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Properties

Label 968.4
Level 968
Weight 4
Dimension 47918
Nonzero newspaces 12
Sturm bound 232320
Trace bound 2

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Defining parameters

Level: \( N \) = \( 968 = 2^{3} \cdot 11^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(232320\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(968))\).

Total New Old
Modular forms 88080 48480 39600
Cusp forms 86160 47918 38242
Eisenstein series 1920 562 1358

Trace form

\( 47918 q - 92 q^{2} - 94 q^{3} - 102 q^{4} - 2 q^{5} - 62 q^{6} - 82 q^{7} - 50 q^{8} - 193 q^{9} + O(q^{10}) \) \( 47918 q - 92 q^{2} - 94 q^{3} - 102 q^{4} - 2 q^{5} - 62 q^{6} - 82 q^{7} - 50 q^{8} - 193 q^{9} - 146 q^{10} - 100 q^{11} - 226 q^{12} + 22 q^{13} - 74 q^{14} + 450 q^{15} - 74 q^{16} - 178 q^{17} - 88 q^{18} - 496 q^{19} + 22 q^{20} - 936 q^{21} - 100 q^{22} - 910 q^{23} - 202 q^{24} - 635 q^{25} + 190 q^{26} + 332 q^{27} + 6 q^{28} + 898 q^{29} - 742 q^{30} + 1578 q^{31} - 2222 q^{32} - 1205 q^{33} - 3902 q^{34} - 1878 q^{35} - 2158 q^{36} - 162 q^{37} + 1014 q^{38} + 2022 q^{39} + 4474 q^{40} + 1702 q^{41} + 8706 q^{42} + 2522 q^{43} + 2910 q^{44} + 2482 q^{45} + 5394 q^{46} + 2970 q^{47} + 5642 q^{48} + 275 q^{49} + 24 q^{50} - 400 q^{51} - 3550 q^{52} + 3398 q^{53} - 10082 q^{54} - 1870 q^{55} - 9530 q^{56} - 3574 q^{57} - 4270 q^{58} - 2368 q^{59} - 3262 q^{60} - 1250 q^{61} - 538 q^{62} - 5598 q^{63} + 486 q^{64} - 4304 q^{65} - 100 q^{66} - 5022 q^{67} + 78 q^{68} - 4016 q^{69} + 7218 q^{70} - 9706 q^{71} + 15170 q^{72} - 8354 q^{73} + 10698 q^{74} - 8896 q^{75} + 7502 q^{76} + 1990 q^{77} + 1110 q^{78} + 6006 q^{79} - 8254 q^{80} + 9049 q^{81} - 11350 q^{82} + 15956 q^{83} - 17642 q^{84} + 9620 q^{85} - 16174 q^{86} + 21698 q^{87} - 14020 q^{88} + 6006 q^{89} - 26114 q^{90} + 23098 q^{91} - 8986 q^{92} + 17260 q^{93} - 11562 q^{94} + 9278 q^{95} - 4078 q^{96} + 3880 q^{97} + 5528 q^{98} - 4550 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(968))\)

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
968.4.a \(\chi_{968}(1, \cdot)\) 968.4.a.a 1 1
968.4.a.b 1
968.4.a.c 1
968.4.a.d 1
968.4.a.e 1
968.4.a.f 2
968.4.a.g 3
968.4.a.h 3
968.4.a.i 3
968.4.a.j 3
968.4.a.k 3
968.4.a.l 4
968.4.a.m 4
968.4.a.n 8
968.4.a.o 8
968.4.a.p 8
968.4.a.q 8
968.4.a.r 10
968.4.a.s 10
968.4.c \(\chi_{968}(485, \cdot)\) n/a 318 1
968.4.e \(\chi_{968}(967, \cdot)\) None 0 1
968.4.g \(\chi_{968}(483, \cdot)\) n/a 316 1
968.4.i \(\chi_{968}(9, \cdot)\) n/a 324 4
968.4.k \(\chi_{968}(403, \cdot)\) n/a 1264 4
968.4.m \(\chi_{968}(215, \cdot)\) None 0 4
968.4.o \(\chi_{968}(245, \cdot)\) n/a 1264 4
968.4.q \(\chi_{968}(89, \cdot)\) n/a 990 10
968.4.r \(\chi_{968}(87, \cdot)\) None 0 10
968.4.t \(\chi_{968}(45, \cdot)\) n/a 3940 10
968.4.w \(\chi_{968}(43, \cdot)\) n/a 3940 10
968.4.y \(\chi_{968}(25, \cdot)\) n/a 3960 40
968.4.ba \(\chi_{968}(19, \cdot)\) n/a 15760 40
968.4.bd \(\chi_{968}(5, \cdot)\) n/a 15760 40
968.4.bf \(\chi_{968}(7, \cdot)\) None 0 40

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(968))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(968)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 2}\)