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Properties

Label 1216.2
Level 1216
Weight 2
Dimension 25402
Nonzero newspaces 24
Sturm bound 184320
Trace bound 49

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Defining parameters

Level: \( N \) = \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(184320\)
Trace bound: \(49\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1216))\).

Total New Old
Modular forms 47376 26150 21226
Cusp forms 44785 25402 19383
Eisenstein series 2591 748 1843

Trace form

\( 25402 q - 128 q^{2} - 96 q^{3} - 128 q^{4} - 128 q^{5} - 128 q^{6} - 92 q^{7} - 128 q^{8} - 154 q^{9} + O(q^{10}) \) \( 25402 q - 128 q^{2} - 96 q^{3} - 128 q^{4} - 128 q^{5} - 128 q^{6} - 92 q^{7} - 128 q^{8} - 154 q^{9} - 128 q^{10} - 88 q^{11} - 128 q^{12} - 112 q^{13} - 128 q^{14} - 84 q^{15} - 128 q^{16} - 208 q^{17} - 128 q^{18} - 94 q^{19} - 272 q^{20} - 136 q^{21} - 144 q^{22} - 92 q^{23} - 208 q^{24} - 182 q^{25} - 208 q^{26} - 108 q^{27} - 208 q^{28} - 160 q^{29} - 288 q^{30} - 140 q^{31} - 208 q^{32} - 148 q^{33} - 208 q^{34} - 100 q^{35} - 288 q^{36} - 144 q^{37} - 176 q^{38} - 200 q^{39} - 208 q^{40} - 160 q^{41} - 208 q^{42} - 72 q^{43} - 144 q^{44} - 120 q^{45} - 128 q^{46} - 60 q^{47} - 128 q^{48} - 206 q^{49} - 80 q^{50} - 148 q^{51} - 32 q^{52} - 80 q^{53} - 220 q^{55} - 16 q^{56} - 164 q^{57} - 128 q^{58} - 232 q^{59} + 64 q^{60} - 112 q^{61} - 64 q^{62} - 228 q^{63} + 64 q^{64} - 348 q^{65} + 32 q^{66} - 272 q^{67} - 32 q^{68} - 104 q^{69} + 64 q^{70} - 220 q^{71} + 16 q^{72} - 160 q^{73} - 16 q^{74} - 208 q^{75} - 72 q^{76} - 280 q^{77} - 80 q^{78} - 156 q^{79} - 208 q^{80} - 230 q^{81} - 288 q^{82} - 96 q^{83} - 352 q^{84} - 144 q^{85} - 336 q^{86} - 92 q^{87} - 288 q^{88} - 256 q^{89} - 416 q^{90} - 84 q^{91} - 432 q^{92} - 208 q^{93} - 320 q^{94} - 120 q^{95} - 544 q^{96} - 176 q^{97} - 400 q^{98} - 144 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1216))\)

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
1216.2.a \(\chi_{1216}(1, \cdot)\) 1216.2.a.a 1 1
1216.2.a.b 1
1216.2.a.c 1
1216.2.a.d 1
1216.2.a.e 1
1216.2.a.f 1
1216.2.a.g 1
1216.2.a.h 1
1216.2.a.i 1
1216.2.a.j 1
1216.2.a.k 1
1216.2.a.l 1
1216.2.a.m 1
1216.2.a.n 1
1216.2.a.o 1
1216.2.a.p 1
1216.2.a.q 1
1216.2.a.r 1
1216.2.a.s 2
1216.2.a.t 2
1216.2.a.u 3
1216.2.a.v 3
1216.2.a.w 4
1216.2.a.x 4
1216.2.b \(\chi_{1216}(607, \cdot)\) 1216.2.b.a 4 1
1216.2.b.b 4
1216.2.b.c 4
1216.2.b.d 8
1216.2.b.e 8
1216.2.b.f 12
1216.2.c \(\chi_{1216}(609, \cdot)\) 1216.2.c.a 2 1
1216.2.c.b 2
1216.2.c.c 2
1216.2.c.d 2
1216.2.c.e 4
1216.2.c.f 4
1216.2.c.g 4
1216.2.c.h 8
1216.2.c.i 8
1216.2.h \(\chi_{1216}(1215, \cdot)\) 1216.2.h.a 2 1
1216.2.h.b 4
1216.2.h.c 4
1216.2.h.d 8
1216.2.h.e 20
1216.2.i \(\chi_{1216}(577, \cdot)\) 1216.2.i.a 2 2
1216.2.i.b 2
1216.2.i.c 2
1216.2.i.d 2
1216.2.i.e 2
1216.2.i.f 2
1216.2.i.g 2
1216.2.i.h 2
1216.2.i.i 2
1216.2.i.j 2
1216.2.i.k 4
1216.2.i.l 4
1216.2.i.m 6
1216.2.i.n 6
1216.2.i.o 8
1216.2.i.p 8
1216.2.i.q 8
1216.2.i.r 12
1216.2.k \(\chi_{1216}(305, \cdot)\) 1216.2.k.a 4 2
1216.2.k.b 68
1216.2.m \(\chi_{1216}(303, \cdot)\) 1216.2.m.a 76 2
1216.2.n \(\chi_{1216}(255, \cdot)\) 1216.2.n.a 2 2
1216.2.n.b 2
1216.2.n.c 4
1216.2.n.d 6
1216.2.n.e 6
1216.2.n.f 16
1216.2.n.g 40
1216.2.s \(\chi_{1216}(31, \cdot)\) 1216.2.s.a 4 2
1216.2.s.b 4
1216.2.s.c 4
1216.2.s.d 4
1216.2.s.e 4
1216.2.s.f 4
1216.2.s.g 12
1216.2.s.h 12
1216.2.s.i 32
1216.2.t \(\chi_{1216}(353, \cdot)\) 1216.2.t.a 8 2
1216.2.t.b 8
1216.2.t.c 16
1216.2.t.d 24
1216.2.t.e 24
1216.2.u \(\chi_{1216}(151, \cdot)\) None 0 4
1216.2.v \(\chi_{1216}(153, \cdot)\) None 0 4
1216.2.y \(\chi_{1216}(321, \cdot)\) n/a 228 6
1216.2.z \(\chi_{1216}(49, \cdot)\) n/a 152 4
1216.2.bb \(\chi_{1216}(335, \cdot)\) n/a 152 4
1216.2.bd \(\chi_{1216}(77, \cdot)\) n/a 1152 8
1216.2.be \(\chi_{1216}(75, \cdot)\) n/a 1264 8
1216.2.bj \(\chi_{1216}(161, \cdot)\) n/a 240 6
1216.2.bl \(\chi_{1216}(223, \cdot)\) n/a 240 6
1216.2.bm \(\chi_{1216}(127, \cdot)\) n/a 228 6
1216.2.bq \(\chi_{1216}(121, \cdot)\) None 0 8
1216.2.br \(\chi_{1216}(103, \cdot)\) None 0 8
1216.2.bs \(\chi_{1216}(15, \cdot)\) n/a 456 12
1216.2.bu \(\chi_{1216}(17, \cdot)\) n/a 456 12
1216.2.bw \(\chi_{1216}(27, \cdot)\) n/a 2528 16
1216.2.bx \(\chi_{1216}(45, \cdot)\) n/a 2528 16
1216.2.ca \(\chi_{1216}(9, \cdot)\) None 0 24
1216.2.cb \(\chi_{1216}(71, \cdot)\) None 0 24
1216.2.cg \(\chi_{1216}(5, \cdot)\) n/a 7584 48
1216.2.ch \(\chi_{1216}(3, \cdot)\) n/a 7584 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1216))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1216)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(608))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1216))\)\(^{\oplus 1}\)