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Properties

Label 243.2
Level 243
Weight 2
Dimension 1632
Nonzero newspaces 5
Newform subspaces 18
Sturm bound 8748
Trace bound 1

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Defining parameters

Level: \( N \) = \( 243 = 3^{5} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 18 \)
Sturm bound: \(8748\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(243))\).

Total New Old
Modular forms 2376 1824 552
Cusp forms 1999 1632 367
Eisenstein series 377 192 185

Trace form

\( 1632 q - 36 q^{2} - 54 q^{3} - 60 q^{4} - 36 q^{5} - 54 q^{6} - 60 q^{7} - 36 q^{8} - 54 q^{9} + O(q^{10}) \) \( 1632 q - 36 q^{2} - 54 q^{3} - 60 q^{4} - 36 q^{5} - 54 q^{6} - 60 q^{7} - 36 q^{8} - 54 q^{9} - 84 q^{10} - 36 q^{11} - 54 q^{12} - 60 q^{13} - 36 q^{14} - 54 q^{15} - 72 q^{16} - 36 q^{17} - 54 q^{18} - 93 q^{19} - 72 q^{20} - 54 q^{21} - 78 q^{22} - 63 q^{23} - 54 q^{24} - 78 q^{25} - 99 q^{26} - 54 q^{27} - 147 q^{28} - 63 q^{29} - 54 q^{30} - 78 q^{31} - 90 q^{32} - 54 q^{33} - 90 q^{34} - 63 q^{35} - 54 q^{36} - 93 q^{37} - 45 q^{38} - 54 q^{39} - 114 q^{40} - 54 q^{41} - 54 q^{42} - 78 q^{43} - 108 q^{44} - 54 q^{45} - 138 q^{46} - 90 q^{47} - 54 q^{48} - 96 q^{49} - 153 q^{50} - 54 q^{51} - 72 q^{52} - 99 q^{53} - 54 q^{54} - 165 q^{55} - 180 q^{56} - 54 q^{57} - 114 q^{58} - 99 q^{59} - 54 q^{60} - 96 q^{61} - 135 q^{62} - 54 q^{63} - 42 q^{64} + 54 q^{66} - 15 q^{67} + 234 q^{68} + 54 q^{69} + 12 q^{70} + 144 q^{71} + 270 q^{72} + 24 q^{73} + 324 q^{74} + 81 q^{75} + 105 q^{76} + 324 q^{77} + 162 q^{78} + 66 q^{79} + 639 q^{80} + 54 q^{81} + 105 q^{82} + 144 q^{83} + 324 q^{84} + 36 q^{85} + 324 q^{86} + 162 q^{87} + 69 q^{88} + 162 q^{89} + 162 q^{90} - 12 q^{91} + 414 q^{92} + 54 q^{93} + 12 q^{94} + 36 q^{95} + 135 q^{96} - 51 q^{97} - 27 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(243))\)

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
243.2.a \(\chi_{243}(1, \cdot)\) 243.2.a.a 1 1
243.2.a.b 1
243.2.a.c 2
243.2.a.d 2
243.2.a.e 3
243.2.a.f 3
243.2.c \(\chi_{243}(82, \cdot)\) 243.2.c.a 2 2
243.2.c.b 2
243.2.c.c 4
243.2.c.d 4
243.2.c.e 6
243.2.c.f 6
243.2.e \(\chi_{243}(28, \cdot)\) 243.2.e.a 12 6
243.2.e.b 12
243.2.e.c 12
243.2.e.d 12
243.2.g \(\chi_{243}(10, \cdot)\) 243.2.g.a 144 18
243.2.i \(\chi_{243}(4, \cdot)\) 243.2.i.a 1404 54

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(243))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(243)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 1}\)