Properties

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

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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

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

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 the 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

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