.2.dd \(\chi_{1848}(601, \cdot)\) n/a 192 4
1848.2.di \(\chi_{1848}(211, \cdot)\) n/a 576 4
1848.2.dj \(\chi_{1848}(71, \cdot)\) None 0 4
1848.2.dm \(\chi_{1848}(281, \cdot)\) n/a 288 4
1848.2.dn \(\chi_{1848}(421, \cdot)\) n/a 576 4
1848.2.do \(\chi_{1848}(223, \cdot)\) None 0 4
1848.2.dp \(\chi_{1848}(83, \cdot)\) n/a 1504 4
1848.2.ds \(\chi_{1848}(25, \cdot)\) n/a 384 8
1848.2.dt \(\chi_{1848}(191, \cdot)\) None 0 8
1848.2.du \(\chi_{1848}(403, \cdot)\) n/a 1536 8
1848.2.dz \(\chi_{1848}(73, \cdot)\) n/a 384 8
1848.2.ea \(\chi_{1848}(5, \cdot)\) n/a 3008 8
1848.2.ed \(\chi_{1848}(227, \cdot)\) n/a 3008 8
1848.2.ee \(\chi_{1848}(31, \cdot)\) None 0 8
1848.2.ef \(\chi_{1848}(37, \cdot)\) n/a 1536 8
1848.2.eg \(\chi_{1848}(233, \cdot)\) n/a 768 8
1848.2.ej \(\chi_{1848}(215, \cdot)\) None 0 8
1848.2.ek \(\chi_{1848}(115, \cdot)\) n/a 1536 8
1848.2.ep \(\chi_{1848}(149, \cdot)\) n/a 3008 8
1848.2.es \(\chi_{1848}(179, \cdot)\) n/a 3008 8
1848.2.et \(\chi_{1848}(79, \cdot)\) None 0 8
1848.2.eu \(\chi_{1848}(61, \cdot)\) n/a 1536 8
1848.2.ev \(\chi_{1848}(185, \cdot)\) n/a 768 8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1848))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1848)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(616))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(924))\)\(^{\oplus 2}\)