# Properties

 Label 847.6 Level 847 Weight 6 Dimension 136157 Nonzero newspaces 16 Sturm bound 348480 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$847 = 7 \cdot 11^{2}$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$16$$ Sturm bound: $$348480$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(847))$$.

Total New Old
Modular forms 146160 137561 8599
Cusp forms 144240 136157 8083
Eisenstein series 1920 1404 516

## Trace form

 $$136157 q - 183 q^{2} - 192 q^{3} - 119 q^{4} - 216 q^{5} - 482 q^{6} + 246 q^{7} + 13 q^{8} - 1489 q^{9} + O(q^{10})$$ $$136157 q - 183 q^{2} - 192 q^{3} - 119 q^{4} - 216 q^{5} - 482 q^{6} + 246 q^{7} + 13 q^{8} - 1489 q^{9} - 2658 q^{10} - 1090 q^{11} - 3930 q^{12} - 498 q^{13} - 2958 q^{14} + 15422 q^{15} + 35981 q^{16} + 9264 q^{17} - 7565 q^{18} - 12124 q^{19} - 39624 q^{20} - 19009 q^{21} - 25640 q^{22} - 37196 q^{23} - 3946 q^{24} + 46201 q^{25} + 133868 q^{26} + 96972 q^{27} + 64026 q^{28} + 12460 q^{29} - 105306 q^{30} - 112592 q^{31} - 306273 q^{32} - 85420 q^{33} + 20138 q^{34} + 67043 q^{35} + 279771 q^{36} + 122284 q^{37} + 207232 q^{38} + 103520 q^{39} + 140720 q^{40} - 58530 q^{41} - 254549 q^{42} - 236370 q^{43} - 185910 q^{44} - 308450 q^{45} + 87542 q^{46} + 165020 q^{47} + 424110 q^{48} + 140028 q^{49} + 291603 q^{50} + 202128 q^{51} - 367196 q^{52} + 44808 q^{53} + 76586 q^{54} + 24320 q^{55} + 19482 q^{56} - 80698 q^{57} + 73026 q^{58} + 261400 q^{59} + 620044 q^{60} + 673720 q^{61} + 98976 q^{62} + 91210 q^{63} - 590449 q^{64} - 909876 q^{65} - 1275110 q^{66} - 1021772 q^{67} - 2169430 q^{68} - 1345100 q^{69} - 1074509 q^{70} - 340450 q^{71} + 1033563 q^{72} + 817300 q^{73} + 2943944 q^{74} + 3732828 q^{75} + 4663206 q^{76} + 906265 q^{77} + 4108358 q^{78} + 1686336 q^{79} + 419008 q^{80} - 1227271 q^{81} - 2409310 q^{82} - 1806456 q^{83} - 3419821 q^{84} - 1909270 q^{85} - 2242844 q^{86} - 2944900 q^{87} - 1475880 q^{88} - 741040 q^{89} - 3725764 q^{90} - 1087413 q^{91} - 761614 q^{92} + 823058 q^{93} + 2025434 q^{94} + 2336912 q^{95} + 3519986 q^{96} + 2623914 q^{97} + 2396350 q^{98} + 1452100 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(847))$$

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
847.6.a $$\chi_{847}(1, \cdot)$$ 847.6.a.a 1 1
847.6.a.b 1
847.6.a.c 2
847.6.a.d 4
847.6.a.e 5
847.6.a.f 6
847.6.a.g 8
847.6.a.h 12
847.6.a.i 12
847.6.a.j 12
847.6.a.k 12
847.6.a.l 13
847.6.a.m 13
847.6.a.n 26
847.6.a.o 26
847.6.a.p 28
847.6.a.q 28
847.6.a.r 32
847.6.a.s 32
847.6.b $$\chi_{847}(846, \cdot)$$ n/a 352 1
847.6.e $$\chi_{847}(485, \cdot)$$ n/a 708 2
847.6.f $$\chi_{847}(148, \cdot)$$ n/a 1080 4
847.6.i $$\chi_{847}(241, \cdot)$$ n/a 704 2
847.6.l $$\chi_{847}(118, \cdot)$$ n/a 1408 4
847.6.m $$\chi_{847}(78, \cdot)$$ n/a 3300 10
847.6.n $$\chi_{847}(9, \cdot)$$ n/a 2816 8
847.6.p $$\chi_{847}(76, \cdot)$$ n/a 4380 10
847.6.r $$\chi_{847}(40, \cdot)$$ n/a 2816 8
847.6.u $$\chi_{847}(23, \cdot)$$ n/a 8760 20
847.6.v $$\chi_{847}(15, \cdot)$$ n/a 13200 40
847.6.x $$\chi_{847}(10, \cdot)$$ n/a 8760 20
847.6.ba $$\chi_{847}(6, \cdot)$$ n/a 17520 40
847.6.bc $$\chi_{847}(4, \cdot)$$ n/a 35040 80
847.6.be $$\chi_{847}(17, \cdot)$$ n/a 35040 80

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

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(847))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(847)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 2}$$