Properties

Label 3888.1
Level 3888
Weight 1
Dimension 33
Nonzero newspaces 4
Newform subspaces 17
Sturm bound 839808
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3888 = 2^{4} \cdot 3^{5} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 17 \)
Sturm bound: \(839808\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3888))\).

Total New Old
Modular forms 5944 897 5047
Cusp forms 652 33 619
Eisenstein series 5292 864 4428

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 27 0 6 0

Trace form

\( 33 q + O(q^{10}) \) \( 33 q + 6 q^{19} + 12 q^{55} + 6 q^{73} + 9 q^{91} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3888))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3888.1.b \(\chi_{3888}(487, \cdot)\) None 0 1
3888.1.e \(\chi_{3888}(1457, \cdot)\) 3888.1.e.a 1 1
3888.1.e.b 1
3888.1.e.c 1
3888.1.e.d 2
3888.1.g \(\chi_{3888}(2431, \cdot)\) 3888.1.g.a 2 1
3888.1.g.b 2
3888.1.g.c 2
3888.1.h \(\chi_{3888}(3401, \cdot)\) None 0 1
3888.1.j \(\chi_{3888}(485, \cdot)\) None 0 2
3888.1.m \(\chi_{3888}(1459, \cdot)\) None 0 2
3888.1.n \(\chi_{3888}(809, \cdot)\) None 0 2
3888.1.o \(\chi_{3888}(1135, \cdot)\) 3888.1.o.a 2 2
3888.1.o.b 2
3888.1.o.c 2
3888.1.o.d 2
3888.1.o.e 2
3888.1.o.f 2
3888.1.q \(\chi_{3888}(161, \cdot)\) 3888.1.q.a 2 2
3888.1.q.b 2
3888.1.q.c 2
3888.1.q.d 4
3888.1.t \(\chi_{3888}(1783, \cdot)\) None 0 2
3888.1.w \(\chi_{3888}(163, \cdot)\) None 0 4
3888.1.x \(\chi_{3888}(1133, \cdot)\) None 0 4
3888.1.z \(\chi_{3888}(55, \cdot)\) None 0 6
3888.1.ba \(\chi_{3888}(271, \cdot)\) None 0 6
3888.1.bc \(\chi_{3888}(593, \cdot)\) None 0 6
3888.1.bf \(\chi_{3888}(377, \cdot)\) None 0 6
3888.1.bi \(\chi_{3888}(379, \cdot)\) None 0 12
3888.1.bj \(\chi_{3888}(53, \cdot)\) None 0 12
3888.1.bl \(\chi_{3888}(89, \cdot)\) None 0 18
3888.1.bm \(\chi_{3888}(127, \cdot)\) None 0 18
3888.1.bo \(\chi_{3888}(17, \cdot)\) None 0 18
3888.1.br \(\chi_{3888}(199, \cdot)\) None 0 18
3888.1.bu \(\chi_{3888}(19, \cdot)\) None 0 36
3888.1.bv \(\chi_{3888}(125, \cdot)\) None 0 36
3888.1.bx \(\chi_{3888}(7, \cdot)\) None 0 54
3888.1.by \(\chi_{3888}(31, \cdot)\) None 0 54
3888.1.ca \(\chi_{3888}(65, \cdot)\) None 0 54
3888.1.cd \(\chi_{3888}(41, \cdot)\) None 0 54
3888.1.cf \(\chi_{3888}(43, \cdot)\) None 0 108
3888.1.cg \(\chi_{3888}(5, \cdot)\) None 0 108

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3888))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3888)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(648))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(972))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1296))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1944))\)\(^{\oplus 2}\)