## Defining parameters

 Level: $$N$$ = $$966 = 2 \cdot 3 \cdot 7 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Newform subspaces: $$70$$ Sturm bound: $$101376$$ Trace bound: $$6$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(966))$$.

Total New Old
Modular forms 26400 6045 20355
Cusp forms 24289 6045 18244
Eisenstein series 2111 0 2111

## Trace form

 $$6045 q - 3 q^{2} + q^{3} + 5 q^{4} + 6 q^{5} + 9 q^{6} + 17 q^{7} - 3 q^{8} + 13 q^{9} + O(q^{10})$$ $$6045 q - 3 q^{2} + q^{3} + 5 q^{4} + 6 q^{5} + 9 q^{6} + 17 q^{7} - 3 q^{8} + 13 q^{9} + 6 q^{10} + 12 q^{11} + q^{12} - 10 q^{13} - 15 q^{14} + 26 q^{15} - 3 q^{16} + 58 q^{17} + 61 q^{18} + 60 q^{19} + 70 q^{20} + 31 q^{21} + 52 q^{22} + 141 q^{23} - 15 q^{24} + 131 q^{25} + 70 q^{26} + 133 q^{27} + 53 q^{28} + 46 q^{29} + 94 q^{30} + 72 q^{31} - 3 q^{32} + 56 q^{33} - 6 q^{34} + 50 q^{35} + 13 q^{36} + 174 q^{37} + 12 q^{38} + 102 q^{39} + 6 q^{40} + 58 q^{41} + 45 q^{42} + 204 q^{43} + 12 q^{44} + 6 q^{45} + q^{46} + 104 q^{47} + q^{48} + 129 q^{49} + 3 q^{50} + 10 q^{51} - 58 q^{52} - 2 q^{53} - 83 q^{54} + 32 q^{55} + 9 q^{56} - 48 q^{57} - 114 q^{58} + 4 q^{59} - 86 q^{60} - 106 q^{61} - 48 q^{62} - 157 q^{63} + 5 q^{64} - 84 q^{65} - 212 q^{66} - 156 q^{67} - 30 q^{68} - 243 q^{69} - 90 q^{70} - 72 q^{71} - 67 q^{72} - 118 q^{73} - 42 q^{74} - 281 q^{75} - 28 q^{76} + 36 q^{77} - 126 q^{78} + 88 q^{79} + 6 q^{80} + 21 q^{81} + 18 q^{82} + 76 q^{83} + 15 q^{84} + 148 q^{85} - 12 q^{86} + 162 q^{87} - 12 q^{88} + 10 q^{89} + 6 q^{90} + 102 q^{91} - 23 q^{92} - 40 q^{93} + 120 q^{95} - 15 q^{96} + 258 q^{97} + 37 q^{98} + 184 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(966))$$

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
966.2.a $$\chi_{966}(1, \cdot)$$ 966.2.a.a 1 1
966.2.a.b 1
966.2.a.c 1
966.2.a.d 1
966.2.a.e 1
966.2.a.f 1
966.2.a.g 1
966.2.a.h 1
966.2.a.i 1
966.2.a.j 1
966.2.a.k 1
966.2.a.l 2
966.2.a.m 2
966.2.a.n 2
966.2.a.o 2
966.2.a.p 2
966.2.f $$\chi_{966}(461, \cdot)$$ 966.2.f.a 4 1
966.2.f.b 24
966.2.f.c 28
966.2.g $$\chi_{966}(643, \cdot)$$ 966.2.g.a 4 1
966.2.g.b 4
966.2.g.c 4
966.2.g.d 4
966.2.g.e 16
966.2.h $$\chi_{966}(827, \cdot)$$ 966.2.h.a 24 1
966.2.h.b 24
966.2.i $$\chi_{966}(277, \cdot)$$ 966.2.i.a 2 2
966.2.i.b 2
966.2.i.c 2
966.2.i.d 2
966.2.i.e 2
966.2.i.f 2
966.2.i.g 2
966.2.i.h 4
966.2.i.i 4
966.2.i.j 4
966.2.i.k 6
966.2.i.l 8
966.2.i.m 8
966.2.i.n 8
966.2.j $$\chi_{966}(137, \cdot)$$ 966.2.j.a 128 2
966.2.k $$\chi_{966}(229, \cdot)$$ 966.2.k.a 32 2
966.2.k.b 32
966.2.l $$\chi_{966}(47, \cdot)$$ 966.2.l.a 4 2
966.2.l.b 4
966.2.l.c 56
966.2.l.d 56
966.2.q $$\chi_{966}(85, \cdot)$$ 966.2.q.a 10 10
966.2.q.b 10
966.2.q.c 10
966.2.q.d 20
966.2.q.e 20
966.2.q.f 30
966.2.q.g 30
966.2.q.h 30
966.2.q.i 40
966.2.q.j 40
966.2.r $$\chi_{966}(113, \cdot)$$ 966.2.r.a 240 10
966.2.r.b 240
966.2.s $$\chi_{966}(97, \cdot)$$ 966.2.s.a 160 10
966.2.s.b 160
966.2.t $$\chi_{966}(41, \cdot)$$ 966.2.t.a 640 10
966.2.y $$\chi_{966}(25, \cdot)$$ 966.2.y.a 160 20
966.2.y.b 160
966.2.y.c 160
966.2.y.d 160
966.2.bd $$\chi_{966}(59, \cdot)$$ 966.2.bd.a 1280 20
966.2.be $$\chi_{966}(19, \cdot)$$ 966.2.be.a 320 20
966.2.be.b 320
966.2.bf $$\chi_{966}(11, \cdot)$$ 966.2.bf.a 1280 20

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(966))$$ into lower level spaces

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