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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

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

Display 100 coefficients 10 coefficients

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 available 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