# Properties

 Label 294.4 Level 294 Weight 4 Dimension 1693 Nonzero newspaces 8 Sturm bound 18816 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$294 = 2 \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$8$$ Sturm bound: $$18816$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(294))$$.

Total New Old
Modular forms 7296 1693 5603
Cusp forms 6816 1693 5123
Eisenstein series 480 0 480

## Trace form

 $$1693 q - 2 q^{2} + 21 q^{3} + 4 q^{4} - 90 q^{5} - 66 q^{6} - 96 q^{7} - 8 q^{8} + 93 q^{9} + O(q^{10})$$ $$1693 q - 2 q^{2} + 21 q^{3} + 4 q^{4} - 90 q^{5} - 66 q^{6} - 96 q^{7} - 8 q^{8} + 93 q^{9} + 132 q^{10} + 180 q^{11} + 84 q^{12} + 14 q^{13} - 522 q^{15} + 16 q^{16} - 150 q^{17} + 318 q^{18} + 788 q^{19} + 24 q^{20} + 648 q^{21} - 24 q^{22} + 120 q^{24} + 751 q^{25} + 836 q^{26} - 135 q^{27} + 96 q^{28} - 162 q^{29} - 1308 q^{30} - 1624 q^{31} - 32 q^{32} - 2664 q^{33} - 1380 q^{34} - 876 q^{35} - 1596 q^{36} - 7978 q^{37} - 4816 q^{38} - 2214 q^{39} - 1488 q^{40} - 534 q^{41} + 828 q^{42} + 2780 q^{43} + 3072 q^{44} + 7002 q^{45} + 9576 q^{46} + 8352 q^{47} + 432 q^{48} + 12228 q^{49} + 3490 q^{50} + 1134 q^{51} - 280 q^{52} + 2382 q^{53} - 306 q^{54} + 5688 q^{55} - 576 q^{56} + 1620 q^{57} - 2076 q^{58} - 6132 q^{59} - 576 q^{60} - 6346 q^{61} - 4648 q^{62} + 2406 q^{63} + 1600 q^{64} + 1572 q^{65} + 4104 q^{66} - 460 q^{67} - 600 q^{68} - 3816 q^{69} - 1008 q^{70} - 6840 q^{71} - 1416 q^{72} - 11590 q^{73} + 500 q^{74} - 9753 q^{75} - 784 q^{76} + 108 q^{77} - 6012 q^{78} - 4552 q^{79} - 1440 q^{80} - 14871 q^{81} - 4020 q^{82} - 13524 q^{83} - 912 q^{84} - 5820 q^{85} - 2248 q^{86} - 7098 q^{87} + 1248 q^{88} - 798 q^{89} - 2268 q^{90} + 8064 q^{91} - 3552 q^{92} + 15216 q^{93} - 3648 q^{94} + 21624 q^{95} + 480 q^{96} + 6674 q^{97} - 816 q^{98} + 16572 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(294))$$

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
294.4.a $$\chi_{294}(1, \cdot)$$ 294.4.a.a 1 1
294.4.a.b 1
294.4.a.c 1
294.4.a.d 1
294.4.a.e 1
294.4.a.f 1
294.4.a.g 1
294.4.a.h 1
294.4.a.i 1
294.4.a.j 2
294.4.a.k 2
294.4.a.l 2
294.4.a.m 2
294.4.a.n 2
294.4.a.o 2
294.4.d $$\chi_{294}(293, \cdot)$$ 294.4.d.a 16 1
294.4.d.b 24
294.4.e $$\chi_{294}(67, \cdot)$$ 294.4.e.a 2 2
294.4.e.b 2
294.4.e.c 2
294.4.e.d 2
294.4.e.e 2
294.4.e.f 2
294.4.e.g 2
294.4.e.h 2
294.4.e.i 2
294.4.e.j 2
294.4.e.k 4
294.4.e.l 4
294.4.e.m 4
294.4.e.n 4
294.4.e.o 4
294.4.f $$\chi_{294}(215, \cdot)$$ 294.4.f.a 16 2
294.4.f.b 16
294.4.f.c 48
294.4.i $$\chi_{294}(43, \cdot)$$ n/a 168 6
294.4.j $$\chi_{294}(41, \cdot)$$ n/a 336 6
294.4.m $$\chi_{294}(25, \cdot)$$ n/a 336 12
294.4.p $$\chi_{294}(5, \cdot)$$ n/a 672 12

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(294))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(294)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 2}$$