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Properties

Label 1296.1
Level 1296
Weight 1
Dimension 22
Nonzero newspaces 4
Newform subspaces 7
Sturm bound 93312
Trace bound 7

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Defining parameters

Level: \( N \) = \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 7 \)
Sturm bound: \(93312\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1296))\).

Total New Old
Modular forms 1693 274 1419
Cusp forms 181 22 159
Eisenstein series 1512 252 1260

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 14 0 8 0

Trace form

\( 22 q - q^{7} + 5 q^{13} + 4 q^{16} + 2 q^{19} + 2 q^{25} + 8 q^{28} - 2 q^{31} + 4 q^{34} - 8 q^{37} + 4 q^{40} + 6 q^{43} + 3 q^{49} - 4 q^{52} + q^{61} - 5 q^{67} - 4 q^{70} + 4 q^{73} - q^{79} + 4 q^{85}+ \cdots - 3 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1296))\)

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
1296.1.b \(\chi_{1296}(487, \cdot)\) None 0 1
1296.1.e \(\chi_{1296}(161, \cdot)\) None 0 1
1296.1.g \(\chi_{1296}(1135, \cdot)\) 1296.1.g.a 2 1
1296.1.h \(\chi_{1296}(809, \cdot)\) None 0 1
1296.1.j \(\chi_{1296}(485, \cdot)\) None 0 2
1296.1.m \(\chi_{1296}(163, \cdot)\) None 0 2
1296.1.n \(\chi_{1296}(377, \cdot)\) None 0 2
1296.1.o \(\chi_{1296}(271, \cdot)\) 1296.1.o.a 2 2
1296.1.o.b 2
1296.1.o.c 2
1296.1.o.d 4
1296.1.q \(\chi_{1296}(593, \cdot)\) 1296.1.q.a 2 2
1296.1.t \(\chi_{1296}(55, \cdot)\) None 0 2
1296.1.w \(\chi_{1296}(379, \cdot)\) None 0 4
1296.1.x \(\chi_{1296}(53, \cdot)\) 1296.1.x.a 8 4
1296.1.z \(\chi_{1296}(199, \cdot)\) None 0 6
1296.1.ba \(\chi_{1296}(127, \cdot)\) None 0 6
1296.1.bc \(\chi_{1296}(17, \cdot)\) None 0 6
1296.1.bf \(\chi_{1296}(89, \cdot)\) None 0 6
1296.1.bi \(\chi_{1296}(19, \cdot)\) None 0 12
1296.1.bj \(\chi_{1296}(125, \cdot)\) None 0 12
1296.1.bl \(\chi_{1296}(41, \cdot)\) None 0 18
1296.1.bm \(\chi_{1296}(31, \cdot)\) None 0 18
1296.1.bo \(\chi_{1296}(65, \cdot)\) None 0 18
1296.1.br \(\chi_{1296}(7, \cdot)\) None 0 18
1296.1.bt \(\chi_{1296}(43, \cdot)\) None 0 36
1296.1.bu \(\chi_{1296}(5, \cdot)\) None 0 36

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1296))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1296)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 25}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 15}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 15}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(648))\)\(^{\oplus 2}\)