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Properties

Label 1248.2
Level 1248
Weight 2
Dimension 17708
Nonzero newspaces 40
Sturm bound 172032
Trace bound 28

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Defining parameters

Level: \( N \) = \( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(172032\)
Trace bound: \(28\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1248))\).

Total New Old
Modular forms 44544 18148 26396
Cusp forms 41473 17708 23765
Eisenstein series 3071 440 2631

Trace form

\( 17708 q - 32 q^{3} - 80 q^{4} - 8 q^{5} - 40 q^{6} - 64 q^{7} - 68 q^{9} + O(q^{10}) \) \( 17708 q - 32 q^{3} - 80 q^{4} - 8 q^{5} - 40 q^{6} - 64 q^{7} - 68 q^{9} - 48 q^{10} - 8 q^{12} - 76 q^{13} + 64 q^{14} - 12 q^{15} + 32 q^{17} - 24 q^{18} - 48 q^{19} + 64 q^{20} - 8 q^{21} - 32 q^{22} + 48 q^{23} - 64 q^{24} - 84 q^{25} - 40 q^{26} + 4 q^{27} - 160 q^{28} - 8 q^{29} - 136 q^{30} + 32 q^{31} - 80 q^{32} - 104 q^{33} - 128 q^{34} + 96 q^{35} - 144 q^{36} - 120 q^{37} - 80 q^{38} - 16 q^{39} - 256 q^{40} - 16 q^{41} - 160 q^{42} - 64 q^{43} - 16 q^{44} - 112 q^{45} - 80 q^{46} - 48 q^{47} - 144 q^{48} - 124 q^{49} - 48 q^{50} - 56 q^{51} - 136 q^{52} + 24 q^{53} - 144 q^{54} - 184 q^{55} - 112 q^{56} - 104 q^{57} - 224 q^{58} - 128 q^{59} - 160 q^{60} + 40 q^{61} - 96 q^{62} - 60 q^{63} - 224 q^{64} - 8 q^{65} - 136 q^{66} - 160 q^{67} + 16 q^{68} + 88 q^{69} - 128 q^{70} - 80 q^{71} + 80 q^{72} - 40 q^{73} + 64 q^{74} - 76 q^{75} - 80 q^{76} + 128 q^{77} + 20 q^{78} - 136 q^{79} + 112 q^{80} + 52 q^{81} + 80 q^{82} + 224 q^{84} + 96 q^{85} + 128 q^{86} - 92 q^{87} + 96 q^{88} + 192 q^{89} + 224 q^{90} + 128 q^{91} + 160 q^{92} + 128 q^{93} + 96 q^{94} + 208 q^{95} + 240 q^{96} + 8 q^{97} + 160 q^{98} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1248))\)

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
1248.2.a \(\chi_{1248}(1, \cdot)\) 1248.2.a.a 1 1
1248.2.a.b 1
1248.2.a.c 1
1248.2.a.d 1
1248.2.a.e 1
1248.2.a.f 1
1248.2.a.g 1
1248.2.a.h 1
1248.2.a.i 1
1248.2.a.j 1
1248.2.a.k 2
1248.2.a.l 2
1248.2.a.m 2
1248.2.a.n 2
1248.2.a.o 3
1248.2.a.p 3
1248.2.c \(\chi_{1248}(961, \cdot)\) 1248.2.c.a 6 1
1248.2.c.b 6
1248.2.c.c 8
1248.2.c.d 8
1248.2.d \(\chi_{1248}(287, \cdot)\) 1248.2.d.a 4 1
1248.2.d.b 8
1248.2.d.c 16
1248.2.d.d 20
1248.2.g \(\chi_{1248}(625, \cdot)\) 1248.2.g.a 8 1
1248.2.g.b 16
1248.2.h \(\chi_{1248}(623, \cdot)\) 1248.2.h.a 8 1
1248.2.h.b 12
1248.2.h.c 32
1248.2.j \(\chi_{1248}(911, \cdot)\) 1248.2.j.a 48 1
1248.2.m \(\chi_{1248}(337, \cdot)\) 1248.2.m.a 2 1
1248.2.m.b 2
1248.2.m.c 24
1248.2.n \(\chi_{1248}(1247, \cdot)\) 1248.2.n.a 4 1
1248.2.n.b 4
1248.2.n.c 4
1248.2.n.d 4
1248.2.n.e 40
1248.2.q \(\chi_{1248}(289, \cdot)\) 1248.2.q.a 2 2
1248.2.q.b 2
1248.2.q.c 2
1248.2.q.d 2
1248.2.q.e 2
1248.2.q.f 2
1248.2.q.g 4
1248.2.q.h 4
1248.2.q.i 4
1248.2.q.j 4
1248.2.q.k 6
1248.2.q.l 6
1248.2.q.m 8
1248.2.q.n 8
1248.2.r \(\chi_{1248}(343, \cdot)\) None 0 2
1248.2.u \(\chi_{1248}(473, \cdot)\) None 0 2
1248.2.v \(\chi_{1248}(311, \cdot)\) None 0 2
1248.2.x \(\chi_{1248}(313, \cdot)\) None 0 2
1248.2.bb \(\chi_{1248}(463, \cdot)\) 1248.2.bb.a 2 2
1248.2.bb.b 2
1248.2.bb.c 2
1248.2.bb.d 2
1248.2.bb.e 24
1248.2.bb.f 24
1248.2.bc \(\chi_{1248}(31, \cdot)\) 1248.2.bc.a 2 2
1248.2.bc.b 2
1248.2.bc.c 2
1248.2.bc.d 2
1248.2.bc.e 2
1248.2.bc.f 2
1248.2.bc.g 2
1248.2.bc.h 2
1248.2.bc.i 2
1248.2.bc.j 2
1248.2.bc.k 2
1248.2.bc.l 2
1248.2.bc.m 2
1248.2.bc.n 2
1248.2.bc.o 4
1248.2.bc.p 4
1248.2.bc.q 4
1248.2.bc.r 4
1248.2.bc.s 6
1248.2.bc.t 6
1248.2.bf \(\chi_{1248}(161, \cdot)\) n/a 112 2
1248.2.bg \(\chi_{1248}(593, \cdot)\) n/a 104 2
1248.2.bh \(\chi_{1248}(599, \cdot)\) None 0 2
1248.2.bj \(\chi_{1248}(25, \cdot)\) None 0 2
1248.2.bm \(\chi_{1248}(281, \cdot)\) None 0 2
1248.2.bn \(\chi_{1248}(151, \cdot)\) None 0 2
1248.2.bq \(\chi_{1248}(335, \cdot)\) n/a 104 2
1248.2.br \(\chi_{1248}(529, \cdot)\) 1248.2.br.a 56 2
1248.2.bu \(\chi_{1248}(191, \cdot)\) n/a 112 2
1248.2.bv \(\chi_{1248}(673, \cdot)\) 1248.2.bv.a 12 2
1248.2.bv.b 12
1248.2.bv.c 16
1248.2.bv.d 16
1248.2.bz \(\chi_{1248}(95, \cdot)\) n/a 112 2
1248.2.ca \(\chi_{1248}(49, \cdot)\) 1248.2.ca.a 8 2
1248.2.ca.b 48
1248.2.cd \(\chi_{1248}(815, \cdot)\) n/a 104 2
1248.2.cf \(\chi_{1248}(5, \cdot)\) n/a 880 4
1248.2.ch \(\chi_{1248}(499, \cdot)\) n/a 448 4
1248.2.ci \(\chi_{1248}(181, \cdot)\) n/a 448 4
1248.2.ck \(\chi_{1248}(157, \cdot)\) n/a 384 4
1248.2.cn \(\chi_{1248}(131, \cdot)\) n/a 768 4
1248.2.cp \(\chi_{1248}(155, \cdot)\) n/a 880 4
1248.2.cq \(\chi_{1248}(317, \cdot)\) n/a 880 4
1248.2.cs \(\chi_{1248}(187, \cdot)\) n/a 448 4
1248.2.cu \(\chi_{1248}(137, \cdot)\) None 0 4
1248.2.cx \(\chi_{1248}(7, \cdot)\) None 0 4
1248.2.cz \(\chi_{1248}(121, \cdot)\) None 0 4
1248.2.db \(\chi_{1248}(263, \cdot)\) None 0 4
1248.2.dc \(\chi_{1248}(305, \cdot)\) n/a 208 4
1248.2.dd \(\chi_{1248}(353, \cdot)\) n/a 224 4
1248.2.dg \(\chi_{1248}(223, \cdot)\) n/a 112 4
1248.2.dh \(\chi_{1248}(175, \cdot)\) n/a 112 4
1248.2.dl \(\chi_{1248}(217, \cdot)\) None 0 4
1248.2.dn \(\chi_{1248}(23, \cdot)\) None 0 4
1248.2.dp \(\chi_{1248}(487, \cdot)\) None 0 4
1248.2.dq \(\chi_{1248}(41, \cdot)\) None 0 4
1248.2.dt \(\chi_{1248}(115, \cdot)\) n/a 896 8
1248.2.dv \(\chi_{1248}(245, \cdot)\) n/a 1760 8
1248.2.dx \(\chi_{1248}(35, \cdot)\) n/a 1760 8
1248.2.dz \(\chi_{1248}(179, \cdot)\) n/a 1760 8
1248.2.ea \(\chi_{1248}(205, \cdot)\) n/a 896 8
1248.2.ec \(\chi_{1248}(61, \cdot)\) n/a 896 8
1248.2.ee \(\chi_{1248}(19, \cdot)\) n/a 896 8
1248.2.eg \(\chi_{1248}(149, \cdot)\) n/a 1760 8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1248))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1248)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(624))\)\(^{\oplus 2}\)