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Properties

Label 966.6
Level 966
Weight 6
Dimension 30244
Nonzero newspaces 16
Sturm bound 304128
Trace bound 6

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Defining parameters

Level: \( N \) = \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(304128\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(966))\).

Total New Old
Modular forms 127776 30244 97532
Cusp forms 125664 30244 95420
Eisenstein series 2112 0 2112

Trace form

\( 30244 q + 16 q^{2} - 64 q^{4} + 288 q^{6} + 1280 q^{7} + 256 q^{8} - 1140 q^{9} + O(q^{10}) \) \( 30244 q + 16 q^{2} - 64 q^{4} + 288 q^{6} + 1280 q^{7} + 256 q^{8} - 1140 q^{9} - 4032 q^{10} - 2016 q^{11} + 6696 q^{13} + 1408 q^{14} + 28964 q^{15} + 1024 q^{16} - 39928 q^{17} - 26672 q^{18} - 5432 q^{19} + 11264 q^{20} + 12138 q^{21} + 41632 q^{22} + 78508 q^{23} + 1536 q^{24} + 45228 q^{25} - 43616 q^{26} - 88572 q^{27} - 58560 q^{28} - 101584 q^{29} - 90752 q^{30} - 14168 q^{31} + 4096 q^{32} + 240140 q^{33} + 48864 q^{34} + 55804 q^{35} - 25536 q^{36} - 205144 q^{37} + 10400 q^{38} - 201720 q^{39} - 64512 q^{40} - 112672 q^{41} - 127440 q^{42} + 108704 q^{43} - 32256 q^{44} - 11592 q^{45} + 97440 q^{46} + 479512 q^{47} + 66328 q^{49} + 203632 q^{50} + 78696 q^{51} + 31104 q^{52} - 386344 q^{53} - 312368 q^{54} - 504968 q^{55} - 61952 q^{56} + 118644 q^{57} - 164736 q^{58} + 378728 q^{59} + 83008 q^{60} - 390264 q^{61} + 221120 q^{62} - 223670 q^{63} + 180224 q^{64} - 195384 q^{65} - 952064 q^{66} + 28448 q^{67} - 130560 q^{68} - 898636 q^{69} + 128832 q^{70} + 259056 q^{71} - 106240 q^{72} + 1019712 q^{73} + 425984 q^{74} + 2494248 q^{75} + 195840 q^{76} - 280968 q^{77} + 862128 q^{78} - 2004888 q^{79} + 642020 q^{81} - 205728 q^{82} - 1216648 q^{83} - 368032 q^{84} - 877496 q^{85} - 222880 q^{86} - 668460 q^{87} - 244224 q^{88} + 550208 q^{89} + 108864 q^{90} + 1136632 q^{91} + 196224 q^{92} + 2382192 q^{93} + 773376 q^{94} + 5663040 q^{95} + 24576 q^{96} + 3041152 q^{97} - 277584 q^{98} + 89484 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(966))\)

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
966.6.a \(\chi_{966}(1, \cdot)\) 966.6.a.a 1 1
966.6.a.b 1
966.6.a.c 4
966.6.a.d 5
966.6.a.e 6
966.6.a.f 6
966.6.a.g 6
966.6.a.h 6
966.6.a.i 6
966.6.a.j 6
966.6.a.k 7
966.6.a.l 7
966.6.a.m 7
966.6.a.n 7
966.6.a.o 8
966.6.a.p 8
966.6.a.q 8
966.6.a.r 9
966.6.f \(\chi_{966}(461, \cdot)\) n/a 296 1
966.6.g \(\chi_{966}(643, \cdot)\) n/a 160 1
966.6.h \(\chi_{966}(827, \cdot)\) n/a 240 1
966.6.i \(\chi_{966}(277, \cdot)\) n/a 296 2
966.6.j \(\chi_{966}(137, \cdot)\) n/a 640 2
966.6.k \(\chi_{966}(229, \cdot)\) n/a 320 2
966.6.l \(\chi_{966}(47, \cdot)\) n/a 584 2
966.6.q \(\chi_{966}(85, \cdot)\) n/a 1200 10
966.6.r \(\chi_{966}(113, \cdot)\) n/a 2400 10
966.6.s \(\chi_{966}(97, \cdot)\) n/a 1600 10
966.6.t \(\chi_{966}(41, \cdot)\) n/a 3200 10
966.6.y \(\chi_{966}(25, \cdot)\) n/a 3200 20
966.6.bd \(\chi_{966}(59, \cdot)\) n/a 6400 20
966.6.be \(\chi_{966}(19, \cdot)\) n/a 3200 20
966.6.bf \(\chi_{966}(11, \cdot)\) n/a 6400 20

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(966))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(966)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(483))\)\(^{\oplus 2}\)