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Properties

Label 968.6
Level 968
Weight 6
Dimension 80050
Nonzero newspaces 12
Sturm bound 348480
Trace bound 2

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Defining parameters

Level: \( N \) = \( 968 = 2^{3} \cdot 11^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(348480\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(968))\).

Total New Old
Modular forms 146160 80612 65548
Cusp forms 144240 80050 64190
Eisenstein series 1920 562 1358

Trace form

\( 80050 q - 92 q^{2} - 70 q^{3} - 70 q^{4} - 74 q^{5} - 206 q^{6} - 18 q^{7} - 338 q^{8} - 187 q^{9} + O(q^{10}) \) \( 80050 q - 92 q^{2} - 70 q^{3} - 70 q^{4} - 74 q^{5} - 206 q^{6} - 18 q^{7} - 338 q^{8} - 187 q^{9} + 542 q^{10} - 100 q^{11} + 1406 q^{12} + 478 q^{13} - 2474 q^{14} - 3966 q^{15} - 3402 q^{16} - 6598 q^{17} + 4664 q^{18} + 7424 q^{19} + 4534 q^{20} + 17160 q^{21} - 100 q^{22} + 7730 q^{23} - 7882 q^{24} - 9033 q^{25} + 5518 q^{26} - 28540 q^{27} + 5062 q^{28} - 15902 q^{29} - 7078 q^{30} + 14474 q^{31} - 75662 q^{32} - 18035 q^{33} + 38658 q^{34} + 85626 q^{35} + 244946 q^{36} + 10326 q^{37} + 93990 q^{38} + 55974 q^{39} - 68198 q^{40} - 85934 q^{41} - 386814 q^{42} - 120238 q^{43} - 126450 q^{44} - 101678 q^{45} - 104590 q^{46} - 43686 q^{47} + 183146 q^{48} + 89117 q^{49} + 295272 q^{50} + 457640 q^{51} + 300450 q^{52} + 37646 q^{53} + 350398 q^{54} - 69630 q^{55} - 223802 q^{56} - 473722 q^{57} - 293086 q^{58} - 94864 q^{59} - 59998 q^{60} + 23478 q^{61} + 34406 q^{62} + 96162 q^{63} - 42010 q^{64} + 282928 q^{65} - 100 q^{66} + 280378 q^{67} + 10254 q^{68} + 140080 q^{69} + 267122 q^{70} - 573802 q^{71} + 637538 q^{72} - 197990 q^{73} - 330726 q^{74} + 531920 q^{75} - 1047506 q^{76} - 48830 q^{77} - 1688394 q^{78} + 690998 q^{79} - 686590 q^{80} + 432703 q^{81} + 400842 q^{82} - 253036 q^{83} + 1365142 q^{84} - 657868 q^{85} + 1123010 q^{86} - 1574398 q^{87} + 1196860 q^{88} - 425118 q^{89} + 1981870 q^{90} - 516022 q^{91} + 301094 q^{92} + 62980 q^{93} - 718314 q^{94} + 201950 q^{95} - 1630798 q^{96} + 115760 q^{97} - 2609512 q^{98} + 728050 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(968))\)

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
968.6.a \(\chi_{968}(1, \cdot)\) 968.6.a.a 1 1
968.6.a.b 2
968.6.a.c 3
968.6.a.d 4
968.6.a.e 4
968.6.a.f 6
968.6.a.g 6
968.6.a.h 6
968.6.a.i 6
968.6.a.j 7
968.6.a.k 7
968.6.a.l 12
968.6.a.m 12
968.6.a.n 14
968.6.a.o 14
968.6.a.p 16
968.6.a.q 16
968.6.c \(\chi_{968}(485, \cdot)\) n/a 536 1
968.6.e \(\chi_{968}(967, \cdot)\) None 0 1
968.6.g \(\chi_{968}(483, \cdot)\) n/a 532 1
968.6.i \(\chi_{968}(9, \cdot)\) n/a 540 4
968.6.k \(\chi_{968}(403, \cdot)\) n/a 2128 4
968.6.m \(\chi_{968}(215, \cdot)\) None 0 4
968.6.o \(\chi_{968}(245, \cdot)\) n/a 2128 4
968.6.q \(\chi_{968}(89, \cdot)\) n/a 1650 10
968.6.r \(\chi_{968}(87, \cdot)\) None 0 10
968.6.t \(\chi_{968}(45, \cdot)\) n/a 6580 10
968.6.w \(\chi_{968}(43, \cdot)\) n/a 6580 10
968.6.y \(\chi_{968}(25, \cdot)\) n/a 6600 40
968.6.ba \(\chi_{968}(19, \cdot)\) n/a 26320 40
968.6.bd \(\chi_{968}(5, \cdot)\) n/a 26320 40
968.6.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 \(S_{6}^{\mathrm{old}}(\Gamma_1(968))\) into lower level spaces

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