## Defining parameters

 Level: $$N$$ = $$354 = 2 \cdot 3 \cdot 59$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$4$$ Sturm bound: $$41760$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(354))$$.

Total New Old
Modular forms 17632 4348 13284
Cusp forms 17168 4348 12820
Eisenstein series 464 0 464

## Trace form

 $$4348q - 8q^{2} + 18q^{3} - 32q^{4} + 132q^{5} + 72q^{6} - 352q^{7} - 128q^{8} - 162q^{9} + O(q^{10})$$ $$4348q - 8q^{2} + 18q^{3} - 32q^{4} + 132q^{5} + 72q^{6} - 352q^{7} - 128q^{8} - 162q^{9} + 528q^{10} + 120q^{11} + 288q^{12} + 1316q^{13} - 1408q^{14} - 1188q^{15} - 512q^{16} + 828q^{17} - 648q^{18} - 1912q^{19} + 2112q^{20} + 3168q^{21} + 480q^{22} - 1200q^{23} + 1152q^{24} - 2462q^{25} + 5264q^{26} + 1458q^{27} - 5632q^{28} - 11148q^{29} - 4752q^{30} + 7184q^{31} - 2048q^{32} - 1080q^{33} + 3312q^{34} + 23232q^{35} - 2592q^{36} + 16916q^{37} - 7648q^{38} - 11844q^{39} + 8448q^{40} - 38388q^{41} + 12672q^{42} - 26632q^{43} + 1920q^{44} - 440026q^{45} - 350480q^{46} + 63836q^{47} + 4608q^{48} + 654902q^{49} + 687080q^{50} + 571388q^{51} + 208512q^{52} + 188044q^{53} - 111908q^{54} - 572028q^{55} - 22528q^{56} - 875702q^{57} - 434816q^{58} - 793100q^{59} - 522912q^{60} - 437780q^{61} - 101648q^{62} + 9478q^{63} - 8192q^{64} + 932436q^{65} + 852340q^{66} + 1247200q^{67} + 683264q^{68} + 1320440q^{69} + 1161056q^{70} + 543400q^{71} - 10368q^{72} - 723648q^{73} - 1577216q^{74} - 1376860q^{75} - 30592q^{76} + 21120q^{77} - 47376q^{78} - 148816q^{79} + 33792q^{80} - 13122q^{81} - 153552q^{82} + 12936q^{83} + 50688q^{84} - 54648q^{85} - 106528q^{86} + 100332q^{87} + 7680q^{88} + 65484q^{89} + 42768q^{90} + 231616q^{91} - 19200q^{92} - 64656q^{93} + 157440q^{94} + 126192q^{95} + 18432q^{96} - 332164q^{97} - 113352q^{98} + 9720q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(354))$$

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
354.6.a $$\chi_{354}(1, \cdot)$$ 354.6.a.a 1 1
354.6.a.b 4
354.6.a.c 5
354.6.a.d 5
354.6.a.e 5
354.6.a.f 6
354.6.a.g 6
354.6.a.h 8
354.6.a.i 8
354.6.c $$\chi_{354}(353, \cdot)$$ 354.6.c.a 50 1
354.6.c.b 50
354.6.e $$\chi_{354}(7, \cdot)$$ n/a 1400 28
354.6.g $$\chi_{354}(11, \cdot)$$ n/a 2800 28

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

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(354))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(354)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(59))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(118))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(177))$$$$^{\oplus 2}$$