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Properties

Label 8.18
Level 8
Weight 18
Dimension 20
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 72
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 18 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(72\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(8))\).

Total New Old
Modular forms 37 22 15
Cusp forms 31 20 11
Eisenstein series 6 2 4

Trace form

\( 20 q + 270 q^{2} + 10640 q^{3} - 27436 q^{4} - 845544 q^{5} + 5839948 q^{6} - 7736160 q^{7} + 24334920 q^{8} - 467714140 q^{9} + O(q^{10}) \) \( 20 q + 270 q^{2} + 10640 q^{3} - 27436 q^{4} - 845544 q^{5} + 5839948 q^{6} - 7736160 q^{7} + 24334920 q^{8} - 467714140 q^{9} + 131002712 q^{10} - 39796560 q^{11} - 2795125400 q^{12} + 163998520 q^{13} + 16363788528 q^{14} - 18256340256 q^{15} + 26500434192 q^{16} + 4739689320 q^{17} - 113450563870 q^{18} + 96146659280 q^{19} - 209445719856 q^{20} - 313163478912 q^{21} + 223126527100 q^{22} + 968504909280 q^{23} - 1099415493232 q^{24} - 2134692449588 q^{25} + 2467726531080 q^{26} + 2500686288800 q^{27} + 3220542267040 q^{28} - 5251084703880 q^{29} - 1188624268048 q^{30} + 8554802676352 q^{31} + 1455647316000 q^{32} - 21441836907520 q^{33} - 4461251980292 q^{34} + 56561374769856 q^{35} - 33088278002484 q^{36} - 71506917316200 q^{37} + 24076283913900 q^{38} + 73593315777120 q^{39} + 60626292962592 q^{40} - 108508081413816 q^{41} - 51630378688160 q^{42} + 136636971765040 q^{43} + 193654716236040 q^{44} - 299350264536008 q^{45} - 195097141003568 q^{46} - 74381803897920 q^{47} - 329350060416480 q^{48} + 402760072905332 q^{49} + 474997408872102 q^{50} - 354576680645600 q^{51} - 272251877663120 q^{52} - 100542682473000 q^{53} + 735354219382520 q^{54} + 1333112492454816 q^{55} - 162767516076480 q^{56} + 1455694770410880 q^{57} - 623262610679960 q^{58} - 1728362237211792 q^{59} - 1973616194963808 q^{60} + 4829676956350456 q^{61} + 695695648144320 q^{62} - 15001128154623200 q^{63} + 1111931745501248 q^{64} + 7841146713161808 q^{65} + 3598826202828312 q^{66} - 4674219417808240 q^{67} + 5981109959771880 q^{68} + 806157717690752 q^{69} - 10044559836180288 q^{70} + 11053250390665632 q^{71} - 19918679666289160 q^{72} + 5421002897168840 q^{73} + 11098735408189464 q^{74} + 16715682746477680 q^{75} + 5959440926938280 q^{76} - 11271437651625600 q^{77} + 4184252259031760 q^{78} - 32840132790305216 q^{79} + 1337342539452480 q^{80} - 16629417913796172 q^{81} + 15639739637081420 q^{82} + 35426115577045200 q^{83} + 19796542864700224 q^{84} - 38070216039124048 q^{85} - 14252032276026564 q^{86} + 75111056122431840 q^{87} - 66964872768837680 q^{88} - 137807112304783608 q^{89} + 136151511125051240 q^{90} + 90023701626551232 q^{91} + 57336249810701280 q^{92} + 29927544138703360 q^{93} - 192318922166254176 q^{94} + 12267616369204320 q^{95} - 342799224184788928 q^{96} + 79484920350709160 q^{97} + 339641261743253790 q^{98} - 37182223131302672 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(8))\)

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
8.18.a \(\chi_{8}(1, \cdot)\) 8.18.a.a 2 1
8.18.a.b 2
8.18.b \(\chi_{8}(5, \cdot)\) 8.18.b.a 16 1

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)