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Properties

Label 672.4
Level 672
Weight 4
Dimension 14804
Nonzero newspaces 24
Sturm bound 98304
Trace bound 14

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Defining parameters

Level: \( N \) = \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(98304\)
Trace bound: \(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(672))\).

Total New Old
Modular forms 37632 15004 22628
Cusp forms 36096 14804 21292
Eisenstein series 1536 200 1336

Trace form

\( 14804 q - 14 q^{3} - 32 q^{4} + 8 q^{5} - 16 q^{6} + 16 q^{9} + O(q^{10}) \) \( 14804 q - 14 q^{3} - 32 q^{4} + 8 q^{5} - 16 q^{6} + 16 q^{9} + 448 q^{10} - 112 q^{12} - 504 q^{13} - 416 q^{14} - 140 q^{15} - 1232 q^{16} - 416 q^{17} - 160 q^{18} - 76 q^{19} + 320 q^{20} - 36 q^{21} + 704 q^{22} + 1968 q^{23} - 104 q^{24} + 628 q^{25} + 80 q^{26} - 800 q^{27} + 720 q^{28} - 568 q^{29} + 2240 q^{30} - 4284 q^{31} + 2480 q^{32} - 124 q^{33} + 2096 q^{34} - 912 q^{35} - 1200 q^{36} + 1288 q^{37} - 880 q^{38} + 1976 q^{39} - 3312 q^{40} + 2128 q^{41} - 920 q^{42} + 6456 q^{43} - 2000 q^{44} + 3784 q^{45} - 32 q^{46} + 408 q^{47} + 4872 q^{48} - 5404 q^{49} - 5712 q^{50} - 3366 q^{51} - 6656 q^{52} - 1272 q^{53} - 8 q^{54} - 4416 q^{55} + 392 q^{56} - 3608 q^{57} + 4720 q^{58} + 1376 q^{59} - 712 q^{60} - 7992 q^{61} + 5856 q^{62} + 798 q^{63} + 19744 q^{64} + 7408 q^{65} + 11984 q^{66} + 10412 q^{67} + 10064 q^{68} + 1344 q^{69} + 2768 q^{70} + 1928 q^{71} - 2776 q^{72} - 9664 q^{73} - 13888 q^{74} - 8592 q^{75} - 20512 q^{76} - 64 q^{77} - 13736 q^{78} - 11420 q^{79} - 22672 q^{80} - 8112 q^{81} - 11712 q^{82} - 2432 q^{84} + 3152 q^{85} - 4736 q^{86} + 4816 q^{87} - 1264 q^{88} - 5656 q^{90} - 976 q^{91} + 2480 q^{92} - 1080 q^{93} - 22928 q^{94} - 1384 q^{95} - 21224 q^{96} - 3680 q^{97} - 13568 q^{98} + 17740 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(672))\)

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
672.4.a \(\chi_{672}(1, \cdot)\) 672.4.a.a 1 1
672.4.a.b 1
672.4.a.c 1
672.4.a.d 1
672.4.a.e 2
672.4.a.f 2
672.4.a.g 2
672.4.a.h 2
672.4.a.i 2
672.4.a.j 2
672.4.a.k 2
672.4.a.l 2
672.4.a.m 2
672.4.a.n 2
672.4.a.o 3
672.4.a.p 3
672.4.a.q 3
672.4.a.r 3
672.4.b \(\chi_{672}(223, \cdot)\) 672.4.b.a 24 1
672.4.b.b 24
672.4.c \(\chi_{672}(337, \cdot)\) 672.4.c.a 16 1
672.4.c.b 20
672.4.h \(\chi_{672}(575, \cdot)\) 672.4.h.a 36 1
672.4.h.b 36
672.4.i \(\chi_{672}(209, \cdot)\) 672.4.i.a 4 1
672.4.i.b 8
672.4.i.c 80
672.4.j \(\chi_{672}(239, \cdot)\) 672.4.j.a 72 1
672.4.k \(\chi_{672}(545, \cdot)\) 672.4.k.a 8 1
672.4.k.b 8
672.4.k.c 16
672.4.k.d 16
672.4.k.e 48
672.4.p \(\chi_{672}(559, \cdot)\) 672.4.p.a 48 1
672.4.q \(\chi_{672}(193, \cdot)\) 672.4.q.a 2 2
672.4.q.b 2
672.4.q.c 4
672.4.q.d 4
672.4.q.e 6
672.4.q.f 6
672.4.q.g 10
672.4.q.h 10
672.4.q.i 12
672.4.q.j 12
672.4.q.k 14
672.4.q.l 14
672.4.s \(\chi_{672}(71, \cdot)\) None 0 2
672.4.u \(\chi_{672}(55, \cdot)\) None 0 2
672.4.w \(\chi_{672}(169, \cdot)\) None 0 2
672.4.y \(\chi_{672}(41, \cdot)\) None 0 2
672.4.bb \(\chi_{672}(271, \cdot)\) 672.4.bb.a 96 2
672.4.bc \(\chi_{672}(257, \cdot)\) n/a 192 2
672.4.bd \(\chi_{672}(431, \cdot)\) n/a 184 2
672.4.bi \(\chi_{672}(17, \cdot)\) n/a 184 2
672.4.bj \(\chi_{672}(95, \cdot)\) n/a 192 2
672.4.bk \(\chi_{672}(529, \cdot)\) 672.4.bk.a 96 2
672.4.bl \(\chi_{672}(31, \cdot)\) 672.4.bl.a 48 2
672.4.bl.b 48
672.4.bo \(\chi_{672}(125, \cdot)\) n/a 1520 4
672.4.bq \(\chi_{672}(85, \cdot)\) n/a 576 4
672.4.bs \(\chi_{672}(155, \cdot)\) n/a 1152 4
672.4.bu \(\chi_{672}(139, \cdot)\) n/a 768 4
672.4.bw \(\chi_{672}(89, \cdot)\) None 0 4
672.4.by \(\chi_{672}(25, \cdot)\) None 0 4
672.4.ca \(\chi_{672}(103, \cdot)\) None 0 4
672.4.cc \(\chi_{672}(23, \cdot)\) None 0 4
672.4.cf \(\chi_{672}(19, \cdot)\) n/a 1536 8
672.4.ch \(\chi_{672}(11, \cdot)\) n/a 3040 8
672.4.cj \(\chi_{672}(37, \cdot)\) n/a 1536 8
672.4.cl \(\chi_{672}(5, \cdot)\) n/a 3040 8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(672))\) into lower level spaces

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