Properties

Label 3456.2
Level 3456
Weight 2
Dimension 146688
Nonzero newspaces 30
Sturm bound 1327104
Trace bound 55

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Defining parameters

Level: \( N \) = \( 3456 = 2^{7} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(1327104\)
Trace bound: \(55\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3456))\).

Total New Old
Modular forms 336576 148224 188352
Cusp forms 326977 146688 180289
Eisenstein series 9599 1536 8063

Trace form

\( 146688 q - 128 q^{2} - 144 q^{3} - 224 q^{4} - 128 q^{5} - 192 q^{6} - 168 q^{7} - 128 q^{8} - 240 q^{9} + O(q^{10}) \) \( 146688 q - 128 q^{2} - 144 q^{3} - 224 q^{4} - 128 q^{5} - 192 q^{6} - 168 q^{7} - 128 q^{8} - 240 q^{9} - 224 q^{10} - 96 q^{11} - 192 q^{12} - 224 q^{13} - 128 q^{14} - 144 q^{15} - 224 q^{16} - 192 q^{17} - 192 q^{18} - 168 q^{19} - 128 q^{20} - 192 q^{21} - 224 q^{22} - 96 q^{23} - 192 q^{24} - 280 q^{25} - 128 q^{26} - 144 q^{27} - 512 q^{28} - 128 q^{29} - 192 q^{30} - 168 q^{31} - 128 q^{32} - 384 q^{33} - 224 q^{34} - 96 q^{35} - 192 q^{36} - 224 q^{37} - 128 q^{38} - 144 q^{39} - 224 q^{40} - 160 q^{41} - 192 q^{42} - 168 q^{43} - 128 q^{44} - 192 q^{45} - 224 q^{46} - 104 q^{47} - 192 q^{48} - 336 q^{49} - 128 q^{50} - 144 q^{51} - 224 q^{52} - 128 q^{53} - 192 q^{54} - 384 q^{55} - 128 q^{56} - 240 q^{57} - 224 q^{58} - 96 q^{59} - 192 q^{60} - 224 q^{61} - 128 q^{62} - 144 q^{63} - 224 q^{64} - 128 q^{65} - 192 q^{66} - 168 q^{67} - 128 q^{68} - 192 q^{69} - 224 q^{70} - 96 q^{71} - 192 q^{72} - 280 q^{73} - 128 q^{74} - 144 q^{75} - 224 q^{76} - 184 q^{77} - 192 q^{78} - 200 q^{79} - 128 q^{80} - 288 q^{81} - 512 q^{82} - 176 q^{83} - 192 q^{84} - 288 q^{85} - 128 q^{86} - 144 q^{87} - 224 q^{88} - 288 q^{89} - 192 q^{90} - 264 q^{91} - 128 q^{92} - 192 q^{93} - 224 q^{94} - 216 q^{95} - 192 q^{96} - 576 q^{97} - 128 q^{98} - 144 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3456))\)

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
3456.2.a \(\chi_{3456}(1, \cdot)\) 3456.2.a.a 1 1
3456.2.a.b 1
3456.2.a.c 1
3456.2.a.d 1
3456.2.a.e 1
3456.2.a.f 1
3456.2.a.g 1
3456.2.a.h 1
3456.2.a.i 1
3456.2.a.j 1
3456.2.a.k 1
3456.2.a.l 1
3456.2.a.m 1
3456.2.a.n 1
3456.2.a.o 1
3456.2.a.p 1
3456.2.a.q 2
3456.2.a.r 2
3456.2.a.s 2
3456.2.a.t 2
3456.2.a.u 2
3456.2.a.v 2
3456.2.a.w 2
3456.2.a.x 2
3456.2.a.y 2
3456.2.a.z 2
3456.2.a.ba 2
3456.2.a.bb 2
3456.2.a.bc 2
3456.2.a.bd 2
3456.2.a.be 2
3456.2.a.bf 2
3456.2.a.bg 2
3456.2.a.bh 2
3456.2.a.bi 2
3456.2.a.bj 2
3456.2.a.bk 2
3456.2.a.bl 2
3456.2.a.bm 2
3456.2.a.bn 2
3456.2.c \(\chi_{3456}(3455, \cdot)\) 3456.2.c.a 8 1
3456.2.c.b 8
3456.2.c.c 8
3456.2.c.d 8
3456.2.c.e 8
3456.2.c.f 8
3456.2.c.g 8
3456.2.c.h 8
3456.2.d \(\chi_{3456}(1729, \cdot)\) 3456.2.d.a 2 1
3456.2.d.b 2
3456.2.d.c 2
3456.2.d.d 2
3456.2.d.e 2
3456.2.d.f 2
3456.2.d.g 2
3456.2.d.h 2
3456.2.d.i 4
3456.2.d.j 4
3456.2.d.k 4
3456.2.d.l 4
3456.2.d.m 8
3456.2.d.n 8
3456.2.d.o 8
3456.2.d.p 8
3456.2.f \(\chi_{3456}(1727, \cdot)\) 3456.2.f.a 4 1
3456.2.f.b 4
3456.2.f.c 8
3456.2.f.d 8
3456.2.f.e 8
3456.2.f.f 8
3456.2.f.g 8
3456.2.f.h 8
3456.2.f.i 8
3456.2.i \(\chi_{3456}(1153, \cdot)\) 3456.2.i.a 2 2
3456.2.i.b 2
3456.2.i.c 2
3456.2.i.d 2
3456.2.i.e 10
3456.2.i.f 10
3456.2.i.g 10
3456.2.i.h 10
3456.2.i.i 12
3456.2.i.j 12
3456.2.i.k 12
3456.2.i.l 12
3456.2.k \(\chi_{3456}(865, \cdot)\) n/a 128 2
3456.2.l \(\chi_{3456}(863, \cdot)\) n/a 128 2
3456.2.p \(\chi_{3456}(575, \cdot)\) 3456.2.p.a 4 2
3456.2.p.b 4
3456.2.p.c 8
3456.2.p.d 16
3456.2.p.e 16
3456.2.p.f 24
3456.2.p.g 24
3456.2.r \(\chi_{3456}(577, \cdot)\) 3456.2.r.a 4 2
3456.2.r.b 4
3456.2.r.c 4
3456.2.r.d 4
3456.2.r.e 16
3456.2.r.f 16
3456.2.r.g 24
3456.2.r.h 24
3456.2.s \(\chi_{3456}(1151, \cdot)\) 3456.2.s.a 24 2
3456.2.s.b 24
3456.2.s.c 24
3456.2.s.d 24
3456.2.v \(\chi_{3456}(433, \cdot)\) n/a 256 4
3456.2.w \(\chi_{3456}(431, \cdot)\) n/a 256 4
3456.2.y \(\chi_{3456}(385, \cdot)\) n/a 864 6
3456.2.z \(\chi_{3456}(287, \cdot)\) n/a 176 4
3456.2.bc \(\chi_{3456}(289, \cdot)\) n/a 176 4
3456.2.be \(\chi_{3456}(217, \cdot)\) None 0 8
3456.2.bf \(\chi_{3456}(215, \cdot)\) None 0 8
3456.2.bj \(\chi_{3456}(193, \cdot)\) n/a 864 6
3456.2.bl \(\chi_{3456}(191, \cdot)\) n/a 864 6
3456.2.bm \(\chi_{3456}(383, \cdot)\) n/a 864 6
3456.2.bo \(\chi_{3456}(145, \cdot)\) n/a 368 8
3456.2.br \(\chi_{3456}(143, \cdot)\) n/a 368 8
3456.2.bt \(\chi_{3456}(109, \cdot)\) n/a 4096 16
3456.2.bu \(\chi_{3456}(107, \cdot)\) n/a 4096 16
3456.2.bw \(\chi_{3456}(97, \cdot)\) n/a 1680 12
3456.2.bz \(\chi_{3456}(95, \cdot)\) n/a 1680 12
3456.2.cb \(\chi_{3456}(71, \cdot)\) None 0 16
3456.2.cc \(\chi_{3456}(73, \cdot)\) None 0 16
3456.2.cf \(\chi_{3456}(47, \cdot)\) n/a 3408 24
3456.2.cg \(\chi_{3456}(49, \cdot)\) n/a 3408 24
3456.2.ci \(\chi_{3456}(35, \cdot)\) n/a 6080 32
3456.2.cl \(\chi_{3456}(37, \cdot)\) n/a 6080 32
3456.2.cm \(\chi_{3456}(25, \cdot)\) None 0 48
3456.2.cp \(\chi_{3456}(23, \cdot)\) None 0 48
3456.2.cr \(\chi_{3456}(13, \cdot)\) n/a 55104 96
3456.2.cs \(\chi_{3456}(11, \cdot)\) n/a 55104 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3456))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3456)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(864))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1728))\)\(^{\oplus 2}\)