# Properties

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

## 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

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

## 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 the 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

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