Properties

Label 984.1
Level 984
Weight 1
Dimension 48
Nonzero newspaces 3
Newform subspaces 9
Sturm bound 53760
Trace bound 3

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Defining parameters

Level: \( N \) = \( 984 = 2^{3} \cdot 3 \cdot 41 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 9 \)
Sturm bound: \(53760\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(984))\).

Total New Old
Modular forms 1102 204 898
Cusp forms 142 48 94
Eisenstein series 960 156 804

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 48 0 0 0

Trace form

\( 48 q + 4 q^{9} + O(q^{10}) \) \( 48 q + 4 q^{9} - 4 q^{10} + 8 q^{16} - 4 q^{18} - 4 q^{25} - 4 q^{31} - 4 q^{33} - 16 q^{36} - 4 q^{40} + 8 q^{46} - 20 q^{48} + 8 q^{49} - 8 q^{57} - 4 q^{66} - 40 q^{67} + 4 q^{72} + 4 q^{73} - 4 q^{78} + 4 q^{82} - 4 q^{87} - 4 q^{90} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(984))\)

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
984.1.b \(\chi_{984}(737, \cdot)\) None 0 1
984.1.c \(\chi_{984}(739, \cdot)\) None 0 1
984.1.h \(\chi_{984}(163, \cdot)\) None 0 1
984.1.i \(\chi_{984}(329, \cdot)\) None 0 1
984.1.l \(\chi_{984}(247, \cdot)\) None 0 1
984.1.m \(\chi_{984}(245, \cdot)\) 984.1.m.a 1 1
984.1.m.b 1
984.1.m.c 1
984.1.m.d 1
984.1.m.e 4
984.1.n \(\chi_{984}(821, \cdot)\) None 0 1
984.1.o \(\chi_{984}(655, \cdot)\) None 0 1
984.1.q \(\chi_{984}(319, \cdot)\) None 0 2
984.1.r \(\chi_{984}(173, \cdot)\) None 0 2
984.1.u \(\chi_{984}(91, \cdot)\) None 0 2
984.1.v \(\chi_{984}(401, \cdot)\) None 0 2
984.1.z \(\chi_{984}(85, \cdot)\) None 0 4
984.1.ba \(\chi_{984}(577, \cdot)\) None 0 4
984.1.bb \(\chi_{984}(659, \cdot)\) 984.1.bb.a 4 4
984.1.bb.b 4
984.1.bc \(\chi_{984}(167, \cdot)\) None 0 4
984.1.bi \(\chi_{984}(31, \cdot)\) None 0 4
984.1.bj \(\chi_{984}(221, \cdot)\) None 0 4
984.1.bk \(\chi_{984}(269, \cdot)\) None 0 4
984.1.bl \(\chi_{984}(223, \cdot)\) None 0 4
984.1.bo \(\chi_{984}(305, \cdot)\) None 0 4
984.1.bp \(\chi_{984}(187, \cdot)\) None 0 4
984.1.bu \(\chi_{984}(139, \cdot)\) None 0 4
984.1.bv \(\chi_{984}(113, \cdot)\) None 0 4
984.1.by \(\chi_{984}(185, \cdot)\) None 0 8
984.1.bz \(\chi_{984}(43, \cdot)\) None 0 8
984.1.cc \(\chi_{984}(5, \cdot)\) None 0 8
984.1.cd \(\chi_{984}(103, \cdot)\) None 0 8
984.1.ci \(\chi_{984}(47, \cdot)\) None 0 16
984.1.cj \(\chi_{984}(11, \cdot)\) 984.1.cj.a 16 16
984.1.cj.b 16
984.1.ck \(\chi_{984}(97, \cdot)\) None 0 16
984.1.cl \(\chi_{984}(13, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(984))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(984)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(328))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(492))\)\(^{\oplus 2}\)