# Properties

 Label 704.2 Level 704 Weight 2 Dimension 8298 Nonzero newspaces 16 Newform subspaces 61 Sturm bound 61440 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$704 = 2^{6} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Newform subspaces: $$61$$ Sturm bound: $$61440$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(704))$$.

Total New Old
Modular forms 16080 8694 7386
Cusp forms 14641 8298 6343
Eisenstein series 1439 396 1043

## Trace form

 $$8298 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 44 q^{7} - 64 q^{8} - 74 q^{9} + O(q^{10})$$ $$8298 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 44 q^{7} - 64 q^{8} - 74 q^{9} - 64 q^{10} - 50 q^{11} - 144 q^{12} - 48 q^{13} - 64 q^{14} - 36 q^{15} - 64 q^{16} - 96 q^{17} - 64 q^{18} - 32 q^{19} - 64 q^{20} - 72 q^{21} - 80 q^{22} - 104 q^{23} - 144 q^{24} - 102 q^{25} - 144 q^{26} - 60 q^{27} - 144 q^{28} - 96 q^{29} - 224 q^{30} - 92 q^{31} - 144 q^{32} - 80 q^{33} - 224 q^{34} - 52 q^{35} - 224 q^{36} - 80 q^{37} - 144 q^{38} - 44 q^{39} - 144 q^{40} - 80 q^{41} - 144 q^{42} - 24 q^{43} - 80 q^{44} - 136 q^{45} - 64 q^{46} - 12 q^{47} - 64 q^{48} - 94 q^{49} - 16 q^{50} - 100 q^{51} + 32 q^{52} - 16 q^{53} + 64 q^{54} - 116 q^{55} - 32 q^{56} - 68 q^{57} + 80 q^{58} - 184 q^{59} + 128 q^{60} - 48 q^{61} - 180 q^{63} + 128 q^{64} - 172 q^{65} + 8 q^{66} - 284 q^{67} + 32 q^{68} - 40 q^{69} + 128 q^{70} - 172 q^{71} + 80 q^{72} - 80 q^{73} + 48 q^{74} - 160 q^{75} + 64 q^{76} - 76 q^{77} - 96 q^{78} - 108 q^{79} - 144 q^{80} - 118 q^{81} - 224 q^{82} - 48 q^{83} - 288 q^{84} - 80 q^{85} - 272 q^{86} - 64 q^{87} - 152 q^{88} - 276 q^{89} - 352 q^{90} - 36 q^{91} - 368 q^{92} - 144 q^{93} - 256 q^{94} - 84 q^{95} - 336 q^{96} - 128 q^{97} - 336 q^{98} - 78 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(704))$$

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
704.2.a $$\chi_{704}(1, \cdot)$$ 704.2.a.a 1 1
704.2.a.b 1
704.2.a.c 1
704.2.a.d 1
704.2.a.e 1
704.2.a.f 1
704.2.a.g 1
704.2.a.h 1
704.2.a.i 1
704.2.a.j 1
704.2.a.k 1
704.2.a.l 1
704.2.a.m 2
704.2.a.n 2
704.2.a.o 2
704.2.a.p 2
704.2.c $$\chi_{704}(353, \cdot)$$ 704.2.c.a 4 1
704.2.c.b 4
704.2.c.c 12
704.2.e $$\chi_{704}(703, \cdot)$$ 704.2.e.a 2 1
704.2.e.b 4
704.2.e.c 4
704.2.e.d 12
704.2.g $$\chi_{704}(351, \cdot)$$ 704.2.g.a 4 1
704.2.g.b 4
704.2.g.c 8
704.2.g.d 8
704.2.i $$\chi_{704}(175, \cdot)$$ 704.2.i.a 44 2
704.2.j $$\chi_{704}(177, \cdot)$$ 704.2.j.a 40 2
704.2.m $$\chi_{704}(257, \cdot)$$ 704.2.m.a 4 4
704.2.m.b 4
704.2.m.c 4
704.2.m.d 4
704.2.m.e 4
704.2.m.f 4
704.2.m.g 4
704.2.m.h 4
704.2.m.i 8
704.2.m.j 8
704.2.m.k 8
704.2.m.l 8
704.2.m.m 12
704.2.m.n 12
704.2.n $$\chi_{704}(89, \cdot)$$ None 0 4
704.2.q $$\chi_{704}(87, \cdot)$$ None 0 4
704.2.s $$\chi_{704}(95, \cdot)$$ 704.2.s.a 8 4
704.2.s.b 8
704.2.s.c 8
704.2.s.d 8
704.2.s.e 64
704.2.u $$\chi_{704}(63, \cdot)$$ 704.2.u.a 8 4
704.2.u.b 16
704.2.u.c 16
704.2.u.d 48
704.2.w $$\chi_{704}(97, \cdot)$$ 704.2.w.a 16 4
704.2.w.b 16
704.2.w.c 64
704.2.z $$\chi_{704}(45, \cdot)$$ 704.2.z.a 640 8
704.2.bb $$\chi_{704}(43, \cdot)$$ 704.2.bb.a 752 8
704.2.be $$\chi_{704}(49, \cdot)$$ 704.2.be.a 176 8
704.2.bf $$\chi_{704}(79, \cdot)$$ 704.2.bf.a 176 8
704.2.bg $$\chi_{704}(7, \cdot)$$ None 0 16
704.2.bj $$\chi_{704}(9, \cdot)$$ None 0 16
704.2.bk $$\chi_{704}(19, \cdot)$$ 704.2.bk.a 3008 32
704.2.bm $$\chi_{704}(5, \cdot)$$ 704.2.bm.a 3008 32

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(704))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(704)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(176))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(352))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(704))$$$$^{\oplus 1}$$