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Properties

Label 1456.2
Level 1456
Weight 2
Dimension 33866
Nonzero newspaces 70
Sturm bound 258048
Trace bound 25

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Defining parameters

Level: \( N \) = \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 70 \)
Sturm bound: \(258048\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1456))\).

Total New Old
Modular forms 66528 34858 31670
Cusp forms 62497 33866 28631
Eisenstein series 4031 992 3039

Trace form

\( 33866 q - 80 q^{2} - 62 q^{3} - 72 q^{4} - 98 q^{5} - 56 q^{6} - 72 q^{7} - 176 q^{8} - 18 q^{9} + O(q^{10}) \) \( 33866 q - 80 q^{2} - 62 q^{3} - 72 q^{4} - 98 q^{5} - 56 q^{6} - 72 q^{7} - 176 q^{8} - 18 q^{9} - 72 q^{10} - 46 q^{11} - 88 q^{12} - 106 q^{13} - 224 q^{14} - 128 q^{15} - 104 q^{16} - 178 q^{17} - 64 q^{18} - 18 q^{19} - 56 q^{20} - 88 q^{21} - 192 q^{22} - 18 q^{23} - 72 q^{24} + 42 q^{25} - 76 q^{26} - 116 q^{27} - 80 q^{28} - 192 q^{29} - 88 q^{30} - 70 q^{31} - 40 q^{32} - 130 q^{33} - 56 q^{34} - 44 q^{35} - 208 q^{36} - 42 q^{37} - 120 q^{38} - 42 q^{39} - 200 q^{40} + 36 q^{41} - 240 q^{42} - 20 q^{43} - 184 q^{44} - 40 q^{45} - 144 q^{46} + 46 q^{47} - 280 q^{48} - 224 q^{49} - 384 q^{50} + 34 q^{51} - 200 q^{52} - 250 q^{53} - 408 q^{54} + 12 q^{55} - 280 q^{56} - 144 q^{57} - 288 q^{58} - 54 q^{59} - 408 q^{60} - 138 q^{61} - 224 q^{62} - 76 q^{63} - 360 q^{64} - 166 q^{65} - 392 q^{66} - 94 q^{67} - 192 q^{68} - 180 q^{69} - 176 q^{70} - 84 q^{71} - 248 q^{72} + 30 q^{73} - 72 q^{74} + 12 q^{75} - 24 q^{76} - 10 q^{77} - 224 q^{78} - 42 q^{79} - 40 q^{80} + 28 q^{81} - 72 q^{82} + 40 q^{83} - 280 q^{84} - 176 q^{85} - 264 q^{86} - 36 q^{87} - 280 q^{88} - 114 q^{89} - 568 q^{90} - 188 q^{91} - 792 q^{92} - 338 q^{93} - 376 q^{94} - 294 q^{95} - 760 q^{96} - 316 q^{97} - 184 q^{98} - 572 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1456))\)

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
1456.2.a \(\chi_{1456}(1, \cdot)\) 1456.2.a.a 1 1
1456.2.a.b 1
1456.2.a.c 1
1456.2.a.d 1
1456.2.a.e 1
1456.2.a.f 1
1456.2.a.g 1
1456.2.a.h 1
1456.2.a.i 1
1456.2.a.j 1
1456.2.a.k 1
1456.2.a.l 1
1456.2.a.m 1
1456.2.a.n 2
1456.2.a.o 2
1456.2.a.p 2
1456.2.a.q 2
1456.2.a.r 2
1456.2.a.s 2
1456.2.a.t 3
1456.2.a.u 4
1456.2.a.v 4
1456.2.b \(\chi_{1456}(727, \cdot)\) None 0 1
1456.2.c \(\chi_{1456}(729, \cdot)\) None 0 1
1456.2.h \(\chi_{1456}(391, \cdot)\) None 0 1
1456.2.i \(\chi_{1456}(1065, \cdot)\) None 0 1
1456.2.j \(\chi_{1456}(1119, \cdot)\) 1456.2.j.a 16 1
1456.2.j.b 32
1456.2.k \(\chi_{1456}(337, \cdot)\) 1456.2.k.a 2 1
1456.2.k.b 6
1456.2.k.c 6
1456.2.k.d 8
1456.2.k.e 8
1456.2.k.f 12
1456.2.p \(\chi_{1456}(1455, \cdot)\) 1456.2.p.a 2 1
1456.2.p.b 2
1456.2.p.c 2
1456.2.p.d 2
1456.2.p.e 4
1456.2.p.f 4
1456.2.p.g 8
1456.2.p.h 8
1456.2.p.i 24
1456.2.q \(\chi_{1456}(289, \cdot)\) n/a 108 2
1456.2.r \(\chi_{1456}(417, \cdot)\) 1456.2.r.a 2 2
1456.2.r.b 2
1456.2.r.c 2
1456.2.r.d 2
1456.2.r.e 2
1456.2.r.f 2
1456.2.r.g 2
1456.2.r.h 2
1456.2.r.i 2
1456.2.r.j 4
1456.2.r.k 4
1456.2.r.l 6
1456.2.r.m 8
1456.2.r.n 8
1456.2.r.o 8
1456.2.r.p 10
1456.2.r.q 14
1456.2.r.r 16
1456.2.s \(\chi_{1456}(113, \cdot)\) 1456.2.s.a 2 2
1456.2.s.b 2
1456.2.s.c 2
1456.2.s.d 2
1456.2.s.e 2
1456.2.s.f 2
1456.2.s.g 2
1456.2.s.h 4
1456.2.s.i 4
1456.2.s.j 4
1456.2.s.k 4
1456.2.s.l 4
1456.2.s.m 4
1456.2.s.n 4
1456.2.s.o 4
1456.2.s.p 8
1456.2.s.q 8
1456.2.s.r 8
1456.2.s.s 14
1456.2.t \(\chi_{1456}(81, \cdot)\) n/a 108 2
1456.2.v \(\chi_{1456}(239, \cdot)\) 1456.2.v.a 8 2
1456.2.v.b 28
1456.2.v.c 48
1456.2.w \(\chi_{1456}(993, \cdot)\) n/a 108 2
1456.2.y \(\chi_{1456}(827, \cdot)\) n/a 336 2
1456.2.z \(\chi_{1456}(125, \cdot)\) n/a 440 2
1456.2.bd \(\chi_{1456}(27, \cdot)\) n/a 384 2
1456.2.be \(\chi_{1456}(701, \cdot)\) n/a 336 2
1456.2.bh \(\chi_{1456}(363, \cdot)\) n/a 440 2
1456.2.bi \(\chi_{1456}(365, \cdot)\) n/a 288 2
1456.2.bm \(\chi_{1456}(99, \cdot)\) n/a 336 2
1456.2.bn \(\chi_{1456}(853, \cdot)\) n/a 440 2
1456.2.bp \(\chi_{1456}(967, \cdot)\) None 0 2
1456.2.bq \(\chi_{1456}(265, \cdot)\) None 0 2
1456.2.bu \(\chi_{1456}(121, \cdot)\) None 0 2
1456.2.bv \(\chi_{1456}(1095, \cdot)\) None 0 2
1456.2.bw \(\chi_{1456}(9, \cdot)\) None 0 2
1456.2.bx \(\chi_{1456}(647, \cdot)\) None 0 2
1456.2.cc \(\chi_{1456}(225, \cdot)\) 1456.2.cc.a 4 2
1456.2.cc.b 4
1456.2.cc.c 12
1456.2.cc.d 12
1456.2.cc.e 12
1456.2.cc.f 16
1456.2.cc.g 24
1456.2.cd \(\chi_{1456}(783, \cdot)\) n/a 112 2
1456.2.ce \(\chi_{1456}(927, \cdot)\) n/a 112 2
1456.2.cf \(\chi_{1456}(831, \cdot)\) n/a 112 2
1456.2.co \(\chi_{1456}(753, \cdot)\) n/a 108 2
1456.2.cp \(\chi_{1456}(495, \cdot)\) 1456.2.cp.a 32 2
1456.2.cp.b 32
1456.2.cp.c 32
1456.2.cq \(\chi_{1456}(159, \cdot)\) n/a 112 2
1456.2.cr \(\chi_{1456}(641, \cdot)\) n/a 108 2
1456.2.cs \(\chi_{1456}(335, \cdot)\) n/a 112 2
1456.2.cx \(\chi_{1456}(393, \cdot)\) None 0 2
1456.2.cy \(\chi_{1456}(615, \cdot)\) None 0 2
1456.2.cz \(\chi_{1456}(25, \cdot)\) None 0 2
1456.2.da \(\chi_{1456}(1223, \cdot)\) None 0 2
1456.2.db \(\chi_{1456}(87, \cdot)\) None 0 2
1456.2.dc \(\chi_{1456}(569, \cdot)\) None 0 2
1456.2.dl \(\chi_{1456}(199, \cdot)\) None 0 2
1456.2.dm \(\chi_{1456}(1017, \cdot)\) None 0 2
1456.2.dn \(\chi_{1456}(1145, \cdot)\) None 0 2
1456.2.do \(\chi_{1456}(103, \cdot)\) None 0 2
1456.2.dp \(\chi_{1456}(953, \cdot)\) None 0 2
1456.2.dq \(\chi_{1456}(55, \cdot)\) None 0 2
1456.2.dv \(\chi_{1456}(719, \cdot)\) n/a 112 2
1456.2.dw \(\chi_{1456}(849, \cdot)\) n/a 108 2
1456.2.dx \(\chi_{1456}(367, \cdot)\) n/a 112 2
1456.2.eb \(\chi_{1456}(33, \cdot)\) n/a 216 4
1456.2.ec \(\chi_{1456}(431, \cdot)\) n/a 224 4
1456.2.ef \(\chi_{1456}(487, \cdot)\) None 0 4
1456.2.ei \(\chi_{1456}(41, \cdot)\) None 0 4
1456.2.ej \(\chi_{1456}(73, \cdot)\) None 0 4
1456.2.ek \(\chi_{1456}(71, \cdot)\) None 0 4
1456.2.el \(\chi_{1456}(135, \cdot)\) None 0 4
1456.2.eo \(\chi_{1456}(89, \cdot)\) None 0 4
1456.2.es \(\chi_{1456}(349, \cdot)\) n/a 880 4
1456.2.et \(\chi_{1456}(267, \cdot)\) n/a 672 4
1456.2.ew \(\chi_{1456}(661, \cdot)\) n/a 880 4
1456.2.ex \(\chi_{1456}(163, \cdot)\) n/a 880 4
1456.2.ey \(\chi_{1456}(123, \cdot)\) n/a 880 4
1456.2.ez \(\chi_{1456}(229, \cdot)\) n/a 880 4
1456.2.fa \(\chi_{1456}(515, \cdot)\) n/a 880 4
1456.2.fb \(\chi_{1456}(45, \cdot)\) n/a 880 4
1456.2.fh \(\chi_{1456}(373, \cdot)\) n/a 880 4
1456.2.fi \(\chi_{1456}(283, \cdot)\) n/a 880 4
1456.2.fl \(\chi_{1456}(485, \cdot)\) n/a 880 4
1456.2.fm \(\chi_{1456}(3, \cdot)\) n/a 880 4
1456.2.fp \(\chi_{1456}(389, \cdot)\) n/a 880 4
1456.2.fq \(\chi_{1456}(131, \cdot)\) n/a 768 4
1456.2.ft \(\chi_{1456}(75, \cdot)\) n/a 880 4
1456.2.fv \(\chi_{1456}(29, \cdot)\) n/a 672 4
1456.2.fw \(\chi_{1456}(251, \cdot)\) n/a 880 4
1456.2.fy \(\chi_{1456}(165, \cdot)\) n/a 880 4
1456.2.gb \(\chi_{1456}(451, \cdot)\) n/a 880 4
1456.2.gd \(\chi_{1456}(309, \cdot)\) n/a 672 4
1456.2.ge \(\chi_{1456}(139, \cdot)\) n/a 880 4
1456.2.gg \(\chi_{1456}(205, \cdot)\) n/a 880 4
1456.2.gj \(\chi_{1456}(53, \cdot)\) n/a 768 4
1456.2.gk \(\chi_{1456}(467, \cdot)\) n/a 880 4
1456.2.gm \(\chi_{1456}(397, \cdot)\) n/a 880 4
1456.2.gn \(\chi_{1456}(11, \cdot)\) n/a 880 4
1456.2.gu \(\chi_{1456}(219, \cdot)\) n/a 880 4
1456.2.gv \(\chi_{1456}(5, \cdot)\) n/a 880 4
1456.2.gw \(\chi_{1456}(291, \cdot)\) n/a 880 4
1456.2.gx \(\chi_{1456}(605, \cdot)\) n/a 880 4
1456.2.gy \(\chi_{1456}(293, \cdot)\) n/a 880 4
1456.2.gz \(\chi_{1456}(323, \cdot)\) n/a 672 4
1456.2.hd \(\chi_{1456}(319, \cdot)\) n/a 224 4
1456.2.hg \(\chi_{1456}(97, \cdot)\) n/a 216 4
1456.2.hh \(\chi_{1456}(369, \cdot)\) n/a 216 4
1456.2.hi \(\chi_{1456}(15, \cdot)\) n/a 168 4
1456.2.hj \(\chi_{1456}(655, \cdot)\) n/a 224 4
1456.2.hm \(\chi_{1456}(145, \cdot)\) n/a 216 4
1456.2.hp \(\chi_{1456}(201, \cdot)\) None 0 4
1456.2.hq \(\chi_{1456}(375, \cdot)\) None 0 4

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1456))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1456)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1456))\)\(^{\oplus 1}\)