Properties

Label 19.11
Level 19
Weight 11
Dimension 141
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 330
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(330\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(19))\).

Total New Old
Modular forms 159 159 0
Cusp forms 141 141 0
Eisenstein series 18 18 0

Trace form

\( 141 q - 9 q^{2} - 9 q^{3} - 9 q^{4} - 9 q^{5} - 9 q^{6} - 9 q^{7} - 9 q^{8} - 9 q^{9} + O(q^{10}) \) \( 141 q - 9 q^{2} - 9 q^{3} - 9 q^{4} - 9 q^{5} - 9 q^{6} - 9 q^{7} - 9 q^{8} - 9 q^{9} - 9 q^{10} - 9 q^{11} - 1493001 q^{12} + 1683291 q^{13} - 1837449 q^{14} - 2838735 q^{15} + 5621751 q^{16} + 2927502 q^{17} - 10958964 q^{19} - 20477970 q^{20} + 3801726 q^{21} + 31261239 q^{22} + 10149516 q^{23} - 22394889 q^{24} - 48982635 q^{25} - 26737929 q^{26} + 91704069 q^{27} - 90040326 q^{28} + 88955847 q^{29} + 219591972 q^{30} - 61388397 q^{31} - 294861384 q^{32} - 158021073 q^{33} + 186514506 q^{34} + 321628383 q^{35} + 674279217 q^{36} - 589570452 q^{38} - 789807150 q^{39} - 713461734 q^{40} + 12010383 q^{41} + 1436577741 q^{42} + 1400808696 q^{43} - 627224148 q^{44} - 436526154 q^{45} - 41114754 q^{46} + 84918888 q^{47} - 1319007006 q^{48} + 232421100 q^{49} - 939859668 q^{50} - 2980284048 q^{51} + 1177921527 q^{52} + 1850052843 q^{53} + 3334550184 q^{54} + 1529593587 q^{55} - 2211476364 q^{57} - 3029355666 q^{58} - 3942302274 q^{59} - 1505042892 q^{60} - 6786033729 q^{61} + 2098697940 q^{62} + 11874071187 q^{63} + 21670953999 q^{64} + 6677673336 q^{65} - 10127964897 q^{66} - 16708223442 q^{67} - 27106013664 q^{68} - 11104580178 q^{69} + 8608058307 q^{70} + 18062248212 q^{71} + 35313966252 q^{72} + 12143243940 q^{73} + 10219891167 q^{74} - 14233684419 q^{76} - 18815451975 q^{77} - 55791103599 q^{78} - 29585665239 q^{79} + 5065788303 q^{80} + 28148719077 q^{81} + 60210552978 q^{82} + 19966920606 q^{83} + 22806365931 q^{84} + 3212431875 q^{85} - 22200957666 q^{86} - 59437940769 q^{87} - 61125759153 q^{88} - 34340405364 q^{89} + 26700041376 q^{90} + 52629401739 q^{91} + 109381595850 q^{92} + 56378608803 q^{93} - 63861958638 q^{95} - 208890859338 q^{96} - 26793284616 q^{97} + 41994560808 q^{98} + 44372036601 q^{99} + O(q^{100}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(19))\)

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
19.11.b \(\chi_{19}(18, \cdot)\) 19.11.b.a 1 1
19.11.b.b 14
19.11.d \(\chi_{19}(8, \cdot)\) 19.11.d.a 30 2
19.11.f \(\chi_{19}(2, \cdot)\) 19.11.f.a 96 6