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Properties

Label 1664.1
Level 1664
Weight 1
Dimension 46
Nonzero newspaces 5
Newform subspaces 16
Sturm bound 172032
Trace bound 9

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Defining parameters

Level: \( N \) = \( 1664 = 2^{7} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 16 \)
Sturm bound: \(172032\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1664))\).

Total New Old
Modular forms 2068 574 1494
Cusp forms 148 46 102
Eisenstein series 1920 528 1392

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 30 0 16 0

Trace form

\( 46 q + 2 q^{9} + O(q^{10}) \) \( 46 q + 2 q^{9} + 4 q^{17} - 6 q^{25} - 8 q^{33} + 6 q^{49} - 16 q^{57} - 4 q^{73} + 2 q^{81} + 4 q^{89} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1664))\)

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
1664.1.c \(\chi_{1664}(1663, \cdot)\) None 0 1
1664.1.d \(\chi_{1664}(1535, \cdot)\) None 0 1
1664.1.g \(\chi_{1664}(703, \cdot)\) None 0 1
1664.1.h \(\chi_{1664}(831, \cdot)\) 1664.1.h.a 1 1
1664.1.h.b 1
1664.1.h.c 2
1664.1.h.d 2
1664.1.h.e 4
1664.1.j \(\chi_{1664}(577, \cdot)\) 1664.1.j.a 2 2
1664.1.j.b 2
1664.1.j.c 4
1664.1.j.d 4
1664.1.m \(\chi_{1664}(161, \cdot)\) None 0 2
1664.1.o \(\chi_{1664}(415, \cdot)\) None 0 2
1664.1.q \(\chi_{1664}(287, \cdot)\) None 0 2
1664.1.r \(\chi_{1664}(801, \cdot)\) None 0 2
1664.1.t \(\chi_{1664}(385, \cdot)\) None 0 2
1664.1.v \(\chi_{1664}(191, \cdot)\) 1664.1.v.a 2 2
1664.1.v.b 2
1664.1.v.c 8
1664.1.x \(\chi_{1664}(959, \cdot)\) 1664.1.x.a 2 2
1664.1.x.b 2
1664.1.y \(\chi_{1664}(127, \cdot)\) None 0 2
1664.1.bb \(\chi_{1664}(1023, \cdot)\) None 0 2
1664.1.bc \(\chi_{1664}(369, \cdot)\) None 0 4
1664.1.be \(\chi_{1664}(207, \cdot)\) None 0 4
1664.1.bh \(\chi_{1664}(79, \cdot)\) None 0 4
1664.1.bj \(\chi_{1664}(177, \cdot)\) None 0 4
1664.1.bl \(\chi_{1664}(513, \cdot)\) None 0 4
1664.1.bm \(\chi_{1664}(609, \cdot)\) None 0 4
1664.1.bo \(\chi_{1664}(159, \cdot)\) None 0 4
1664.1.bq \(\chi_{1664}(95, \cdot)\) None 0 4
1664.1.bt \(\chi_{1664}(33, \cdot)\) None 0 4
1664.1.bv \(\chi_{1664}(193, \cdot)\) 1664.1.bv.a 4 4
1664.1.bv.b 4
1664.1.bx \(\chi_{1664}(265, \cdot)\) None 0 8
1664.1.bz \(\chi_{1664}(103, \cdot)\) None 0 8
1664.1.ca \(\chi_{1664}(183, \cdot)\) None 0 8
1664.1.cd \(\chi_{1664}(57, \cdot)\) None 0 8
1664.1.ce \(\chi_{1664}(145, \cdot)\) None 0 8
1664.1.cg \(\chi_{1664}(367, \cdot)\) None 0 8
1664.1.cj \(\chi_{1664}(303, \cdot)\) None 0 8
1664.1.cl \(\chi_{1664}(305, \cdot)\) None 0 8
1664.1.cm \(\chi_{1664}(21, \cdot)\) None 0 16
1664.1.co \(\chi_{1664}(51, \cdot)\) None 0 16
1664.1.cq \(\chi_{1664}(27, \cdot)\) None 0 16
1664.1.ct \(\chi_{1664}(5, \cdot)\) None 0 16
1664.1.cu \(\chi_{1664}(137, \cdot)\) None 0 16
1664.1.cw \(\chi_{1664}(23, \cdot)\) None 0 16
1664.1.cz \(\chi_{1664}(55, \cdot)\) None 0 16
1664.1.da \(\chi_{1664}(41, \cdot)\) None 0 16
1664.1.dd \(\chi_{1664}(37, \cdot)\) None 0 32
1664.1.df \(\chi_{1664}(3, \cdot)\) None 0 32
1664.1.dh \(\chi_{1664}(43, \cdot)\) None 0 32
1664.1.di \(\chi_{1664}(141, \cdot)\) None 0 32

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1664))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1664)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(832))\)\(^{\oplus 2}\)