## Defining parameters

 Level: $$N$$ = $$714 = 2 \cdot 3 \cdot 7 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$20$$ Newform subspaces: $$86$$ Sturm bound: $$55296$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(714))$$.

Total New Old
Modular forms 14592 3285 11307
Cusp forms 13057 3285 9772
Eisenstein series 1535 0 1535

## Trace form

 $$3285 q - 3 q^{2} + q^{3} + 5 q^{4} + 6 q^{5} + 9 q^{6} + 17 q^{7} - 3 q^{8} + 13 q^{9} + O(q^{10})$$ $$3285 q - 3 q^{2} + q^{3} + 5 q^{4} + 6 q^{5} + 9 q^{6} + 17 q^{7} - 3 q^{8} + 13 q^{9} + 22 q^{10} + 76 q^{11} + 17 q^{12} + 54 q^{13} + 17 q^{14} + 78 q^{15} + 13 q^{16} + 41 q^{17} + 37 q^{18} + 36 q^{19} - 2 q^{20} + 13 q^{21} + 28 q^{22} + 16 q^{23} + q^{24} + 99 q^{25} - 2 q^{26} + q^{27} + 9 q^{28} + 38 q^{29} + 6 q^{30} + 112 q^{31} - 3 q^{32} + 76 q^{33} - 11 q^{34} + 70 q^{35} + 13 q^{36} + 126 q^{37} + 12 q^{38} + 14 q^{39} + 6 q^{40} + 50 q^{41} - 3 q^{42} + 124 q^{43} + 12 q^{44} - 106 q^{45} + 24 q^{46} - 72 q^{47} + q^{48} - 3 q^{49} + 3 q^{50} - 175 q^{51} - 58 q^{52} - 74 q^{53} - 151 q^{54} - 80 q^{55} + 9 q^{56} - 148 q^{57} - 114 q^{58} - 20 q^{59} - 106 q^{60} - 42 q^{61} - 48 q^{62} - 47 q^{63} + 5 q^{64} - 68 q^{65} - 52 q^{66} - 92 q^{67} - 7 q^{68} + 104 q^{69} - 26 q^{70} + 120 q^{71} + 37 q^{72} + 218 q^{73} + 102 q^{74} + 207 q^{75} - 28 q^{76} + 196 q^{77} + 134 q^{78} + 320 q^{79} + 70 q^{80} + 125 q^{81} + 290 q^{82} + 244 q^{83} + 69 q^{84} + 382 q^{85} + 116 q^{86} + 126 q^{87} + 116 q^{88} + 114 q^{89} + 22 q^{90} + 206 q^{91} + 40 q^{92} - 40 q^{93} + 256 q^{94} + 112 q^{95} - 15 q^{96} + 162 q^{97} - 35 q^{98} - 244 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(714))$$

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
714.2.a $$\chi_{714}(1, \cdot)$$ 714.2.a.a 1 1
714.2.a.b 1
714.2.a.c 1
714.2.a.d 1
714.2.a.e 1
714.2.a.f 1
714.2.a.g 1
714.2.a.h 1
714.2.a.i 1
714.2.a.j 2
714.2.a.k 2
714.2.a.l 2
714.2.a.m 2
714.2.b $$\chi_{714}(169, \cdot)$$ 714.2.b.a 2 1
714.2.b.b 2
714.2.b.c 2
714.2.b.d 2
714.2.b.e 4
714.2.b.f 8
714.2.e $$\chi_{714}(713, \cdot)$$ 714.2.e.a 48 1
714.2.f $$\chi_{714}(545, \cdot)$$ 714.2.f.a 20 1
714.2.f.b 20
714.2.i $$\chi_{714}(205, \cdot)$$ 714.2.i.a 2 2
714.2.i.b 2
714.2.i.c 2
714.2.i.d 2
714.2.i.e 2
714.2.i.f 2
714.2.i.g 2
714.2.i.h 2
714.2.i.i 2
714.2.i.j 2
714.2.i.k 2
714.2.i.l 4
714.2.i.m 4
714.2.i.n 4
714.2.i.o 6
714.2.k $$\chi_{714}(251, \cdot)$$ 714.2.k.a 8 2
714.2.k.b 8
714.2.k.c 40
714.2.k.d 40
714.2.m $$\chi_{714}(421, \cdot)$$ 714.2.m.a 4 2
714.2.m.b 4
714.2.m.c 8
714.2.m.d 12
714.2.m.e 12
714.2.p $$\chi_{714}(341, \cdot)$$ 714.2.p.a 44 2
714.2.p.b 44
714.2.q $$\chi_{714}(101, \cdot)$$ 714.2.q.a 96 2
714.2.t $$\chi_{714}(67, \cdot)$$ 714.2.t.a 4 2
714.2.t.b 4
714.2.t.c 4
714.2.t.d 8
714.2.t.e 8
714.2.t.f 8
714.2.t.g 12
714.2.u $$\chi_{714}(43, \cdot)$$ 714.2.u.a 8 4
714.2.u.b 16
714.2.u.c 16
714.2.u.d 24
714.2.w $$\chi_{714}(83, \cdot)$$ 714.2.w.a 8 4
714.2.w.b 8
714.2.w.c 8
714.2.w.d 8
714.2.w.e 80
714.2.w.f 80
714.2.y $$\chi_{714}(47, \cdot)$$ 714.2.y.a 96 4
714.2.y.b 96
714.2.ba $$\chi_{714}(319, \cdot)$$ 714.2.ba.a 8 4
714.2.ba.b 8
714.2.ba.c 8
714.2.ba.d 16
714.2.ba.e 24
714.2.ba.f 32
714.2.be $$\chi_{714}(97, \cdot)$$ 714.2.be.a 96 8
714.2.be.b 96
714.2.bf $$\chi_{714}(29, \cdot)$$ 714.2.bf.a 144 8
714.2.bf.b 144
714.2.bh $$\chi_{714}(25, \cdot)$$ 714.2.bh.a 96 8
714.2.bh.b 96
714.2.bj $$\chi_{714}(59, \cdot)$$ 714.2.bj.a 192 8
714.2.bj.b 192
714.2.bk $$\chi_{714}(11, \cdot)$$ 714.2.bk.a 384 16
714.2.bk.b 384
714.2.bl $$\chi_{714}(31, \cdot)$$ 714.2.bl.a 192 16
714.2.bl.b 192

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(714))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(714)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(102))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(119))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(238))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(357))$$$$^{\oplus 2}$$