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Properties

Label 992.1
Level 992
Weight 1
Dimension 25
Nonzero newspaces 3
Newform subspaces 6
Sturm bound 61440
Trace bound 1

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Defining parameters

Level: \( N \) = \( 992 = 2^{5} \cdot 31 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
Sturm bound: \(61440\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(992))\).

Total New Old
Modular forms 1036 315 721
Cusp forms 76 25 51
Eisenstein series 960 290 670

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 17 0 0 8

Trace form

\( 25 q + 4 q^{5} - q^{9} + O(q^{10}) \) \( 25 q + 4 q^{5} - q^{9} - 4 q^{13} + 2 q^{17} - 2 q^{21} + 3 q^{25} - 6 q^{29} - 13 q^{31} - 4 q^{33} - 12 q^{35} - 8 q^{37} + 4 q^{39} + 6 q^{47} + q^{49} + 12 q^{50} - 2 q^{53} + 8 q^{57} - 12 q^{64} - 2 q^{65} + 2 q^{69} - 4 q^{71} - 6 q^{73} + 12 q^{80} + 3 q^{81} - 4 q^{85} - 4 q^{87} + 6 q^{89} + 8 q^{93} - 6 q^{95} - 2 q^{97} - 12 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(992))\)

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
992.1.d \(\chi_{992}(63, \cdot)\) None 0 1
992.1.e \(\chi_{992}(929, \cdot)\) None 0 1
992.1.f \(\chi_{992}(559, \cdot)\) None 0 1
992.1.g \(\chi_{992}(433, \cdot)\) 992.1.g.a 1 1
992.1.g.b 2
992.1.g.c 2
992.1.j \(\chi_{992}(185, \cdot)\) None 0 2
992.1.l \(\chi_{992}(311, \cdot)\) None 0 2
992.1.p \(\chi_{992}(305, \cdot)\) None 0 2
992.1.q \(\chi_{992}(335, \cdot)\) None 0 2
992.1.r \(\chi_{992}(161, \cdot)\) None 0 2
992.1.s \(\chi_{992}(191, \cdot)\) None 0 2
992.1.x \(\chi_{992}(187, \cdot)\) None 0 4
992.1.y \(\chi_{992}(61, \cdot)\) 992.1.y.a 4 4
992.1.y.b 8
992.1.z \(\chi_{992}(209, \cdot)\) None 0 4
992.1.ba \(\chi_{992}(47, \cdot)\) None 0 4
992.1.be \(\chi_{992}(449, \cdot)\) None 0 4
992.1.bf \(\chi_{992}(95, \cdot)\) 992.1.bf.a 8 4
992.1.bg \(\chi_{992}(87, \cdot)\) None 0 4
992.1.bi \(\chi_{992}(57, \cdot)\) None 0 4
992.1.bm \(\chi_{992}(39, \cdot)\) None 0 8
992.1.bo \(\chi_{992}(89, \cdot)\) None 0 8
992.1.br \(\chi_{992}(37, \cdot)\) None 0 8
992.1.bs \(\chi_{992}(67, \cdot)\) None 0 8
992.1.bt \(\chi_{992}(255, \cdot)\) None 0 8
992.1.bu \(\chi_{992}(65, \cdot)\) None 0 8
992.1.by \(\chi_{992}(111, \cdot)\) None 0 8
992.1.bz \(\chi_{992}(17, \cdot)\) None 0 8
992.1.ca \(\chi_{992}(29, \cdot)\) None 0 16
992.1.cb \(\chi_{992}(35, \cdot)\) None 0 16
992.1.cf \(\chi_{992}(73, \cdot)\) None 0 16
992.1.ch \(\chi_{992}(7, \cdot)\) None 0 16
992.1.ci \(\chi_{992}(19, \cdot)\) None 0 32
992.1.cj \(\chi_{992}(13, \cdot)\) None 0 32

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(992))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(992)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(248))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(496))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(992))\)\(^{\oplus 1}\)