Properties

Label 3584.1
Level 3584
Weight 1
Dimension 136
Nonzero newspaces 6
Newform subspaces 14
Sturm bound 786432
Trace bound 109

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Defining parameters

Level: \( N \) = \( 3584 = 2^{9} \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 14 \)
Sturm bound: \(786432\)
Trace bound: \(109\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3584))\).

Total New Old
Modular forms 5098 1256 3842
Cusp forms 490 136 354
Eisenstein series 4608 1120 3488

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 136 0 0 0

Trace form

\( 136 q + O(q^{10}) \) \( 136 q + 8 q^{49} - 16 q^{65} + 24 q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3584))\)

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
3584.1.c \(\chi_{3584}(2561, \cdot)\) 3584.1.c.a 4 1
3584.1.c.b 4
3584.1.c.c 4
3584.1.d \(\chi_{3584}(1023, \cdot)\) None 0 1
3584.1.g \(\chi_{3584}(2815, \cdot)\) None 0 1
3584.1.h \(\chi_{3584}(769, \cdot)\) 3584.1.h.a 4 1
3584.1.h.b 4
3584.1.h.c 4
3584.1.k \(\chi_{3584}(127, \cdot)\) None 0 2
3584.1.l \(\chi_{3584}(1665, \cdot)\) None 0 2
3584.1.n \(\chi_{3584}(257, \cdot)\) None 0 2
3584.1.o \(\chi_{3584}(767, \cdot)\) None 0 2
3584.1.r \(\chi_{3584}(1535, \cdot)\) None 0 2
3584.1.s \(\chi_{3584}(1025, \cdot)\) None 0 2
3584.1.v \(\chi_{3584}(321, \cdot)\) 3584.1.v.a 4 4
3584.1.v.b 4
3584.1.v.c 4
3584.1.v.d 4
3584.1.w \(\chi_{3584}(575, \cdot)\) None 0 4
3584.1.y \(\chi_{3584}(639, \cdot)\) None 0 4
3584.1.bb \(\chi_{3584}(129, \cdot)\) None 0 4
3584.1.be \(\chi_{3584}(351, \cdot)\) None 0 8
3584.1.bf \(\chi_{3584}(97, \cdot)\) 3584.1.bf.a 8 8
3584.1.bf.b 8
3584.1.bg \(\chi_{3584}(577, \cdot)\) None 0 8
3584.1.bj \(\chi_{3584}(191, \cdot)\) None 0 8
3584.1.bl \(\chi_{3584}(15, \cdot)\) None 0 16
3584.1.bm \(\chi_{3584}(209, \cdot)\) 3584.1.bm.a 16 16
3584.1.bo \(\chi_{3584}(33, \cdot)\) None 0 16
3584.1.bp \(\chi_{3584}(95, \cdot)\) None 0 16
3584.1.bt \(\chi_{3584}(41, \cdot)\) None 0 32
3584.1.bu \(\chi_{3584}(71, \cdot)\) None 0 32
3584.1.bw \(\chi_{3584}(79, \cdot)\) None 0 32
3584.1.bz \(\chi_{3584}(17, \cdot)\) None 0 32
3584.1.cc \(\chi_{3584}(43, \cdot)\) None 0 64
3584.1.cd \(\chi_{3584}(13, \cdot)\) 3584.1.cd.a 64 64
3584.1.ce \(\chi_{3584}(73, \cdot)\) None 0 64
3584.1.ch \(\chi_{3584}(23, \cdot)\) None 0 64
3584.1.ci \(\chi_{3584}(5, \cdot)\) None 0 128
3584.1.cj \(\chi_{3584}(11, \cdot)\) None 0 128

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3584))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3584)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(512))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(896))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1792))\)\(^{\oplus 2}\)