# Properties

 Label 294.2 Level 294 Weight 2 Dimension 563 Nonzero newspaces 8 Newform subspaces 28 Sturm bound 9408 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$294 = 2 \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$28$$ Sturm bound: $$9408$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(294))$$.

Total New Old
Modular forms 2592 563 2029
Cusp forms 2113 563 1550
Eisenstein series 479 0 479

## Trace form

 $$563 q - q^{2} + 3 q^{3} + 7 q^{4} + 18 q^{5} + 11 q^{6} + 16 q^{7} - q^{8} + 15 q^{9} + O(q^{10})$$ $$563 q - q^{2} + 3 q^{3} + 7 q^{4} + 18 q^{5} + 11 q^{6} + 16 q^{7} - q^{8} + 15 q^{9} + 18 q^{10} + 36 q^{11} + 3 q^{12} + 18 q^{13} - 6 q^{15} - q^{16} + 6 q^{17} - 25 q^{18} + 12 q^{19} - 6 q^{20} - 10 q^{21} - 12 q^{22} - 13 q^{24} + 17 q^{25} + 10 q^{26} + 3 q^{27} + 12 q^{28} + 18 q^{29} + 18 q^{30} + 48 q^{31} - q^{32} + 36 q^{33} + 30 q^{34} + 48 q^{35} + 15 q^{36} - 38 q^{37} - 32 q^{38} - 56 q^{39} - 66 q^{40} - 114 q^{41} - 54 q^{42} - 52 q^{43} - 48 q^{44} - 66 q^{45} - 180 q^{46} - 144 q^{47} - 11 q^{48} - 288 q^{49} - 103 q^{50} - 210 q^{51} - 58 q^{52} - 150 q^{53} - 37 q^{54} - 420 q^{55} - 72 q^{56} - 48 q^{57} - 222 q^{58} - 132 q^{59} - 72 q^{60} - 178 q^{61} - 68 q^{62} - 30 q^{63} + 7 q^{64} + 84 q^{65} - 12 q^{66} - 20 q^{67} + 6 q^{68} + 24 q^{69} + 72 q^{71} + 23 q^{72} + 30 q^{73} + 34 q^{74} + 45 q^{75} + 12 q^{76} + 108 q^{77} + 34 q^{78} + 160 q^{79} + 18 q^{80} + 27 q^{81} + 102 q^{82} - 12 q^{83} + 26 q^{84} + 108 q^{85} + 76 q^{86} - 78 q^{87} + 12 q^{88} - 66 q^{89} + 18 q^{90} - 56 q^{91} + 24 q^{92} - 228 q^{93} + 96 q^{94} - 240 q^{95} - 13 q^{96} - 66 q^{97} + 24 q^{98} - 180 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(294))$$

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
294.2.a $$\chi_{294}(1, \cdot)$$ 294.2.a.a 1 1
294.2.a.b 1
294.2.a.c 1
294.2.a.d 1
294.2.a.e 1
294.2.a.f 1
294.2.a.g 1
294.2.d $$\chi_{294}(293, \cdot)$$ 294.2.d.a 4 1
294.2.d.b 8
294.2.e $$\chi_{294}(67, \cdot)$$ 294.2.e.a 2 2
294.2.e.b 2
294.2.e.c 2
294.2.e.d 2
294.2.e.e 2
294.2.e.f 2
294.2.f $$\chi_{294}(215, \cdot)$$ 294.2.f.a 4 2
294.2.f.b 8
294.2.f.c 16
294.2.i $$\chi_{294}(43, \cdot)$$ 294.2.i.a 6 6
294.2.i.b 12
294.2.i.c 12
294.2.i.d 18
294.2.j $$\chi_{294}(41, \cdot)$$ 294.2.j.a 120 6
294.2.m $$\chi_{294}(25, \cdot)$$ 294.2.m.a 24 12
294.2.m.b 24
294.2.m.c 36
294.2.m.d 36
294.2.p $$\chi_{294}(5, \cdot)$$ 294.2.p.a 216 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(294))$$ into lower level spaces

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