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Properties

Label 27.11
Level 27
Weight 11
Dimension 205
Nonzero newspaces 3
Newform subspaces 6
Sturm bound 594
Trace bound 1

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Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
Sturm bound: \(594\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(27))\).

Total New Old
Modular forms 285 221 64
Cusp forms 255 205 50
Eisenstein series 30 16 14

Trace form

\( 205 q - 3 q^{2} - 6 q^{3} - 1445 q^{4} - 9921 q^{5} + 18234 q^{6} - 2251 q^{7} - 9 q^{8} + 119124 q^{9} + O(q^{10}) \) \( 205 q - 3 q^{2} - 6 q^{3} - 1445 q^{4} - 9921 q^{5} + 18234 q^{6} - 2251 q^{7} - 9 q^{8} + 119124 q^{9} + 118203 q^{10} - 1947 q^{11} - 1015107 q^{12} + 1085009 q^{13} + 4269147 q^{14} - 2548539 q^{15} - 5220893 q^{16} - 9 q^{17} + 6676947 q^{18} + 2961788 q^{19} + 1382619 q^{20} - 21049824 q^{21} + 4763667 q^{22} + 18382074 q^{23} + 87359400 q^{24} - 30114521 q^{25} - 60562494 q^{27} - 32040310 q^{28} + 49204824 q^{29} + 216153117 q^{30} - 61387645 q^{31} - 88960311 q^{32} - 198927081 q^{33} + 68254983 q^{34} - 260153622 q^{35} + 199074744 q^{36} + 241950578 q^{37} + 872307201 q^{38} + 152777949 q^{39} - 291257781 q^{40} - 1290257895 q^{41} - 1627952634 q^{42} - 256662289 q^{43} + 2245906431 q^{44} + 1041263847 q^{45} + 1034553165 q^{46} - 1396552593 q^{47} - 1664196711 q^{48} + 243627225 q^{49} + 633323244 q^{50} + 1007158626 q^{51} - 3934516009 q^{52} - 1206704682 q^{54} + 2976295686 q^{55} + 12087321 q^{56} - 1000586442 q^{57} - 1546680345 q^{58} - 1259431401 q^{59} + 1176655374 q^{60} - 4606895863 q^{61} + 2786630112 q^{62} + 2270781765 q^{63} + 18213872389 q^{64} + 8132984925 q^{65} - 5594499243 q^{66} - 3043478038 q^{67} - 10057534110 q^{68} - 7767764199 q^{69} - 11450703309 q^{70} - 5512912173 q^{71} - 15991303644 q^{72} + 12362794889 q^{73} + 52110403707 q^{74} + 15296936925 q^{75} + 2257486991 q^{76} - 27704034489 q^{77} - 12511026108 q^{78} - 4245017005 q^{79} + 440880768 q^{81} + 28601897622 q^{82} + 31066927863 q^{83} - 31766160684 q^{84} - 19384067907 q^{85} - 72352863939 q^{86} - 10927113525 q^{87} + 4648657227 q^{88} + 34430237370 q^{89} + 12602186028 q^{90} + 38947403245 q^{91} + 81165252693 q^{92} + 57140838285 q^{93} - 53592094113 q^{94} - 34440428625 q^{95} - 78182924274 q^{96} - 600622336 q^{97} - 103117506282 q^{98} - 72892391589 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(27))\)

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
27.11.b \(\chi_{27}(26, \cdot)\) 27.11.b.a 1 1
27.11.b.b 2
27.11.b.c 4
27.11.b.d 6
27.11.d \(\chi_{27}(8, \cdot)\) 27.11.d.a 18 2
27.11.f \(\chi_{27}(2, \cdot)\) 27.11.f.a 174 6

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(27)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)