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Properties

Label 928.1
Level 928
Weight 1
Dimension 18
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 53760
Trace bound 1

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Defining parameters

Level: \( N \) = \( 928 = 2^{5} \cdot 29 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(53760\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(928))\).

Total New Old
Modular forms 964 288 676
Cusp forms 68 18 50
Eisenstein series 896 270 626

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 14 0 4 0

Trace form

\( 18 q + O(q^{10}) \) \( 18 q + 4 q^{21} - 4 q^{29} - 4 q^{41} + 4 q^{49} + 4 q^{53} - 4 q^{65} - 4 q^{77} + 4 q^{81} - 4 q^{89} - 10 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(928))\)

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
928.1.b \(\chi_{928}(463, \cdot)\) None 0 1
928.1.d \(\chi_{928}(639, \cdot)\) None 0 1
928.1.f \(\chi_{928}(175, \cdot)\) None 0 1
928.1.h \(\chi_{928}(927, \cdot)\) None 0 1
928.1.i \(\chi_{928}(41, \cdot)\) None 0 2
928.1.l \(\chi_{928}(481, \cdot)\) 928.1.l.a 2 2
928.1.l.b 4
928.1.o \(\chi_{928}(407, \cdot)\) None 0 2
928.1.p \(\chi_{928}(231, \cdot)\) None 0 2
928.1.r \(\chi_{928}(17, \cdot)\) None 0 2
928.1.s \(\chi_{928}(505, \cdot)\) None 0 2
928.1.w \(\chi_{928}(115, \cdot)\) None 0 4
928.1.y \(\chi_{928}(133, \cdot)\) None 0 4
928.1.z \(\chi_{928}(365, \cdot)\) None 0 4
928.1.bb \(\chi_{928}(59, \cdot)\) None 0 4
928.1.bd \(\chi_{928}(63, \cdot)\) None 0 6
928.1.bf \(\chi_{928}(111, \cdot)\) None 0 6
928.1.bh \(\chi_{928}(223, \cdot)\) None 0 6
928.1.bj \(\chi_{928}(207, \cdot)\) None 0 6
928.1.bl \(\chi_{928}(137, \cdot)\) None 0 12
928.1.bm \(\chi_{928}(113, \cdot)\) None 0 12
928.1.bo \(\chi_{928}(71, \cdot)\) None 0 12
928.1.bp \(\chi_{928}(7, \cdot)\) None 0 12
928.1.bs \(\chi_{928}(97, \cdot)\) 928.1.bs.a 12 12
928.1.bv \(\chi_{928}(73, \cdot)\) None 0 12
928.1.bw \(\chi_{928}(83, \cdot)\) None 0 24
928.1.by \(\chi_{928}(37, \cdot)\) None 0 24
928.1.cb \(\chi_{928}(21, \cdot)\) None 0 24
928.1.cd \(\chi_{928}(35, \cdot)\) None 0 24

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(928))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(928)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(464))\)\(^{\oplus 2}\)