# Properties

 Label 704.6 Level 704 Weight 6 Dimension 42282 Nonzero newspaces 16 Sturm bound 184320 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$704 = 2^{6} \cdot 11$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$16$$ Sturm bound: $$184320$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(704))$$.

Total New Old
Modular forms 77520 42678 34842
Cusp forms 76080 42282 33798
Eisenstein series 1440 396 1044

## Trace form

 $$42282 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 44 q^{7} - 64 q^{8} + 406 q^{9} + O(q^{10})$$ $$42282 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 44 q^{7} - 64 q^{8} + 406 q^{9} - 64 q^{10} - 658 q^{11} - 144 q^{12} + 400 q^{13} - 64 q^{14} + 3548 q^{15} - 64 q^{16} + 1504 q^{17} - 64 q^{18} - 4768 q^{19} - 64 q^{20} - 10504 q^{21} - 13664 q^{22} - 104 q^{23} + 44016 q^{24} + 31098 q^{25} + 51856 q^{26} + 8388 q^{27} - 8784 q^{28} - 16352 q^{29} - 129824 q^{30} - 23132 q^{31} - 74384 q^{32} - 22256 q^{33} - 25664 q^{34} + 17228 q^{35} + 124576 q^{36} + 46832 q^{37} + 139216 q^{38} - 44 q^{39} + 124656 q^{40} - 26704 q^{41} - 92784 q^{42} - 30808 q^{43} - 65584 q^{44} + 46904 q^{45} - 64 q^{46} + 88308 q^{47} - 64 q^{48} + 24802 q^{49} + 274064 q^{50} - 89060 q^{51} - 147040 q^{52} - 77776 q^{53} - 466624 q^{54} + 220044 q^{55} - 301984 q^{56} - 70788 q^{57} - 52048 q^{58} - 175352 q^{59} + 395648 q^{60} + 100240 q^{61} + 350688 q^{62} - 659380 q^{63} + 749696 q^{64} - 27692 q^{65} + 254552 q^{66} - 395164 q^{67} + 14240 q^{68} - 287080 q^{69} - 573952 q^{70} + 575316 q^{71} - 828208 q^{72} + 169904 q^{73} - 755504 q^{74} + 1082400 q^{75} - 537024 q^{76} + 53204 q^{77} - 665472 q^{78} - 816492 q^{79} + 599664 q^{80} + 411146 q^{81} + 1006176 q^{82} + 455632 q^{83} + 1970016 q^{84} + 497904 q^{85} + 1443664 q^{86} - 64 q^{87} + 223208 q^{88} - 230548 q^{89} - 568864 q^{90} - 462372 q^{91} - 1842608 q^{92} - 722704 q^{93} - 1642624 q^{94} - 500820 q^{95} - 2428752 q^{96} - 1030592 q^{97} - 1914672 q^{98} - 298766 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(704))$$

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
704.6.a $$\chi_{704}(1, \cdot)$$ 704.6.a.a 1 1
704.6.a.b 1
704.6.a.c 1
704.6.a.d 1
704.6.a.e 1
704.6.a.f 1
704.6.a.g 1
704.6.a.h 1
704.6.a.i 1
704.6.a.j 1
704.6.a.k 2
704.6.a.l 2
704.6.a.m 2
704.6.a.n 2
704.6.a.o 2
704.6.a.p 2
704.6.a.q 3
704.6.a.r 3
704.6.a.s 3
704.6.a.t 3
704.6.a.u 4
704.6.a.v 4
704.6.a.w 4
704.6.a.x 4
704.6.a.y 6
704.6.a.z 6
704.6.a.ba 6
704.6.a.bb 6
704.6.a.bc 6
704.6.a.bd 6
704.6.a.be 7
704.6.a.bf 7
704.6.c $$\chi_{704}(353, \cdot)$$ 704.6.c.a 16 1
704.6.c.b 20
704.6.c.c 28
704.6.c.d 36
704.6.e $$\chi_{704}(703, \cdot)$$ n/a 118 1
704.6.g $$\chi_{704}(351, \cdot)$$ n/a 120 1
704.6.i $$\chi_{704}(175, \cdot)$$ n/a 236 2
704.6.j $$\chi_{704}(177, \cdot)$$ n/a 200 2
704.6.m $$\chi_{704}(257, \cdot)$$ n/a 472 4
704.6.n $$\chi_{704}(89, \cdot)$$ None 0 4
704.6.q $$\chi_{704}(87, \cdot)$$ None 0 4
704.6.s $$\chi_{704}(95, \cdot)$$ n/a 480 4
704.6.u $$\chi_{704}(63, \cdot)$$ n/a 472 4
704.6.w $$\chi_{704}(97, \cdot)$$ n/a 480 4
704.6.z $$\chi_{704}(45, \cdot)$$ n/a 3200 8
704.6.bb $$\chi_{704}(43, \cdot)$$ n/a 3824 8
704.6.be $$\chi_{704}(49, \cdot)$$ n/a 944 8
704.6.bf $$\chi_{704}(79, \cdot)$$ n/a 944 8
704.6.bg $$\chi_{704}(7, \cdot)$$ None 0 16
704.6.bj $$\chi_{704}(9, \cdot)$$ None 0 16
704.6.bk $$\chi_{704}(19, \cdot)$$ n/a 15296 32
704.6.bm $$\chi_{704}(5, \cdot)$$ n/a 15296 32

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

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(704))$$ into lower level spaces

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