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Properties

Label 1344.3
Level 1344
Weight 3
Dimension 39524
Nonzero newspaces 32
Sturm bound 294912
Trace bound 25

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Defining parameters

Level: \( N \) = \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(294912\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1344))\).

Total New Old
Modular forms 100032 39964 60068
Cusp forms 96576 39524 57052
Eisenstein series 3456 440 3016

Trace form

\( 39524 q - 24 q^{3} - 64 q^{4} - 32 q^{6} - 56 q^{7} - 40 q^{9} + O(q^{10}) \) \( 39524 q - 24 q^{3} - 64 q^{4} - 32 q^{6} - 56 q^{7} - 40 q^{9} - 64 q^{10} + 64 q^{11} - 32 q^{12} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 32 q^{18} - 176 q^{19} - 124 q^{21} - 448 q^{22} - 256 q^{23} - 592 q^{24} - 564 q^{25} - 800 q^{26} - 120 q^{27} - 320 q^{28} - 128 q^{29} - 192 q^{30} - 88 q^{31} + 160 q^{32} + 68 q^{33} + 416 q^{34} + 96 q^{35} + 720 q^{36} + 320 q^{37} + 1120 q^{38} - 20 q^{39} + 1376 q^{40} + 640 q^{41} + 400 q^{42} + 72 q^{43} + 416 q^{44} + 72 q^{45} - 64 q^{46} - 32 q^{48} - 140 q^{49} + 1248 q^{50} - 788 q^{51} + 2048 q^{52} + 256 q^{54} - 2624 q^{55} + 784 q^{56} + 64 q^{57} + 1376 q^{58} - 1280 q^{59} + 544 q^{60} - 64 q^{61} + 192 q^{62} + 172 q^{63} - 544 q^{64} + 576 q^{65} - 544 q^{66} + 2128 q^{67} - 960 q^{68} + 520 q^{69} - 1424 q^{70} + 3072 q^{71} - 32 q^{72} + 944 q^{73} - 2464 q^{74} + 2256 q^{75} - 3392 q^{76} + 96 q^{77} - 704 q^{78} + 2504 q^{79} - 1632 q^{80} + 712 q^{81} - 64 q^{82} - 320 q^{83} + 1192 q^{84} - 736 q^{85} - 20 q^{87} - 64 q^{88} - 640 q^{89} + 1408 q^{90} - 1424 q^{91} - 1232 q^{93} - 64 q^{94} - 2304 q^{95} - 304 q^{96} - 2416 q^{97} - 1024 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1344))\)

We only show spaces with odd 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
1344.3.d \(\chi_{1344}(449, \cdot)\) 1344.3.d.a 4 1
1344.3.d.b 4
1344.3.d.c 4
1344.3.d.d 4
1344.3.d.e 4
1344.3.d.f 4
1344.3.d.g 4
1344.3.d.h 8
1344.3.d.i 12
1344.3.d.j 12
1344.3.d.k 12
1344.3.d.l 24
1344.3.e \(\chi_{1344}(671, \cdot)\) n/a 128 1
1344.3.f \(\chi_{1344}(769, \cdot)\) 1344.3.f.a 2 1
1344.3.f.b 2
1344.3.f.c 2
1344.3.f.d 2
1344.3.f.e 4
1344.3.f.f 4
1344.3.f.g 8
1344.3.f.h 8
1344.3.f.i 16
1344.3.f.j 16
1344.3.g \(\chi_{1344}(799, \cdot)\) 1344.3.g.a 16 1
1344.3.g.b 16
1344.3.g.c 16
1344.3.l \(\chi_{1344}(97, \cdot)\) 1344.3.l.a 20 1
1344.3.l.b 20
1344.3.l.c 24
1344.3.m \(\chi_{1344}(127, \cdot)\) 1344.3.m.a 4 1
1344.3.m.b 4
1344.3.m.c 4
1344.3.m.d 8
1344.3.m.e 12
1344.3.m.f 16
1344.3.n \(\chi_{1344}(1121, \cdot)\) 1344.3.n.a 8 1
1344.3.n.b 8
1344.3.n.c 16
1344.3.n.d 64
1344.3.o \(\chi_{1344}(1343, \cdot)\) n/a 124 1
1344.3.r \(\chi_{1344}(433, \cdot)\) n/a 128 2
1344.3.t \(\chi_{1344}(113, \cdot)\) n/a 192 2
1344.3.v \(\chi_{1344}(335, \cdot)\) n/a 248 2
1344.3.x \(\chi_{1344}(463, \cdot)\) 1344.3.x.a 96 2
1344.3.z \(\chi_{1344}(383, \cdot)\) n/a 248 2
1344.3.ba \(\chi_{1344}(737, \cdot)\) n/a 256 2
1344.3.be \(\chi_{1344}(319, \cdot)\) n/a 128 2
1344.3.bf \(\chi_{1344}(481, \cdot)\) n/a 128 2
1344.3.bg \(\chi_{1344}(415, \cdot)\) n/a 128 2
1344.3.bh \(\chi_{1344}(577, \cdot)\) n/a 128 2
1344.3.bm \(\chi_{1344}(479, \cdot)\) n/a 256 2
1344.3.bn \(\chi_{1344}(65, \cdot)\) n/a 248 2
1344.3.bp \(\chi_{1344}(295, \cdot)\) None 0 4
1344.3.br \(\chi_{1344}(167, \cdot)\) None 0 4
1344.3.bt \(\chi_{1344}(265, \cdot)\) None 0 4
1344.3.bv \(\chi_{1344}(281, \cdot)\) None 0 4
1344.3.bx \(\chi_{1344}(79, \cdot)\) n/a 256 4
1344.3.bz \(\chi_{1344}(47, \cdot)\) n/a 496 4
1344.3.cb \(\chi_{1344}(305, \cdot)\) n/a 496 4
1344.3.cd \(\chi_{1344}(145, \cdot)\) n/a 256 4
1344.3.ce \(\chi_{1344}(83, \cdot)\) n/a 4064 8
1344.3.cf \(\chi_{1344}(29, \cdot)\) n/a 3072 8
1344.3.ck \(\chi_{1344}(13, \cdot)\) n/a 2048 8
1344.3.cl \(\chi_{1344}(43, \cdot)\) n/a 1536 8
1344.3.cm \(\chi_{1344}(137, \cdot)\) None 0 8
1344.3.co \(\chi_{1344}(73, \cdot)\) None 0 8
1344.3.cq \(\chi_{1344}(215, \cdot)\) None 0 8
1344.3.cs \(\chi_{1344}(151, \cdot)\) None 0 8
1344.3.cu \(\chi_{1344}(67, \cdot)\) n/a 4096 16
1344.3.cv \(\chi_{1344}(61, \cdot)\) n/a 4096 16
1344.3.da \(\chi_{1344}(53, \cdot)\) n/a 8128 16
1344.3.db \(\chi_{1344}(59, \cdot)\) n/a 8128 16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1344))\) into lower level spaces

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