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Properties

Label 1648.1
Level 1648
Weight 1
Dimension 20
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 169728
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1648 = 2^{4} \cdot 103 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(169728\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1648))\).

Total New Old
Modular forms 1488 475 1013
Cusp forms 60 20 40
Eisenstein series 1428 455 973

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 8 0

Trace form

\( 20 q + 2 q^{2} + 2 q^{5} + 4 q^{6} + q^{7} - 4 q^{8} + 2 q^{9} + O(q^{10}) \) \( 20 q + 2 q^{2} + 2 q^{5} + 4 q^{6} + q^{7} - 4 q^{8} + 2 q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} - 5 q^{13} - 4 q^{16} - 5 q^{17} - 2 q^{18} + 3 q^{19} + 2 q^{20} + 8 q^{22} + q^{23} + 2 q^{25} - 2 q^{26} + 10 q^{28} - 5 q^{29} + 2 q^{32} - 4 q^{34} + 12 q^{38} + 8 q^{39} - 2 q^{40} - q^{41} + 2 q^{43} - 2 q^{45} - 12 q^{46} - 5 q^{49} + 2 q^{50} - 2 q^{52} - 4 q^{55} + 4 q^{58} - q^{59} - q^{61} + 2 q^{62} + q^{63} + 8 q^{66} - 2 q^{67} - 10 q^{68} - 8 q^{69} - 4 q^{71} - 4 q^{72} + 4 q^{75} + 4 q^{76} + q^{79} - 4 q^{80} - 2 q^{82} + q^{83} + 2 q^{85} - 2 q^{86} - 4 q^{90} + 2 q^{91} + 4 q^{92} - 8 q^{93} + 4 q^{94} + 4 q^{96} - q^{97} - 2 q^{98} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1648))\)

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
1648.1.c \(\chi_{1648}(1441, \cdot)\) 1648.1.c.a 2 1
1648.1.e \(\chi_{1648}(207, \cdot)\) None 0 1
1648.1.f \(\chi_{1648}(1031, \cdot)\) None 0 1
1648.1.h \(\chi_{1648}(617, \cdot)\) None 0 1
1648.1.j \(\chi_{1648}(205, \cdot)\) 1648.1.j.a 2 2
1648.1.j.b 8
1648.1.l \(\chi_{1648}(619, \cdot)\) None 0 2
1648.1.o \(\chi_{1648}(159, \cdot)\) None 0 2
1648.1.q \(\chi_{1648}(881, \cdot)\) None 0 2
1648.1.r \(\chi_{1648}(57, \cdot)\) None 0 2
1648.1.s \(\chi_{1648}(983, \cdot)\) None 0 2
1648.1.u \(\chi_{1648}(355, \cdot)\) 1648.1.u.a 4 4
1648.1.u.b 4
1648.1.w \(\chi_{1648}(253, \cdot)\) None 0 4
1648.1.z \(\chi_{1648}(73, \cdot)\) None 0 16
1648.1.bb \(\chi_{1648}(23, \cdot)\) None 0 16
1648.1.bc \(\chi_{1648}(79, \cdot)\) None 0 16
1648.1.be \(\chi_{1648}(113, \cdot)\) None 0 16
1648.1.bi \(\chi_{1648}(179, \cdot)\) None 0 32
1648.1.bk \(\chi_{1648}(37, \cdot)\) None 0 32
1648.1.bm \(\chi_{1648}(7, \cdot)\) None 0 32
1648.1.bn \(\chi_{1648}(217, \cdot)\) None 0 32
1648.1.bo \(\chi_{1648}(65, \cdot)\) None 0 32
1648.1.bq \(\chi_{1648}(15, \cdot)\) None 0 32
1648.1.bt \(\chi_{1648}(5, \cdot)\) None 0 64
1648.1.bv \(\chi_{1648}(19, \cdot)\) None 0 64

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1648))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1648)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(103))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(824))\)\(^{\oplus 2}\)