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Properties

Label 847.4
Level 847
Weight 4
Dimension 81413
Nonzero newspaces 16
Sturm bound 232320
Trace bound 2

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Defining parameters

Level: \( N \) = \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(232320\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(847))\).

Total New Old
Modular forms 88080 82817 5263
Cusp forms 86160 81413 4747
Eisenstein series 1920 1404 516

Trace form

\( 81413 q - 183 q^{2} - 189 q^{3} - 183 q^{4} - 171 q^{5} - 350 q^{6} - 224 q^{7} - 323 q^{8} + 95 q^{9} + O(q^{10}) \) \( 81413 q - 183 q^{2} - 189 q^{3} - 183 q^{4} - 171 q^{5} - 350 q^{6} - 224 q^{7} - 323 q^{8} + 95 q^{9} + 170 q^{10} - 100 q^{11} + 342 q^{12} - 100 q^{13} - 594 q^{14} - 1624 q^{15} - 1643 q^{16} - 705 q^{17} - 221 q^{18} + 561 q^{19} + 1392 q^{20} + 374 q^{21} + 760 q^{22} - 533 q^{23} - 802 q^{24} - 213 q^{25} - 880 q^{26} - 570 q^{27} - 366 q^{28} - 644 q^{29} - 1746 q^{30} - 1875 q^{31} + 399 q^{32} - 610 q^{33} - 1838 q^{34} - 148 q^{35} - 285 q^{36} - 85 q^{37} + 1372 q^{38} + 2942 q^{39} + 408 q^{40} + 2742 q^{41} + 223 q^{42} - 3390 q^{43} - 2430 q^{44} + 2698 q^{45} + 3670 q^{46} + 1979 q^{47} + 5214 q^{48} + 1902 q^{49} - 525 q^{50} - 1761 q^{51} - 5012 q^{52} - 8565 q^{53} - 13030 q^{54} - 3400 q^{55} - 4062 q^{56} - 5164 q^{57} + 4634 q^{58} + 5995 q^{59} + 20020 q^{60} + 10865 q^{61} + 26856 q^{62} + 19540 q^{63} + 22279 q^{64} + 14106 q^{65} + 10570 q^{66} + 4569 q^{67} + 3338 q^{68} - 4802 q^{69} - 12553 q^{70} - 11242 q^{71} - 39597 q^{72} - 21489 q^{73} - 23032 q^{74} - 38130 q^{75} - 44562 q^{76} - 9320 q^{77} - 43786 q^{78} - 14397 q^{79} - 51632 q^{80} - 31060 q^{81} - 24022 q^{82} - 3318 q^{83} - 16549 q^{84} + 10520 q^{85} + 8620 q^{86} + 23894 q^{87} + 19240 q^{88} + 18119 q^{89} + 51104 q^{90} + 26147 q^{91} + 29906 q^{92} + 23207 q^{93} + 24906 q^{94} + 20237 q^{95} + 30962 q^{96} + 1770 q^{97} - 2306 q^{98} + 2740 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(847))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
847.4.a \(\chi_{847}(1, \cdot)\) 847.4.a.a 1 1
847.4.a.b 1
847.4.a.c 2
847.4.a.d 4
847.4.a.e 4
847.4.a.f 5
847.4.a.g 7
847.4.a.h 7
847.4.a.i 8
847.4.a.j 8
847.4.a.k 8
847.4.a.l 8
847.4.a.m 14
847.4.a.n 14
847.4.a.o 16
847.4.a.p 16
847.4.a.q 20
847.4.a.r 20
847.4.b \(\chi_{847}(846, \cdot)\) n/a 208 1
847.4.e \(\chi_{847}(485, \cdot)\) n/a 418 2
847.4.f \(\chi_{847}(148, \cdot)\) n/a 648 4
847.4.i \(\chi_{847}(241, \cdot)\) n/a 416 2
847.4.l \(\chi_{847}(118, \cdot)\) n/a 832 4
847.4.m \(\chi_{847}(78, \cdot)\) n/a 1980 10
847.4.n \(\chi_{847}(9, \cdot)\) n/a 1664 8
847.4.p \(\chi_{847}(76, \cdot)\) n/a 2620 10
847.4.r \(\chi_{847}(40, \cdot)\) n/a 1664 8
847.4.u \(\chi_{847}(23, \cdot)\) n/a 5240 20
847.4.v \(\chi_{847}(15, \cdot)\) n/a 7920 40
847.4.x \(\chi_{847}(10, \cdot)\) n/a 5240 20
847.4.ba \(\chi_{847}(6, \cdot)\) n/a 10480 40
847.4.bc \(\chi_{847}(4, \cdot)\) n/a 20960 80
847.4.be \(\chi_{847}(17, \cdot)\) n/a 20960 80

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(847))\) into lower level spaces

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