Properties

Label 1312.2
Level 1312
Weight 2
Dimension 29814
Nonzero newspaces 32
Sturm bound 215040
Trace bound 11

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Defining parameters

Level: \( N \) = \( 1312 = 2^{5} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(215040\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1312))\).

Total New Old
Modular forms 55040 30594 24446
Cusp forms 52481 29814 22667
Eisenstein series 2559 780 1779

Trace form

\( 29814 q - 152 q^{2} - 112 q^{3} - 152 q^{4} - 148 q^{5} - 152 q^{6} - 112 q^{7} - 152 q^{8} - 226 q^{9} + O(q^{10}) \) \( 29814 q - 152 q^{2} - 112 q^{3} - 152 q^{4} - 148 q^{5} - 152 q^{6} - 112 q^{7} - 152 q^{8} - 226 q^{9} - 168 q^{10} - 112 q^{11} - 184 q^{12} - 164 q^{13} - 184 q^{14} - 120 q^{15} - 192 q^{16} - 84 q^{17} - 192 q^{18} - 112 q^{19} - 184 q^{20} - 152 q^{21} - 176 q^{22} - 128 q^{23} - 128 q^{24} - 230 q^{25} - 112 q^{26} - 160 q^{27} - 112 q^{28} - 132 q^{29} - 88 q^{30} - 152 q^{31} - 112 q^{32} - 384 q^{33} - 128 q^{34} - 160 q^{35} - 96 q^{36} - 148 q^{37} - 168 q^{38} - 160 q^{39} - 176 q^{40} - 246 q^{41} - 352 q^{42} - 128 q^{43} - 232 q^{44} - 188 q^{45} - 216 q^{46} - 120 q^{47} - 256 q^{48} - 66 q^{49} - 232 q^{50} - 104 q^{51} - 168 q^{52} - 212 q^{53} - 176 q^{54} - 48 q^{55} - 176 q^{56} - 232 q^{57} - 144 q^{58} - 48 q^{59} - 144 q^{60} - 196 q^{61} - 112 q^{62} - 24 q^{63} - 80 q^{64} - 360 q^{65} - 104 q^{66} - 32 q^{67} - 192 q^{68} - 216 q^{69} - 128 q^{70} - 48 q^{71} - 200 q^{72} - 220 q^{73} - 184 q^{74} - 88 q^{75} - 152 q^{76} - 184 q^{77} - 232 q^{78} - 120 q^{79} - 144 q^{80} - 98 q^{81} - 156 q^{82} - 312 q^{83} - 192 q^{84} - 184 q^{85} - 112 q^{86} - 224 q^{87} - 160 q^{88} - 252 q^{89} - 176 q^{90} - 208 q^{91} - 80 q^{92} - 128 q^{93} - 176 q^{94} - 232 q^{95} - 160 q^{96} - 420 q^{97} - 112 q^{98} - 216 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1312))\)

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
1312.2.a \(\chi_{1312}(1, \cdot)\) 1312.2.a.a 1 1
1312.2.a.b 1
1312.2.a.c 2
1312.2.a.d 3
1312.2.a.e 3
1312.2.a.f 4
1312.2.a.g 4
1312.2.a.h 7
1312.2.a.i 7
1312.2.a.j 8
1312.2.b \(\chi_{1312}(657, \cdot)\) 1312.2.b.a 20 1
1312.2.b.b 20
1312.2.d \(\chi_{1312}(737, \cdot)\) 1312.2.d.a 2 1
1312.2.d.b 2
1312.2.d.c 2
1312.2.d.d 8
1312.2.d.e 8
1312.2.d.f 10
1312.2.d.g 10
1312.2.g \(\chi_{1312}(81, \cdot)\) 1312.2.g.a 40 1
1312.2.i \(\chi_{1312}(9, \cdot)\) None 0 2
1312.2.l \(\chi_{1312}(993, \cdot)\) 1312.2.l.a 2 2
1312.2.l.b 2
1312.2.l.c 2
1312.2.l.d 2
1312.2.l.e 2
1312.2.l.f 2
1312.2.l.g 4
1312.2.l.h 4
1312.2.l.i 12
1312.2.l.j 16
1312.2.l.k 18
1312.2.l.l 18
1312.2.n \(\chi_{1312}(329, \cdot)\) None 0 2
1312.2.o \(\chi_{1312}(409, \cdot)\) None 0 2
1312.2.r \(\chi_{1312}(337, \cdot)\) 1312.2.r.a 80 2
1312.2.t \(\chi_{1312}(73, \cdot)\) None 0 2
1312.2.u \(\chi_{1312}(385, \cdot)\) n/a 168 4
1312.2.v \(\chi_{1312}(355, \cdot)\) n/a 664 4
1312.2.x \(\chi_{1312}(55, \cdot)\) None 0 4
1312.2.ba \(\chi_{1312}(237, \cdot)\) n/a 664 4
1312.2.bc \(\chi_{1312}(3, \cdot)\) n/a 664 4
1312.2.be \(\chi_{1312}(219, \cdot)\) n/a 664 4
1312.2.bf \(\chi_{1312}(165, \cdot)\) n/a 640 4
1312.2.bj \(\chi_{1312}(79, \cdot)\) n/a 160 4
1312.2.bk \(\chi_{1312}(191, \cdot)\) n/a 168 4
1312.2.bm \(\chi_{1312}(245, \cdot)\) n/a 664 4
1312.2.bo \(\chi_{1312}(173, \cdot)\) n/a 664 4
1312.2.bp \(\chi_{1312}(407, \cdot)\) None 0 4
1312.2.bs \(\chi_{1312}(331, \cdot)\) n/a 664 4
1312.2.bu \(\chi_{1312}(353, \cdot)\) n/a 168 4
1312.2.bw \(\chi_{1312}(305, \cdot)\) n/a 160 4
1312.2.by \(\chi_{1312}(113, \cdot)\) n/a 160 4
1312.2.cb \(\chi_{1312}(169, \cdot)\) None 0 8
1312.2.cc \(\chi_{1312}(49, \cdot)\) n/a 320 8
1312.2.cf \(\chi_{1312}(25, \cdot)\) None 0 8
1312.2.cg \(\chi_{1312}(57, \cdot)\) None 0 8
1312.2.ci \(\chi_{1312}(33, \cdot)\) n/a 336 8
1312.2.ck \(\chi_{1312}(121, \cdot)\) None 0 8
1312.2.cn \(\chi_{1312}(11, \cdot)\) n/a 2656 16
1312.2.cp \(\chi_{1312}(151, \cdot)\) None 0 16
1312.2.cq \(\chi_{1312}(197, \cdot)\) n/a 2656 16
1312.2.cs \(\chi_{1312}(275, \cdot)\) n/a 2656 16
1312.2.cu \(\chi_{1312}(259, \cdot)\) n/a 2656 16
1312.2.cw \(\chi_{1312}(45, \cdot)\) n/a 2656 16
1312.2.cy \(\chi_{1312}(63, \cdot)\) n/a 672 16
1312.2.cz \(\chi_{1312}(15, \cdot)\) n/a 640 16
1312.2.dd \(\chi_{1312}(37, \cdot)\) n/a 2656 16
1312.2.de \(\chi_{1312}(5, \cdot)\) n/a 2656 16
1312.2.dh \(\chi_{1312}(7, \cdot)\) None 0 16
1312.2.di \(\chi_{1312}(67, \cdot)\) n/a 2656 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1312))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1312)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(328))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(656))\)\(^{\oplus 2}\)