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

\( 1632 q - 36 q^{2} - 54 q^{3} - 60 q^{4} - 36 q^{5} - 54 q^{6} - 60 q^{7} - 36 q^{8} - 54 q^{9} - 84 q^{10} - 36 q^{11} - 54 q^{12} - 60 q^{13} - 36 q^{14} - 54 q^{15} - 72 q^{16} - 36 q^{17} - 54 q^{18}+ \cdots - 27 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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

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