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Properties

Label 11.18
Level 11
Weight 18
Dimension 78
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 180
Trace bound 1

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 18 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(180\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(11))\).

Total New Old
Modular forms 90 86 4
Cusp forms 80 78 2
Eisenstein series 10 8 2

Trace form

\( 78 q + 1051 q^{2} + 8563 q^{3} - 295429 q^{4} + 2051695 q^{5} + 8008571 q^{6} + 17349706 q^{7} - 160030725 q^{8} + 639292539 q^{9} + O(q^{10}) \) \( 78 q + 1051 q^{2} + 8563 q^{3} - 295429 q^{4} + 2051695 q^{5} + 8008571 q^{6} + 17349706 q^{7} - 160030725 q^{8} + 639292539 q^{9} - 2083297610 q^{10} + 1667015978 q^{11} - 1095010314 q^{12} - 7463836712 q^{13} + 23550314932 q^{14} - 3356234865 q^{15} - 3594208857 q^{16} + 68412818866 q^{17} - 328521527452 q^{18} + 180589385940 q^{19} + 514096352510 q^{20} - 728816887774 q^{21} + 3467179681 q^{22} + 1676199090803 q^{23} + 494240508045 q^{24} - 4843040370685 q^{25} + 8749788468796 q^{26} + 3612866603605 q^{27} - 24730020567818 q^{28} - 4827998392560 q^{29} + 42507517577680 q^{30} - 1930386715729 q^{31} - 20363346524884 q^{32} - 33084973617147 q^{33} + 71892076164362 q^{34} - 34208734447250 q^{35} - 3815009081372 q^{36} + 15138248056541 q^{37} + 25776433736400 q^{38} - 70105703834952 q^{39} - 29311077087840 q^{40} - 12864276678464 q^{41} - 606604092918 q^{42} + 101226064161238 q^{43} - 332866683355644 q^{44} + 439949946603220 q^{45} + 371734991309466 q^{46} + 336681052110356 q^{47} - 2086256086134092 q^{48} - 794376233455204 q^{49} + 1448765882276165 q^{50} + 2792440959274906 q^{51} - 2368698942255814 q^{52} - 453870769521342 q^{53} + 268528869828870 q^{54} - 1021445927813145 q^{55} + 520549506405600 q^{56} + 6372866148688200 q^{57} + 4465262426120800 q^{58} - 6717022319544775 q^{59} - 17387535775057900 q^{60} + 7441128243764576 q^{61} + 7315000103611762 q^{62} + 16631800121987988 q^{63} - 6990390119259969 q^{64} - 20354748795408140 q^{65} - 15107217943935764 q^{66} + 11909154706636861 q^{67} + 43310897408825702 q^{68} - 8843733808762237 q^{69} - 20229183959711580 q^{70} - 9973195170005259 q^{71} - 44523871281170825 q^{72} + 47412873193758308 q^{73} + 108454012314581922 q^{74} - 48128251810398560 q^{75} - 121873401153164570 q^{76} - 45301965632301864 q^{77} + 90331204904461436 q^{78} + 71676365616869290 q^{79} - 15934134640618900 q^{80} - 150069260838146742 q^{81} - 14530367059301343 q^{82} + 129981958804299918 q^{83} + 207201554770036652 q^{84} + 7976947187726640 q^{85} - 178904958897230589 q^{86} - 120962400647443200 q^{87} - 74445971729850325 q^{88} - 18510399976240785 q^{89} + 240211857216623070 q^{90} + 273549674246277976 q^{91} - 236337811568518034 q^{92} - 231304874140485519 q^{93} + 75495389599314342 q^{94} + 12783311986204980 q^{95} - 390802714949829324 q^{96} + 339811022929880341 q^{97} + 318163474177106052 q^{98} + 143895838895148019 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(11))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
11.18.a \(\chi_{11}(1, \cdot)\) 11.18.a.a 6 1
11.18.a.b 8
11.18.c \(\chi_{11}(3, \cdot)\) 11.18.c.a 64 4

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(11))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(11)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)