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Properties

Label 1360.2
Level 1360
Weight 2
Dimension 27908
Nonzero newspaces 50
Sturm bound 221184
Trace bound 15

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Defining parameters

Level: \( N \) = \( 1360 = 2^{4} \cdot 5 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 50 \)
Sturm bound: \(221184\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1360))\).

Total New Old
Modular forms 57088 28720 28368
Cusp forms 53505 27908 25597
Eisenstein series 3583 812 2771

Trace form

\( 27908 q - 56 q^{2} - 44 q^{3} - 48 q^{4} - 104 q^{5} - 144 q^{6} - 36 q^{7} - 32 q^{8} - 8 q^{9} + O(q^{10}) \) \( 27908 q - 56 q^{2} - 44 q^{3} - 48 q^{4} - 104 q^{5} - 144 q^{6} - 36 q^{7} - 32 q^{8} - 8 q^{9} - 80 q^{10} - 112 q^{11} - 64 q^{12} - 60 q^{13} - 64 q^{14} - 28 q^{15} - 192 q^{16} - 126 q^{17} - 104 q^{18} + 8 q^{19} - 72 q^{20} - 152 q^{21} - 48 q^{22} - 12 q^{23} - 48 q^{24} - 4 q^{25} - 144 q^{26} - 56 q^{27} - 80 q^{28} - 40 q^{29} - 152 q^{30} - 200 q^{31} - 96 q^{32} - 160 q^{33} - 112 q^{34} - 164 q^{35} - 304 q^{36} - 116 q^{37} - 208 q^{38} - 88 q^{39} - 256 q^{40} - 104 q^{41} - 208 q^{42} - 28 q^{43} - 176 q^{44} - 156 q^{45} - 240 q^{46} + 28 q^{47} - 144 q^{48} - 112 q^{49} - 192 q^{50} - 108 q^{51} - 192 q^{52} - 36 q^{53} - 144 q^{54} + 16 q^{55} - 192 q^{56} + 192 q^{57} - 96 q^{58} + 104 q^{59} - 16 q^{60} - 112 q^{61} + 16 q^{62} + 188 q^{63} - 52 q^{65} - 16 q^{66} - 68 q^{67} + 72 q^{69} + 80 q^{70} - 136 q^{71} + 208 q^{72} + 156 q^{73} + 128 q^{74} - 140 q^{75} + 16 q^{76} + 64 q^{77} + 208 q^{78} - 128 q^{79} + 96 q^{80} - 188 q^{81} + 80 q^{82} - 124 q^{83} + 224 q^{84} - 94 q^{85} - 224 q^{86} - 280 q^{87} + 160 q^{88} + 32 q^{89} + 152 q^{90} - 168 q^{91} - 64 q^{92} + 32 q^{93} - 176 q^{95} - 96 q^{96} - 68 q^{97} - 136 q^{98} - 240 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1360))\)

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
1360.2.a \(\chi_{1360}(1, \cdot)\) 1360.2.a.a 1 1
1360.2.a.b 1
1360.2.a.c 1
1360.2.a.d 1
1360.2.a.e 1
1360.2.a.f 1
1360.2.a.g 1
1360.2.a.h 1
1360.2.a.i 1
1360.2.a.j 1
1360.2.a.k 2
1360.2.a.l 2
1360.2.a.m 2
1360.2.a.n 2
1360.2.a.o 2
1360.2.a.p 3
1360.2.a.q 3
1360.2.a.r 3
1360.2.a.s 3
1360.2.c \(\chi_{1360}(1121, \cdot)\) 1360.2.c.a 2 1
1360.2.c.b 2
1360.2.c.c 2
1360.2.c.d 2
1360.2.c.e 6
1360.2.c.f 6
1360.2.c.g 8
1360.2.c.h 8
1360.2.e \(\chi_{1360}(1089, \cdot)\) 1360.2.e.a 2 1
1360.2.e.b 2
1360.2.e.c 6
1360.2.e.d 8
1360.2.e.e 8
1360.2.e.f 10
1360.2.e.g 12
1360.2.f \(\chi_{1360}(681, \cdot)\) None 0 1
1360.2.h \(\chi_{1360}(169, \cdot)\) None 0 1
1360.2.j \(\chi_{1360}(409, \cdot)\) None 0 1
1360.2.l \(\chi_{1360}(441, \cdot)\) None 0 1
1360.2.o \(\chi_{1360}(849, \cdot)\) 1360.2.o.a 2 1
1360.2.o.b 2
1360.2.o.c 4
1360.2.o.d 4
1360.2.o.e 8
1360.2.o.f 8
1360.2.o.g 24
1360.2.q \(\chi_{1360}(47, \cdot)\) n/a 108 2
1360.2.s \(\chi_{1360}(21, \cdot)\) n/a 288 2
1360.2.v \(\chi_{1360}(747, \cdot)\) n/a 424 2
1360.2.x \(\chi_{1360}(307, \cdot)\) n/a 384 2
1360.2.z \(\chi_{1360}(149, \cdot)\) n/a 424 2
1360.2.bb \(\chi_{1360}(183, \cdot)\) None 0 2
1360.2.bc \(\chi_{1360}(523, \cdot)\) n/a 424 2
1360.2.bf \(\chi_{1360}(509, \cdot)\) n/a 424 2
1360.2.bg \(\chi_{1360}(341, \cdot)\) n/a 256 2
1360.2.bj \(\chi_{1360}(667, \cdot)\) n/a 424 2
1360.2.bk \(\chi_{1360}(407, \cdot)\) None 0 2
1360.2.bn \(\chi_{1360}(783, \cdot)\) 1360.2.bn.a 32 2
1360.2.bn.b 64
1360.2.bp \(\chi_{1360}(769, \cdot)\) n/a 104 2
1360.2.bq \(\chi_{1360}(361, \cdot)\) None 0 2
1360.2.bt \(\chi_{1360}(81, \cdot)\) 1360.2.bt.a 4 2
1360.2.bt.b 8
1360.2.bt.c 12
1360.2.bt.d 12
1360.2.bt.e 16
1360.2.bt.f 20
1360.2.bu \(\chi_{1360}(89, \cdot)\) None 0 2
1360.2.bw \(\chi_{1360}(103, \cdot)\) None 0 2
1360.2.bz \(\chi_{1360}(543, \cdot)\) n/a 108 2
1360.2.ca \(\chi_{1360}(803, \cdot)\) n/a 424 2
1360.2.cd \(\chi_{1360}(101, \cdot)\) n/a 288 2
1360.2.ce \(\chi_{1360}(69, \cdot)\) n/a 384 2
1360.2.ch \(\chi_{1360}(123, \cdot)\) n/a 424 2
1360.2.cj \(\chi_{1360}(727, \cdot)\) None 0 2
1360.2.ck \(\chi_{1360}(829, \cdot)\) n/a 424 2
1360.2.cm \(\chi_{1360}(987, \cdot)\) n/a 384 2
1360.2.co \(\chi_{1360}(67, \cdot)\) n/a 424 2
1360.2.cr \(\chi_{1360}(421, \cdot)\) n/a 288 2
1360.2.cs \(\chi_{1360}(863, \cdot)\) n/a 108 2
1360.2.cv \(\chi_{1360}(43, \cdot)\) n/a 848 4
1360.2.cw \(\chi_{1360}(161, \cdot)\) n/a 144 4
1360.2.cz \(\chi_{1360}(9, \cdot)\) None 0 4
1360.2.db \(\chi_{1360}(467, \cdot)\) n/a 848 4
1360.2.dd \(\chi_{1360}(189, \cdot)\) n/a 848 4
1360.2.de \(\chi_{1360}(461, \cdot)\) n/a 576 4
1360.2.dg \(\chi_{1360}(127, \cdot)\) n/a 216 4
1360.2.dj \(\chi_{1360}(287, \cdot)\) n/a 216 4
1360.2.dk \(\chi_{1360}(87, \cdot)\) None 0 4
1360.2.dn \(\chi_{1360}(247, \cdot)\) None 0 4
1360.2.dp \(\chi_{1360}(349, \cdot)\) n/a 848 4
1360.2.dq \(\chi_{1360}(621, \cdot)\) n/a 576 4
1360.2.ds \(\chi_{1360}(83, \cdot)\) n/a 848 4
1360.2.dv \(\chi_{1360}(49, \cdot)\) n/a 208 4
1360.2.dw \(\chi_{1360}(121, \cdot)\) None 0 4
1360.2.dy \(\chi_{1360}(427, \cdot)\) n/a 848 4
1360.2.eb \(\chi_{1360}(11, \cdot)\) n/a 1152 8
1360.2.ed \(\chi_{1360}(313, \cdot)\) None 0 8
1360.2.ee \(\chi_{1360}(177, \cdot)\) n/a 416 8
1360.2.eg \(\chi_{1360}(139, \cdot)\) n/a 1696 8
1360.2.ej \(\chi_{1360}(453, \cdot)\) n/a 1696 8
1360.2.ek \(\chi_{1360}(173, \cdot)\) n/a 1696 8
1360.2.em \(\chi_{1360}(71, \cdot)\) None 0 8
1360.2.ep \(\chi_{1360}(31, \cdot)\) n/a 288 8
1360.2.er \(\chi_{1360}(79, \cdot)\) n/a 432 8
1360.2.es \(\chi_{1360}(39, \cdot)\) None 0 8
1360.2.ev \(\chi_{1360}(37, \cdot)\) n/a 1696 8
1360.2.ew \(\chi_{1360}(133, \cdot)\) n/a 1696 8
1360.2.ey \(\chi_{1360}(99, \cdot)\) n/a 1696 8
1360.2.fa \(\chi_{1360}(97, \cdot)\) n/a 416 8
1360.2.fd \(\chi_{1360}(57, \cdot)\) None 0 8
1360.2.ff \(\chi_{1360}(211, \cdot)\) n/a 1152 8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1360))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1360)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(340))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(680))\)\(^{\oplus 2}\)