## Defining parameters

 Level: $$N$$ = $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$30$$ Sturm bound: $$64512$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(546))$$.

Total New Old
Modular forms 24768 5728 19040
Cusp forms 23616 5728 17888
Eisenstein series 1152 0 1152

## Trace form

 $$5728q - 8q^{2} + 12q^{3} + 16q^{4} - 72q^{5} - 48q^{6} - 80q^{7} + 64q^{8} + 120q^{9} + O(q^{10})$$ $$5728q - 8q^{2} + 12q^{3} + 16q^{4} - 72q^{5} - 48q^{6} - 80q^{7} + 64q^{8} + 120q^{9} - 264q^{10} - 264q^{11} - 48q^{12} - 1088q^{13} - 176q^{14} - 864q^{15} + 64q^{16} + 420q^{17} + 480q^{18} + 3584q^{19} + 624q^{20} + 1512q^{21} - 96q^{22} - 408q^{23} + 192q^{24} - 1016q^{25} + 304q^{26} - 1872q^{27} + 64q^{28} - 852q^{29} - 2832q^{30} - 1648q^{31} - 128q^{32} - 708q^{33} - 624q^{34} - 384q^{35} + 48q^{36} + 3476q^{37} + 272q^{38} + 5268q^{39} + 384q^{40} + 1644q^{41} + 1392q^{42} + 944q^{43} + 864q^{44} + 3552q^{45} - 2016q^{46} - 1152q^{47} - 384q^{48} - 9020q^{49} - 1952q^{50} - 7236q^{51} + 688q^{52} + 2448q^{53} + 3168q^{54} + 3384q^{55} + 640q^{56} + 2328q^{57} + 2424q^{58} - 2352q^{59} + 624q^{60} + 10556q^{61} - 1216q^{62} + 984q^{63} + 1024q^{64} - 9588q^{65} - 1632q^{66} - 5920q^{67} - 2736q^{68} - 12360q^{69} - 4080q^{70} - 6576q^{71} - 2016q^{72} - 16696q^{73} - 15688q^{74} - 11712q^{75} - 12640q^{76} - 26664q^{77} - 504q^{78} - 8224q^{79} + 960q^{80} + 16296q^{81} + 5544q^{82} + 13776q^{83} + 5280q^{84} + 39252q^{85} + 11504q^{86} + 16032q^{87} + 960q^{88} + 36360q^{89} + 6048q^{90} + 45016q^{91} + 15360q^{92} + 2676q^{93} + 34368q^{94} + 18288q^{95} + 768q^{96} + 5888q^{97} + 8248q^{98} - 12744q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(546))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
546.4.a $$\chi_{546}(1, \cdot)$$ 546.4.a.a 1 1
546.4.a.b 1
546.4.a.c 1
546.4.a.d 1
546.4.a.e 1
546.4.a.f 2
546.4.a.g 2
546.4.a.h 2
546.4.a.i 2
546.4.a.j 2
546.4.a.k 2
546.4.a.l 3
546.4.a.m 3
546.4.a.n 3
546.4.a.o 3
546.4.a.p 3
546.4.a.q 4
546.4.c $$\chi_{546}(337, \cdot)$$ 546.4.c.a 10 1
546.4.c.b 10
546.4.c.c 12
546.4.c.d 12
546.4.e $$\chi_{546}(545, \cdot)$$ n/a 112 1
546.4.g $$\chi_{546}(209, \cdot)$$ 546.4.g.a 48 1
546.4.g.b 48
546.4.i $$\chi_{546}(79, \cdot)$$ 546.4.i.a 4 2
546.4.i.b 8
546.4.i.c 10
546.4.i.d 10
546.4.i.e 12
546.4.i.f 12
546.4.i.g 12
546.4.i.h 14
546.4.i.i 14
546.4.j $$\chi_{546}(289, \cdot)$$ n/a 112 2
546.4.k $$\chi_{546}(373, \cdot)$$ n/a 112 2
546.4.l $$\chi_{546}(211, \cdot)$$ 546.4.l.a 2 2
546.4.l.b 2
546.4.l.c 8
546.4.l.d 8
546.4.l.e 10
546.4.l.f 10
546.4.l.g 10
546.4.l.h 10
546.4.l.i 10
546.4.l.j 10
546.4.o $$\chi_{546}(265, \cdot)$$ n/a 112 2
546.4.p $$\chi_{546}(239, \cdot)$$ n/a 168 2
546.4.q $$\chi_{546}(251, \cdot)$$ n/a 224 2
546.4.s $$\chi_{546}(43, \cdot)$$ 546.4.s.a 20 2
546.4.s.b 20
546.4.s.c 24
546.4.s.d 24
546.4.u $$\chi_{546}(185, \cdot)$$ n/a 224 2
546.4.z $$\chi_{546}(131, \cdot)$$ n/a 192 2
546.4.bb $$\chi_{546}(269, \cdot)$$ n/a 224 2
546.4.bd $$\chi_{546}(121, \cdot)$$ n/a 112 2
546.4.bg $$\chi_{546}(311, \cdot)$$ n/a 224 2
546.4.bi $$\chi_{546}(17, \cdot)$$ n/a 224 2
546.4.bk $$\chi_{546}(25, \cdot)$$ n/a 112 2
546.4.bm $$\chi_{546}(205, \cdot)$$ n/a 112 2
546.4.bn $$\chi_{546}(101, \cdot)$$ n/a 224 2
546.4.bq $$\chi_{546}(419, \cdot)$$ n/a 224 2
546.4.bu $$\chi_{546}(71, \cdot)$$ n/a 336 4
546.4.bv $$\chi_{546}(317, \cdot)$$ n/a 448 4
546.4.bw $$\chi_{546}(11, \cdot)$$ n/a 448 4
546.4.bx $$\chi_{546}(97, \cdot)$$ n/a 224 4
546.4.by $$\chi_{546}(19, \cdot)$$ n/a 224 4
546.4.bz $$\chi_{546}(31, \cdot)$$ n/a 224 4
546.4.cg $$\chi_{546}(145, \cdot)$$ n/a 224 4
546.4.ch $$\chi_{546}(137, \cdot)$$ n/a 448 4

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(546))$$ into lower level spaces

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