# Properties

 Label 966.4 Level 966 Weight 4 Dimension 18148 Nonzero newspaces 16 Sturm bound 202752 Trace bound 6

## Defining parameters

 Level: $$N$$ = $$966 = 2 \cdot 3 \cdot 7 \cdot 23$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$16$$ Sturm bound: $$202752$$ Trace bound: $$6$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(966))$$.

Total New Old
Modular forms 77088 18148 58940
Cusp forms 74976 18148 56828
Eisenstein series 2112 0 2112

## Trace form

 $$18148 q - 8 q^{2} + 12 q^{3} + 16 q^{4} - 72 q^{5} - 48 q^{6} - 224 q^{7} - 32 q^{8} + 120 q^{9} + O(q^{10})$$ $$18148 q - 8 q^{2} + 12 q^{3} + 16 q^{4} - 72 q^{5} - 48 q^{6} - 224 q^{7} - 32 q^{8} + 120 q^{9} + 96 q^{10} + 216 q^{11} + 48 q^{12} + 128 q^{13} + 64 q^{14} + 920 q^{15} + 64 q^{16} + 176 q^{17} + 88 q^{18} - 32 q^{19} - 1312 q^{20} + 72 q^{21} - 2032 q^{22} - 3620 q^{23} + 192 q^{24} - 2332 q^{25} - 272 q^{26} - 480 q^{27} + 416 q^{28} + 1688 q^{29} + 1792 q^{30} + 2512 q^{31} - 128 q^{32} + 1100 q^{33} - 624 q^{34} + 916 q^{35} - 1488 q^{36} + 6944 q^{37} + 272 q^{38} + 1296 q^{39} + 384 q^{40} - 1264 q^{41} + 456 q^{42} - 7264 q^{43} + 864 q^{44} + 4140 q^{45} - 1008 q^{46} - 7232 q^{47} - 384 q^{48} - 13016 q^{49} - 3704 q^{50} - 6108 q^{51} - 832 q^{52} - 760 q^{53} - 6392 q^{54} + 11304 q^{55} + 448 q^{56} + 2664 q^{57} + 4800 q^{58} + 14360 q^{59} + 2560 q^{60} + 13208 q^{61} + 7136 q^{62} + 13240 q^{63} + 1792 q^{64} + 2256 q^{65} + 15232 q^{66} + 2192 q^{67} - 2112 q^{68} + 12296 q^{69} - 1632 q^{70} - 4464 q^{71} + 3296 q^{72} - 10936 q^{73} - 1024 q^{74} + 7020 q^{75} - 544 q^{76} - 168 q^{77} - 8232 q^{78} - 392 q^{79} - 1152 q^{80} - 13744 q^{81} - 4272 q^{82} + 2312 q^{83} - 5224 q^{84} - 2488 q^{85} - 1936 q^{86} - 14556 q^{87} + 960 q^{88} - 10048 q^{89} - 2592 q^{90} - 11576 q^{91} - 768 q^{92} - 3396 q^{93} - 3072 q^{94} + 912 q^{95} + 768 q^{96} + 39160 q^{97} + 13992 q^{98} + 7404 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(966))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
966.4.a $$\chi_{966}(1, \cdot)$$ 966.4.a.a 1 1
966.4.a.b 1
966.4.a.c 2
966.4.a.d 3
966.4.a.e 3
966.4.a.f 3
966.4.a.g 3
966.4.a.h 4
966.4.a.i 4
966.4.a.j 4
966.4.a.k 4
966.4.a.l 5
966.4.a.m 5
966.4.a.n 5
966.4.a.o 5
966.4.a.p 5
966.4.a.q 5
966.4.a.r 6
966.4.f $$\chi_{966}(461, \cdot)$$ n/a 176 1
966.4.g $$\chi_{966}(643, \cdot)$$ 966.4.g.a 48 1
966.4.g.b 48
966.4.h $$\chi_{966}(827, \cdot)$$ n/a 144 1
966.4.i $$\chi_{966}(277, \cdot)$$ n/a 176 2
966.4.j $$\chi_{966}(137, \cdot)$$ n/a 384 2
966.4.k $$\chi_{966}(229, \cdot)$$ n/a 192 2
966.4.l $$\chi_{966}(47, \cdot)$$ n/a 352 2
966.4.q $$\chi_{966}(85, \cdot)$$ n/a 720 10
966.4.r $$\chi_{966}(113, \cdot)$$ n/a 1440 10
966.4.s $$\chi_{966}(97, \cdot)$$ n/a 960 10
966.4.t $$\chi_{966}(41, \cdot)$$ n/a 1920 10
966.4.y $$\chi_{966}(25, \cdot)$$ n/a 1920 20
966.4.bd $$\chi_{966}(59, \cdot)$$ n/a 3840 20
966.4.be $$\chi_{966}(19, \cdot)$$ n/a 1920 20
966.4.bf $$\chi_{966}(11, \cdot)$$ n/a 3840 20

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(966))$$ into lower level spaces

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