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Properties

Label 1216.3
Level 1216
Weight 3
Dimension 51178
Nonzero newspaces 24
Sturm bound 276480
Trace bound 49

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Defining parameters

Level: \( N \) = \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(276480\)
Trace bound: \(49\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1216))\).

Total New Old
Modular forms 93456 51926 41530
Cusp forms 90864 51178 39686
Eisenstein series 2592 748 1844

Trace form

\( 51178 q - 128 q^{2} - 96 q^{3} - 128 q^{4} - 128 q^{5} - 128 q^{6} - 100 q^{7} - 128 q^{8} - 178 q^{9} + O(q^{10}) \) \( 51178 q - 128 q^{2} - 96 q^{3} - 128 q^{4} - 128 q^{5} - 128 q^{6} - 100 q^{7} - 128 q^{8} - 178 q^{9} - 128 q^{10} - 128 q^{11} - 128 q^{12} - 160 q^{13} - 128 q^{14} - 92 q^{15} - 128 q^{16} - 192 q^{17} - 128 q^{18} - 70 q^{19} - 272 q^{20} + 40 q^{21} + 16 q^{22} + 28 q^{23} + 432 q^{24} + 82 q^{25} + 272 q^{26} + 36 q^{27} + 112 q^{28} - 64 q^{29} + 32 q^{30} - 76 q^{31} - 208 q^{32} - 260 q^{33} - 368 q^{34} - 292 q^{35} - 928 q^{36} - 480 q^{37} - 416 q^{38} - 592 q^{39} - 848 q^{40} - 672 q^{41} - 1008 q^{42} - 320 q^{43} - 336 q^{44} - 424 q^{45} - 128 q^{46} - 92 q^{47} - 128 q^{48} - 62 q^{49} - 752 q^{50} + 988 q^{51} - 1184 q^{52} + 160 q^{53} - 1280 q^{54} + 1436 q^{55} - 912 q^{56} + 68 q^{57} - 992 q^{58} + 832 q^{59} - 704 q^{60} + 96 q^{61} - 160 q^{62} - 108 q^{63} + 64 q^{64} - 540 q^{65} + 384 q^{66} - 1184 q^{67} + 352 q^{68} - 536 q^{69} + 1216 q^{70} - 1636 q^{71} + 1168 q^{72} - 672 q^{73} + 1104 q^{74} - 2104 q^{75} + 696 q^{76} + 24 q^{77} + 2128 q^{78} - 1116 q^{79} + 2608 q^{80} + 602 q^{81} + 1952 q^{82} + 544 q^{83} + 2336 q^{84} + 800 q^{85} + 1744 q^{86} + 796 q^{87} + 992 q^{88} + 928 q^{89} + 1312 q^{90} + 284 q^{91} + 784 q^{92} + 592 q^{93} + 64 q^{94} - 92 q^{95} - 544 q^{96} - 512 q^{97} - 944 q^{98} - 688 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1216))\)

We only show spaces with odd 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
1216.3.d \(\chi_{1216}(191, \cdot)\) 1216.3.d.a 4 1
1216.3.d.b 6
1216.3.d.c 12
1216.3.d.d 14
1216.3.d.e 16
1216.3.d.f 20
1216.3.e \(\chi_{1216}(1025, \cdot)\) 1216.3.e.a 1 1
1216.3.e.b 1
1216.3.e.c 2
1216.3.e.d 2
1216.3.e.e 2
1216.3.e.f 2
1216.3.e.g 2
1216.3.e.h 2
1216.3.e.i 2
1216.3.e.j 2
1216.3.e.k 2
1216.3.e.l 2
1216.3.e.m 8
1216.3.e.n 8
1216.3.e.o 20
1216.3.e.p 20
1216.3.f \(\chi_{1216}(799, \cdot)\) 1216.3.f.a 24 1
1216.3.f.b 48
1216.3.g \(\chi_{1216}(417, \cdot)\) 1216.3.g.a 4 1
1216.3.g.b 4
1216.3.g.c 8
1216.3.g.d 16
1216.3.g.e 48
1216.3.j \(\chi_{1216}(113, \cdot)\) n/a 156 2
1216.3.l \(\chi_{1216}(495, \cdot)\) n/a 144 2
1216.3.o \(\chi_{1216}(159, \cdot)\) n/a 160 2
1216.3.p \(\chi_{1216}(673, \cdot)\) n/a 160 2
1216.3.q \(\chi_{1216}(767, \cdot)\) n/a 156 2
1216.3.r \(\chi_{1216}(65, \cdot)\) n/a 156 2
1216.3.w \(\chi_{1216}(265, \cdot)\) None 0 4
1216.3.x \(\chi_{1216}(39, \cdot)\) None 0 4
1216.3.ba \(\chi_{1216}(145, \cdot)\) n/a 312 4
1216.3.bc \(\chi_{1216}(239, \cdot)\) n/a 312 4
1216.3.bf \(\chi_{1216}(115, \cdot)\) n/a 2304 8
1216.3.bg \(\chi_{1216}(37, \cdot)\) n/a 2544 8
1216.3.bh \(\chi_{1216}(129, \cdot)\) n/a 468 6
1216.3.bi \(\chi_{1216}(33, \cdot)\) n/a 480 6
1216.3.bk \(\chi_{1216}(351, \cdot)\) n/a 480 6
1216.3.bn \(\chi_{1216}(63, \cdot)\) n/a 468 6
1216.3.bo \(\chi_{1216}(7, \cdot)\) None 0 8
1216.3.bp \(\chi_{1216}(217, \cdot)\) None 0 8
1216.3.bt \(\chi_{1216}(47, \cdot)\) n/a 936 12
1216.3.bv \(\chi_{1216}(241, \cdot)\) n/a 936 12
1216.3.by \(\chi_{1216}(69, \cdot)\) n/a 5088 16
1216.3.bz \(\chi_{1216}(11, \cdot)\) n/a 5088 16
1216.3.cc \(\chi_{1216}(23, \cdot)\) None 0 24
1216.3.cd \(\chi_{1216}(41, \cdot)\) None 0 24
1216.3.ce \(\chi_{1216}(35, \cdot)\) n/a 15264 48
1216.3.cf \(\chi_{1216}(13, \cdot)\) n/a 15264 48

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1216))\) into lower level spaces

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