# Properties

 Label 19.7 Level 19 Weight 7 Dimension 81 Nonzero newspaces 3 Newform subspaces 4 Sturm bound 210 Trace bound 1

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## Defining parameters

 Level: $$N$$ = $$19$$ Weight: $$k$$ = $$7$$ Nonzero newspaces: $$3$$ Newform subspaces: $$4$$ Sturm bound: $$210$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(\Gamma_1(19))$$.

Total New Old
Modular forms 99 99 0
Cusp forms 81 81 0
Eisenstein series 18 18 0

## Trace form

 $$81q - 9q^{2} - 9q^{3} - 9q^{4} - 9q^{5} - 9q^{6} - 9q^{7} - 9q^{8} - 9q^{9} + O(q^{10})$$ $$81q - 9q^{2} - 9q^{3} - 9q^{4} - 9q^{5} - 9q^{6} - 9q^{7} - 9q^{8} - 9q^{9} - 9q^{10} - 9q^{11} - 9q^{12} - 10089q^{13} - 3753q^{14} + 11655q^{15} + 38007q^{16} + 7191q^{17} - 21177q^{19} - 64530q^{20} - 40833q^{21} - 32409q^{22} + 3951q^{23} + 93303q^{24} + 78615q^{25} + 76599q^{26} + 124821q^{27} - 176886q^{28} - 115929q^{29} - 343548q^{30} - 30789q^{31} + 111816q^{32} + 304767q^{33} + 313866q^{34} + 225423q^{35} + 337617q^{36} - 263412q^{38} - 427158q^{39} - 650934q^{40} - 192609q^{41} - 772659q^{42} + 55935q^{43} + 519516q^{44} + 266751q^{45} + 69246q^{46} - 104589q^{47} + 518418q^{48} + 61551q^{49} - 104148q^{50} - 36819q^{51} + 1330551q^{52} + 712791q^{53} + 859752q^{54} + 318807q^{55} - 428409q^{57} - 660978q^{58} - 1134009q^{59} - 1119132q^{60} - 286749q^{61} - 2327724q^{62} - 2593449q^{63} - 3205233q^{64} - 1056789q^{65} + 1261791q^{66} + 1234647q^{67} + 4746096q^{68} + 3771567q^{69} + 5384547q^{70} + 811791q^{71} + 2138940q^{72} + 1632141q^{73} + 1162143q^{74} - 1532259q^{76} - 1101510q^{77} - 1936719q^{78} - 5151177q^{79} - 8152497q^{80} - 7574715q^{81} - 8875422q^{82} - 2456937q^{83} - 3125205q^{84} + 1899495q^{85} + 4552110q^{86} + 9822231q^{87} + 13604751q^{88} + 7834203q^{89} + 13468176q^{90} + 4492215q^{91} + 1487610q^{92} - 3771837q^{93} + 5066487q^{95} - 7288650q^{96} - 5215545q^{97} - 19578312q^{98} - 15887043q^{99} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(\Gamma_1(19))$$

We only show spaces with odd 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
19.7.b $$\chi_{19}(18, \cdot)$$ 19.7.b.a 1 1
19.7.b.b 8
19.7.d $$\chi_{19}(8, \cdot)$$ 19.7.d.a 18 2
19.7.f $$\chi_{19}(2, \cdot)$$ 19.7.f.a 54 6