Properties

 Label 1344.2 Level 1344 Weight 2 Dimension 19652 Nonzero newspaces 32 Sturm bound 196608 Trace bound 25

Defining parameters

 Level: $$N$$ = $$1344 = 2^{6} \cdot 3 \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$196608$$ Trace bound: $$25$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1344))$$.

Total New Old
Modular forms 50880 20092 30788
Cusp forms 47425 19652 27773
Eisenstein series 3455 440 3015

Trace form

 $$19652 q - 24 q^{3} - 64 q^{4} - 32 q^{6} - 64 q^{7} - 40 q^{9} + O(q^{10})$$ $$19652 q - 24 q^{3} - 64 q^{4} - 32 q^{6} - 64 q^{7} - 40 q^{9} - 64 q^{10} - 16 q^{11} - 32 q^{12} - 96 q^{13} - 72 q^{15} - 64 q^{16} - 32 q^{17} - 32 q^{18} - 80 q^{19} - 36 q^{21} - 128 q^{22} + 48 q^{24} - 36 q^{25} + 160 q^{26} + 64 q^{29} + 128 q^{30} + 40 q^{31} + 160 q^{32} + 52 q^{33} + 96 q^{34} + 24 q^{35} + 80 q^{36} + 160 q^{38} + 20 q^{39} + 96 q^{40} + 64 q^{41} - 104 q^{43} + 32 q^{44} + 56 q^{45} - 64 q^{46} - 32 q^{48} - 140 q^{49} - 96 q^{50} + 108 q^{51} - 256 q^{52} - 64 q^{54} + 288 q^{55} - 112 q^{56} - 48 q^{57} - 352 q^{58} + 320 q^{59} - 224 q^{60} - 64 q^{61} - 192 q^{62} + 4 q^{63} - 544 q^{64} + 32 q^{65} - 192 q^{66} + 304 q^{67} - 192 q^{68} - 104 q^{69} - 272 q^{70} + 256 q^{71} - 32 q^{72} - 80 q^{73} - 224 q^{74} + 72 q^{75} - 320 q^{76} - 48 q^{77} - 224 q^{78} + 40 q^{79} - 96 q^{80} - 184 q^{81} - 64 q^{82} - 80 q^{83} - 152 q^{84} - 256 q^{85} - 140 q^{87} - 64 q^{88} - 64 q^{89} - 320 q^{90} + 48 q^{91} - 96 q^{93} - 64 q^{94} + 48 q^{95} - 304 q^{96} + 48 q^{97} - 128 q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1344))$$

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
1344.2.a $$\chi_{1344}(1, \cdot)$$ 1344.2.a.a 1 1
1344.2.a.b 1
1344.2.a.c 1
1344.2.a.d 1
1344.2.a.e 1
1344.2.a.f 1
1344.2.a.g 1
1344.2.a.h 1
1344.2.a.i 1
1344.2.a.j 1
1344.2.a.k 1
1344.2.a.l 1
1344.2.a.m 1
1344.2.a.n 1
1344.2.a.o 1
1344.2.a.p 1
1344.2.a.q 1
1344.2.a.r 1
1344.2.a.s 1
1344.2.a.t 1
1344.2.a.u 2
1344.2.a.v 2
1344.2.b $$\chi_{1344}(895, \cdot)$$ 1344.2.b.a 2 1
1344.2.b.b 2
1344.2.b.c 2
1344.2.b.d 2
1344.2.b.e 4
1344.2.b.f 4
1344.2.b.g 8
1344.2.b.h 8
1344.2.c $$\chi_{1344}(673, \cdot)$$ 1344.2.c.a 2 1
1344.2.c.b 2
1344.2.c.c 2
1344.2.c.d 2
1344.2.c.e 4
1344.2.c.f 4
1344.2.c.g 4
1344.2.c.h 4
1344.2.h $$\chi_{1344}(575, \cdot)$$ 1344.2.h.a 4 1
1344.2.h.b 4
1344.2.h.c 4
1344.2.h.d 4
1344.2.h.e 4
1344.2.h.f 8
1344.2.h.g 8
1344.2.h.h 12
1344.2.i $$\chi_{1344}(545, \cdot)$$ 1344.2.i.a 4 1
1344.2.i.b 4
1344.2.i.c 8
1344.2.i.d 8
1344.2.i.e 8
1344.2.i.f 16
1344.2.i.g 16
1344.2.j $$\chi_{1344}(1247, \cdot)$$ 1344.2.j.a 4 1
1344.2.j.b 4
1344.2.j.c 4
1344.2.j.d 4
1344.2.j.e 4
1344.2.j.f 4
1344.2.j.g 8
1344.2.j.h 8
1344.2.j.i 8
1344.2.k $$\chi_{1344}(1217, \cdot)$$ 1344.2.k.a 2 1
1344.2.k.b 2
1344.2.k.c 4
1344.2.k.d 4
1344.2.k.e 8
1344.2.k.f 8
1344.2.k.g 8
1344.2.k.h 8
1344.2.k.i 8
1344.2.k.j 8
1344.2.p $$\chi_{1344}(223, \cdot)$$ 1344.2.p.a 4 1
1344.2.p.b 4
1344.2.p.c 12
1344.2.p.d 12
1344.2.q $$\chi_{1344}(193, \cdot)$$ 1344.2.q.a 2 2
1344.2.q.b 2
1344.2.q.c 2
1344.2.q.d 2
1344.2.q.e 2
1344.2.q.f 2
1344.2.q.g 2
1344.2.q.h 2
1344.2.q.i 2
1344.2.q.j 2
1344.2.q.k 2
1344.2.q.l 2
1344.2.q.m 2
1344.2.q.n 2
1344.2.q.o 2
1344.2.q.p 2
1344.2.q.q 2
1344.2.q.r 2
1344.2.q.s 2
1344.2.q.t 2
1344.2.q.u 2
1344.2.q.v 2
1344.2.q.w 4
1344.2.q.x 4
1344.2.q.y 6
1344.2.q.z 6
1344.2.s $$\chi_{1344}(239, \cdot)$$ 1344.2.s.a 4 2
1344.2.s.b 4
1344.2.s.c 40
1344.2.s.d 48
1344.2.u $$\chi_{1344}(559, \cdot)$$ 1344.2.u.a 64 2
1344.2.w $$\chi_{1344}(337, \cdot)$$ 1344.2.w.a 20 2
1344.2.w.b 28
1344.2.y $$\chi_{1344}(209, \cdot)$$ n/a 120 2
1344.2.bb $$\chi_{1344}(31, \cdot)$$ 1344.2.bb.a 4 2
1344.2.bb.b 4
1344.2.bb.c 4
1344.2.bb.d 4
1344.2.bb.e 12
1344.2.bb.f 12
1344.2.bb.g 12
1344.2.bb.h 12
1344.2.bc $$\chi_{1344}(257, \cdot)$$ n/a 120 2
1344.2.bd $$\chi_{1344}(95, \cdot)$$ n/a 128 2
1344.2.bi $$\chi_{1344}(353, \cdot)$$ n/a 128 2
1344.2.bj $$\chi_{1344}(191, \cdot)$$ n/a 120 2
1344.2.bk $$\chi_{1344}(289, \cdot)$$ 1344.2.bk.a 4 2
1344.2.bk.b 4
1344.2.bk.c 4
1344.2.bk.d 4
1344.2.bk.e 4
1344.2.bk.f 4
1344.2.bk.g 4
1344.2.bk.h 4
1344.2.bk.i 8
1344.2.bk.j 8
1344.2.bk.k 8
1344.2.bk.l 8
1344.2.bl $$\chi_{1344}(703, \cdot)$$ 1344.2.bl.a 2 2
1344.2.bl.b 2
1344.2.bl.c 2
1344.2.bl.d 2
1344.2.bl.e 2
1344.2.bl.f 2
1344.2.bl.g 2
1344.2.bl.h 2
1344.2.bl.i 8
1344.2.bl.j 8
1344.2.bl.k 16
1344.2.bl.l 16
1344.2.bo $$\chi_{1344}(41, \cdot)$$ None 0 4
1344.2.bq $$\chi_{1344}(169, \cdot)$$ None 0 4
1344.2.bs $$\chi_{1344}(71, \cdot)$$ None 0 4
1344.2.bu $$\chi_{1344}(55, \cdot)$$ None 0 4
1344.2.bw $$\chi_{1344}(17, \cdot)$$ n/a 240 4
1344.2.by $$\chi_{1344}(529, \cdot)$$ n/a 128 4
1344.2.ca $$\chi_{1344}(271, \cdot)$$ n/a 128 4
1344.2.cc $$\chi_{1344}(431, \cdot)$$ n/a 240 4
1344.2.cg $$\chi_{1344}(85, \cdot)$$ n/a 768 8
1344.2.ch $$\chi_{1344}(139, \cdot)$$ n/a 1024 8
1344.2.ci $$\chi_{1344}(155, \cdot)$$ n/a 1536 8
1344.2.cj $$\chi_{1344}(125, \cdot)$$ n/a 2016 8
1344.2.cn $$\chi_{1344}(103, \cdot)$$ None 0 8
1344.2.cp $$\chi_{1344}(23, \cdot)$$ None 0 8
1344.2.cr $$\chi_{1344}(25, \cdot)$$ None 0 8
1344.2.ct $$\chi_{1344}(89, \cdot)$$ None 0 8
1344.2.cw $$\chi_{1344}(5, \cdot)$$ n/a 4032 16
1344.2.cx $$\chi_{1344}(11, \cdot)$$ n/a 4032 16
1344.2.cy $$\chi_{1344}(19, \cdot)$$ n/a 2048 16
1344.2.cz $$\chi_{1344}(37, \cdot)$$ n/a 2048 16

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1344))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1344)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(336))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(448))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(672))$$$$^{\oplus 2}$$