# Properties

 Label 672.2 Level 672 Weight 2 Dimension 4868 Nonzero newspaces 24 Newform subspaces 69 Sturm bound 49152 Trace bound 14

## Defining parameters

 Level: $$N$$ = $$672 = 2^{5} \cdot 3 \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Newform subspaces: $$69$$ Sturm bound: $$49152$$ Trace bound: $$14$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(672))$$.

Total New Old
Modular forms 13056 5068 7988
Cusp forms 11521 4868 6653
Eisenstein series 1535 200 1335

## Trace form

 $$4868 q - 14 q^{3} - 32 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 32 q^{9} + O(q^{10})$$ $$4868 q - 14 q^{3} - 32 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 32 q^{9} + 16 q^{12} - 8 q^{13} + 32 q^{14} - 12 q^{15} + 48 q^{16} + 32 q^{17} - 12 q^{19} + 64 q^{20} - 4 q^{21} - 32 q^{22} + 48 q^{23} - 40 q^{24} - 12 q^{25} - 80 q^{26} + 64 q^{27} - 80 q^{28} - 8 q^{29} - 112 q^{30} + 68 q^{31} - 80 q^{32} - 44 q^{33} - 80 q^{34} + 48 q^{35} - 144 q^{36} - 72 q^{37} - 80 q^{38} + 40 q^{39} - 112 q^{40} - 16 q^{41} - 80 q^{42} - 40 q^{43} - 16 q^{44} - 40 q^{45} - 32 q^{46} + 24 q^{47} - 120 q^{48} + 20 q^{49} - 48 q^{50} + 10 q^{51} - 128 q^{52} + 120 q^{53} - 120 q^{54} - 64 q^{55} - 56 q^{56} - 8 q^{57} - 176 q^{58} - 32 q^{59} - 136 q^{60} + 184 q^{61} - 96 q^{62} + 30 q^{63} - 224 q^{64} + 80 q^{65} - 64 q^{66} - 52 q^{67} + 16 q^{68} + 160 q^{69} - 64 q^{70} - 56 q^{71} + 104 q^{72} + 32 q^{73} + 64 q^{74} - 64 q^{75} - 32 q^{76} + 64 q^{77} + 88 q^{78} - 28 q^{79} + 112 q^{80} + 64 q^{81} + 128 q^{82} + 112 q^{84} + 48 q^{85} + 128 q^{86} - 128 q^{87} + 144 q^{88} + 248 q^{90} - 112 q^{91} + 112 q^{92} - 88 q^{93} - 144 q^{94} - 104 q^{95} + 24 q^{96} - 256 q^{97} - 256 q^{98} - 212 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(672))$$

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
672.2.a $$\chi_{672}(1, \cdot)$$ 672.2.a.a 1 1
672.2.a.b 1
672.2.a.c 1
672.2.a.d 1
672.2.a.e 1
672.2.a.f 1
672.2.a.g 1
672.2.a.h 1
672.2.a.i 2
672.2.a.j 2
672.2.b $$\chi_{672}(223, \cdot)$$ 672.2.b.a 8 1
672.2.b.b 8
672.2.c $$\chi_{672}(337, \cdot)$$ 672.2.c.a 4 1
672.2.c.b 8
672.2.h $$\chi_{672}(575, \cdot)$$ 672.2.h.a 4 1
672.2.h.b 4
672.2.h.c 4
672.2.h.d 4
672.2.h.e 8
672.2.i $$\chi_{672}(209, \cdot)$$ 672.2.i.a 4 1
672.2.i.b 4
672.2.i.c 4
672.2.i.d 8
672.2.i.e 8
672.2.j $$\chi_{672}(239, \cdot)$$ 672.2.j.a 4 1
672.2.j.b 4
672.2.j.c 4
672.2.j.d 12
672.2.k $$\chi_{672}(545, \cdot)$$ 672.2.k.a 8 1
672.2.k.b 8
672.2.k.c 8
672.2.k.d 8
672.2.p $$\chi_{672}(559, \cdot)$$ 672.2.p.a 16 1
672.2.q $$\chi_{672}(193, \cdot)$$ 672.2.q.a 2 2
672.2.q.b 2
672.2.q.c 2
672.2.q.d 2
672.2.q.e 2
672.2.q.f 2
672.2.q.g 2
672.2.q.h 2
672.2.q.i 2
672.2.q.j 2
672.2.q.k 6
672.2.q.l 6
672.2.s $$\chi_{672}(71, \cdot)$$ None 0 2
672.2.u $$\chi_{672}(55, \cdot)$$ None 0 2
672.2.w $$\chi_{672}(169, \cdot)$$ None 0 2
672.2.y $$\chi_{672}(41, \cdot)$$ None 0 2
672.2.bb $$\chi_{672}(271, \cdot)$$ 672.2.bb.a 32 2
672.2.bc $$\chi_{672}(257, \cdot)$$ 672.2.bc.a 4 2
672.2.bc.b 4
672.2.bc.c 8
672.2.bc.d 16
672.2.bc.e 32
672.2.bd $$\chi_{672}(431, \cdot)$$ 672.2.bd.a 56 2
672.2.bi $$\chi_{672}(17, \cdot)$$ 672.2.bi.a 4 2
672.2.bi.b 4
672.2.bi.c 48
672.2.bj $$\chi_{672}(95, \cdot)$$ 672.2.bj.a 64 2
672.2.bk $$\chi_{672}(529, \cdot)$$ 672.2.bk.a 32 2
672.2.bl $$\chi_{672}(31, \cdot)$$ 672.2.bl.a 16 2
672.2.bl.b 16
672.2.bo $$\chi_{672}(125, \cdot)$$ 672.2.bo.a 496 4
672.2.bq $$\chi_{672}(85, \cdot)$$ 672.2.bq.a 88 4
672.2.bq.b 104
672.2.bs $$\chi_{672}(155, \cdot)$$ 672.2.bs.a 192 4
672.2.bs.b 192
672.2.bu $$\chi_{672}(139, \cdot)$$ 672.2.bu.a 256 4
672.2.bw $$\chi_{672}(89, \cdot)$$ None 0 4
672.2.by $$\chi_{672}(25, \cdot)$$ None 0 4
672.2.ca $$\chi_{672}(103, \cdot)$$ None 0 4
672.2.cc $$\chi_{672}(23, \cdot)$$ None 0 4
672.2.cf $$\chi_{672}(19, \cdot)$$ 672.2.cf.a 512 8
672.2.ch $$\chi_{672}(11, \cdot)$$ 672.2.ch.a 992 8
672.2.cj $$\chi_{672}(37, \cdot)$$ 672.2.cj.a 512 8
672.2.cl $$\chi_{672}(5, \cdot)$$ 672.2.cl.a 992 8

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(672))$$ into lower level spaces

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