Properties

Label 2464.2
Level 2464
Weight 2
Dimension 96804
Nonzero newspaces 48
Sturm bound 737280
Trace bound 25

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Defining parameters

Level: \( N \) = \( 2464 = 2^{5} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(737280\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2464))\).

Total New Old
Modular forms 188160 98604 89556
Cusp forms 180481 96804 83677
Eisenstein series 7679 1800 5879

Trace form

\( 96804 q - 128 q^{2} - 100 q^{3} - 128 q^{4} - 136 q^{5} - 128 q^{6} - 122 q^{7} - 320 q^{8} - 196 q^{9} + O(q^{10}) \) \( 96804 q - 128 q^{2} - 100 q^{3} - 128 q^{4} - 136 q^{5} - 128 q^{6} - 122 q^{7} - 320 q^{8} - 196 q^{9} - 96 q^{10} - 110 q^{11} - 224 q^{12} - 104 q^{13} - 128 q^{14} - 228 q^{15} - 48 q^{16} - 48 q^{17} - 48 q^{18} - 100 q^{19} - 64 q^{20} - 160 q^{21} - 336 q^{22} - 188 q^{23} - 176 q^{24} - 188 q^{25} - 208 q^{26} + 8 q^{27} - 200 q^{28} - 360 q^{29} - 256 q^{30} - 20 q^{31} - 208 q^{32} - 356 q^{33} - 336 q^{34} - 74 q^{35} - 432 q^{36} - 136 q^{37} - 96 q^{38} + 32 q^{39} - 80 q^{40} - 144 q^{41} - 120 q^{42} - 168 q^{43} - 64 q^{44} - 120 q^{45} - 12 q^{47} + 80 q^{48} - 8 q^{49} - 160 q^{50} + 4 q^{51} - 96 q^{52} + 88 q^{53} - 80 q^{54} - 132 q^{55} - 336 q^{56} - 280 q^{57} - 144 q^{58} - 132 q^{59} - 144 q^{60} + 56 q^{61} - 208 q^{62} - 60 q^{63} - 464 q^{64} - 264 q^{65} - 192 q^{66} - 308 q^{67} - 48 q^{68} + 96 q^{69} - 184 q^{70} - 308 q^{71} - 32 q^{72} - 48 q^{73} - 64 q^{74} + 72 q^{75} - 128 q^{76} - 84 q^{77} - 560 q^{78} + 116 q^{79} - 144 q^{80} + 148 q^{81} - 128 q^{82} + 272 q^{83} - 120 q^{84} + 64 q^{85} - 208 q^{86} + 380 q^{87} - 136 q^{88} - 224 q^{89} - 368 q^{90} + 10 q^{91} - 512 q^{92} + 48 q^{93} - 368 q^{94} + 268 q^{95} - 592 q^{96} - 192 q^{97} - 536 q^{98} - 28 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2464))\)

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
2464.2.a \(\chi_{2464}(1, \cdot)\) 2464.2.a.a 1 1
2464.2.a.b 1
2464.2.a.c 1
2464.2.a.d 1
2464.2.a.e 1
2464.2.a.f 1
2464.2.a.g 1
2464.2.a.h 1
2464.2.a.i 1
2464.2.a.j 1
2464.2.a.k 1
2464.2.a.l 1
2464.2.a.m 2
2464.2.a.n 2
2464.2.a.o 2
2464.2.a.p 2
2464.2.a.q 3
2464.2.a.r 3
2464.2.a.s 4
2464.2.a.t 4
2464.2.a.u 4
2464.2.a.v 4
2464.2.a.w 4
2464.2.a.x 4
2464.2.a.y 5
2464.2.a.z 5
2464.2.c \(\chi_{2464}(1233, \cdot)\) 2464.2.c.a 2 1
2464.2.c.b 4
2464.2.c.c 24
2464.2.c.d 30
2464.2.e \(\chi_{2464}(769, \cdot)\) 2464.2.e.a 8 1
2464.2.e.b 8
2464.2.e.c 16
2464.2.e.d 16
2464.2.e.e 48
2464.2.f \(\chi_{2464}(351, \cdot)\) 2464.2.f.a 36 1
2464.2.f.b 36
2464.2.h \(\chi_{2464}(111, \cdot)\) 2464.2.h.a 40 1
2464.2.h.b 40
2464.2.j \(\chi_{2464}(1343, \cdot)\) 2464.2.j.a 8 1
2464.2.j.b 32
2464.2.j.c 40
2464.2.l \(\chi_{2464}(1583, \cdot)\) 2464.2.l.a 2 1
2464.2.l.b 2
2464.2.l.c 34
2464.2.l.d 34
2464.2.o \(\chi_{2464}(2001, \cdot)\) 2464.2.o.a 2 1
2464.2.o.b 2
2464.2.o.c 88
2464.2.q \(\chi_{2464}(1409, \cdot)\) n/a 160 2
2464.2.r \(\chi_{2464}(967, \cdot)\) None 0 2
2464.2.s \(\chi_{2464}(727, \cdot)\) None 0 2
2464.2.x \(\chi_{2464}(153, \cdot)\) None 0 2
2464.2.y \(\chi_{2464}(617, \cdot)\) None 0 2
2464.2.z \(\chi_{2464}(225, \cdot)\) n/a 288 4
2464.2.ba \(\chi_{2464}(241, \cdot)\) n/a 184 2
2464.2.be \(\chi_{2464}(2047, \cdot)\) n/a 160 2
2464.2.bg \(\chi_{2464}(527, \cdot)\) n/a 184 2
2464.2.bi \(\chi_{2464}(1759, \cdot)\) n/a 192 2
2464.2.bk \(\chi_{2464}(815, \cdot)\) n/a 160 2
2464.2.bl \(\chi_{2464}(177, \cdot)\) n/a 160 2
2464.2.bn \(\chi_{2464}(1473, \cdot)\) n/a 192 2
2464.2.bp \(\chi_{2464}(461, \cdot)\) n/a 1520 4
2464.2.bq \(\chi_{2464}(309, \cdot)\) n/a 960 4
2464.2.bv \(\chi_{2464}(43, \cdot)\) n/a 1152 4
2464.2.bw \(\chi_{2464}(419, \cdot)\) n/a 1280 4
2464.2.by \(\chi_{2464}(657, \cdot)\) n/a 368 4
2464.2.cb \(\chi_{2464}(239, \cdot)\) n/a 288 4
2464.2.cd \(\chi_{2464}(223, \cdot)\) n/a 384 4
2464.2.cf \(\chi_{2464}(335, \cdot)\) n/a 368 4
2464.2.ch \(\chi_{2464}(127, \cdot)\) n/a 288 4
2464.2.ci \(\chi_{2464}(321, \cdot)\) n/a 384 4
2464.2.ck \(\chi_{2464}(113, \cdot)\) n/a 288 4
2464.2.co \(\chi_{2464}(199, \cdot)\) None 0 4
2464.2.cp \(\chi_{2464}(263, \cdot)\) None 0 4
2464.2.cq \(\chi_{2464}(793, \cdot)\) None 0 4
2464.2.cr \(\chi_{2464}(857, \cdot)\) None 0 4
2464.2.cu \(\chi_{2464}(289, \cdot)\) n/a 768 8
2464.2.cv \(\chi_{2464}(169, \cdot)\) None 0 8
2464.2.cw \(\chi_{2464}(41, \cdot)\) None 0 8
2464.2.db \(\chi_{2464}(279, \cdot)\) None 0 8
2464.2.dc \(\chi_{2464}(183, \cdot)\) None 0 8
2464.2.df \(\chi_{2464}(221, \cdot)\) n/a 2560 8
2464.2.dg \(\chi_{2464}(285, \cdot)\) n/a 3040 8
2464.2.dh \(\chi_{2464}(243, \cdot)\) n/a 2560 8
2464.2.di \(\chi_{2464}(219, \cdot)\) n/a 3040 8
2464.2.dm \(\chi_{2464}(129, \cdot)\) n/a 768 8
2464.2.do \(\chi_{2464}(81, \cdot)\) n/a 736 8
2464.2.dp \(\chi_{2464}(47, \cdot)\) n/a 736 8
2464.2.dr \(\chi_{2464}(95, \cdot)\) n/a 768 8
2464.2.dt \(\chi_{2464}(79, \cdot)\) n/a 736 8
2464.2.dv \(\chi_{2464}(31, \cdot)\) n/a 768 8
2464.2.dz \(\chi_{2464}(17, \cdot)\) n/a 736 8
2464.2.ea \(\chi_{2464}(27, \cdot)\) n/a 6080 16
2464.2.eb \(\chi_{2464}(211, \cdot)\) n/a 4608 16
2464.2.eg \(\chi_{2464}(141, \cdot)\) n/a 4608 16
2464.2.eh \(\chi_{2464}(13, \cdot)\) n/a 6080 16
2464.2.ek \(\chi_{2464}(73, \cdot)\) None 0 16
2464.2.el \(\chi_{2464}(9, \cdot)\) None 0 16
2464.2.em \(\chi_{2464}(39, \cdot)\) None 0 16
2464.2.en \(\chi_{2464}(103, \cdot)\) None 0 16
2464.2.es \(\chi_{2464}(51, \cdot)\) n/a 12160 32
2464.2.et \(\chi_{2464}(3, \cdot)\) n/a 12160 32
2464.2.eu \(\chi_{2464}(61, \cdot)\) n/a 12160 32
2464.2.ev \(\chi_{2464}(37, \cdot)\) n/a 12160 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2464))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2464)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(616))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1232))\)\(^{\oplus 2}\)