# Properties

 Label 546.2 Level 546 Weight 2 Dimension 1905 Nonzero newspaces 30 Newform subspaces 124 Sturm bound 32256 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$30$$ Newform subspaces: $$124$$ Sturm bound: $$32256$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(546))$$.

Total New Old
Modular forms 8640 1905 6735
Cusp forms 7489 1905 5584
Eisenstein series 1151 0 1151

## Trace form

 $$1905 q - 3 q^{2} + q^{3} + 5 q^{4} + 6 q^{5} + 9 q^{6} + 25 q^{7} + 9 q^{8} + 21 q^{9} + O(q^{10})$$ $$1905 q - 3 q^{2} + q^{3} + 5 q^{4} + 6 q^{5} + 9 q^{6} + 25 q^{7} + 9 q^{8} + 21 q^{9} + 66 q^{10} + 60 q^{11} + 9 q^{12} + 85 q^{13} + 9 q^{14} + 30 q^{15} + 13 q^{16} + 30 q^{17} - 15 q^{18} + 84 q^{19} - 6 q^{20} - 7 q^{21} - 36 q^{22} - 15 q^{24} + 15 q^{25} - 15 q^{26} + 73 q^{27} + 9 q^{28} + 18 q^{29} - 42 q^{30} + 32 q^{31} - 3 q^{32} - 12 q^{33} - 6 q^{34} + 30 q^{35} - 35 q^{36} + 10 q^{37} + 12 q^{38} - 87 q^{39} + 6 q^{40} - 18 q^{41} + 9 q^{42} + 92 q^{43} + 12 q^{44} - 102 q^{45} + 24 q^{46} - 24 q^{47} + q^{48} + 5 q^{49} + 15 q^{50} - 30 q^{51} - 23 q^{52} + 54 q^{53} + 33 q^{54} + 96 q^{55} + 33 q^{56} + 124 q^{57} - 6 q^{58} + 108 q^{59} + 6 q^{60} + 50 q^{61} + 96 q^{62} + 17 q^{63} + 17 q^{64} + 126 q^{65} + 60 q^{66} + 52 q^{67} - 18 q^{68} + 72 q^{69} - 18 q^{70} + 24 q^{71} + 69 q^{72} - 6 q^{73} - 30 q^{74} - 129 q^{75} - 108 q^{76} - 252 q^{77} - 27 q^{78} - 288 q^{79} + 18 q^{80} + 45 q^{81} - 354 q^{82} - 300 q^{83} - 103 q^{84} - 504 q^{85} - 204 q^{86} - 354 q^{87} - 12 q^{88} - 414 q^{89} - 90 q^{90} - 519 q^{91} - 216 q^{92} - 272 q^{93} - 480 q^{94} - 528 q^{95} - 15 q^{96} - 670 q^{97} - 291 q^{98} - 108 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(546))$$

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
546.2.a $$\chi_{546}(1, \cdot)$$ 546.2.a.a 1 1
546.2.a.b 1
546.2.a.c 1
546.2.a.d 1
546.2.a.e 1
546.2.a.f 1
546.2.a.g 1
546.2.a.h 2
546.2.a.i 2
546.2.a.j 2
546.2.c $$\chi_{546}(337, \cdot)$$ 546.2.c.a 2 1
546.2.c.b 2
546.2.c.c 2
546.2.c.d 2
546.2.c.e 4
546.2.e $$\chi_{546}(545, \cdot)$$ 546.2.e.a 2 1
546.2.e.b 2
546.2.e.c 2
546.2.e.d 2
546.2.e.e 8
546.2.e.f 8
546.2.e.g 8
546.2.e.h 8
546.2.g $$\chi_{546}(209, \cdot)$$ 546.2.g.a 4 1
546.2.g.b 4
546.2.g.c 12
546.2.g.d 12
546.2.i $$\chi_{546}(79, \cdot)$$ 546.2.i.a 2 2
546.2.i.b 2
546.2.i.c 2
546.2.i.d 2
546.2.i.e 2
546.2.i.f 2
546.2.i.g 2
546.2.i.h 4
546.2.i.i 4
546.2.i.j 4
546.2.i.k 6
546.2.j $$\chi_{546}(289, \cdot)$$ 546.2.j.a 2 2
546.2.j.b 8
546.2.j.c 8
546.2.j.d 8
546.2.j.e 10
546.2.k $$\chi_{546}(373, \cdot)$$ 546.2.k.a 2 2
546.2.k.b 8
546.2.k.c 8
546.2.k.d 8
546.2.k.e 10
546.2.l $$\chi_{546}(211, \cdot)$$ 546.2.l.a 2 2
546.2.l.b 2
546.2.l.c 2
546.2.l.d 2
546.2.l.e 2
546.2.l.f 2
546.2.l.g 2
546.2.l.h 2
546.2.l.i 4
546.2.l.j 4
546.2.l.k 4
546.2.l.l 4
546.2.o $$\chi_{546}(265, \cdot)$$ 546.2.o.a 8 2
546.2.o.b 8
546.2.o.c 8
546.2.o.d 8
546.2.p $$\chi_{546}(239, \cdot)$$ 546.2.p.a 8 2
546.2.p.b 8
546.2.p.c 20
546.2.p.d 20
546.2.q $$\chi_{546}(251, \cdot)$$ 546.2.q.a 2 2
546.2.q.b 2
546.2.q.c 2
546.2.q.d 2
546.2.q.e 4
546.2.q.f 4
546.2.q.g 4
546.2.q.h 4
546.2.q.i 24
546.2.q.j 24
546.2.s $$\chi_{546}(43, \cdot)$$ 546.2.s.a 4 2
546.2.s.b 4
546.2.s.c 4
546.2.s.d 4
546.2.s.e 8
546.2.u $$\chi_{546}(185, \cdot)$$ 546.2.u.a 76 2
546.2.z $$\chi_{546}(131, \cdot)$$ 546.2.z.a 32 2
546.2.z.b 32
546.2.bb $$\chi_{546}(269, \cdot)$$ 546.2.bb.a 76 2
546.2.bd $$\chi_{546}(121, \cdot)$$ 546.2.bd.a 16 2
546.2.bd.b 20
546.2.bg $$\chi_{546}(311, \cdot)$$ 546.2.bg.a 36 2
546.2.bg.b 36
546.2.bi $$\chi_{546}(17, \cdot)$$ 546.2.bi.a 2 2
546.2.bi.b 2
546.2.bi.c 2
546.2.bi.d 2
546.2.bi.e 34
546.2.bi.f 34
546.2.bk $$\chi_{546}(25, \cdot)$$ 546.2.bk.a 8 2
546.2.bk.b 12
546.2.bk.c 20
546.2.bm $$\chi_{546}(205, \cdot)$$ 546.2.bm.a 16 2
546.2.bm.b 20
546.2.bn $$\chi_{546}(101, \cdot)$$ 546.2.bn.a 2 2
546.2.bn.b 2
546.2.bn.c 2
546.2.bn.d 2
546.2.bn.e 34
546.2.bn.f 34
546.2.bq $$\chi_{546}(419, \cdot)$$ 546.2.bq.a 4 2
546.2.bq.b 4
546.2.bq.c 64
546.2.bu $$\chi_{546}(71, \cdot)$$ 546.2.bu.a 56 4
546.2.bu.b 56
546.2.bv $$\chi_{546}(317, \cdot)$$ 546.2.bv.a 144 4
546.2.bw $$\chi_{546}(11, \cdot)$$ 546.2.bw.a 152 4
546.2.bx $$\chi_{546}(97, \cdot)$$ 546.2.bx.a 40 4
546.2.bx.b 40
546.2.by $$\chi_{546}(19, \cdot)$$ 546.2.by.a 32 4
546.2.by.b 40
546.2.bz $$\chi_{546}(31, \cdot)$$ 546.2.bz.a 40 4
546.2.bz.b 40
546.2.cg $$\chi_{546}(145, \cdot)$$ 546.2.cg.a 32 4
546.2.cg.b 40
546.2.ch $$\chi_{546}(137, \cdot)$$ 546.2.ch.a 152 4

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(546))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(546)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(182))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(273))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(546))$$$$^{\oplus 1}$$