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Properties

Label 820.1
Level 820
Weight 1
Dimension 106
Nonzero newspaces 9
Newform subspaces 19
Sturm bound 40320
Trace bound 5

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Defining parameters

Level: \( N \) = \( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 19 \)
Sturm bound: \(40320\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(820))\).

Total New Old
Modular forms 928 342 586
Cusp forms 128 106 22
Eisenstein series 800 236 564

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 106 0 0 0

Trace form

\( 106 q - 10 q^{4} - 2 q^{5} - 4 q^{6} - 14 q^{9} + O(q^{10}) \) \( 106 q - 10 q^{4} - 2 q^{5} - 4 q^{6} - 14 q^{9} - 4 q^{14} + 6 q^{16} - 2 q^{20} - 8 q^{21} - 4 q^{24} - 2 q^{25} - 4 q^{29} + 36 q^{30} - 20 q^{32} - 20 q^{34} + 2 q^{36} - 10 q^{41} + 2 q^{45} - 4 q^{46} - 14 q^{49} + 8 q^{50} - 20 q^{52} + 32 q^{54} - 4 q^{56} - 4 q^{61} - 10 q^{64} - 10 q^{65} - 16 q^{66} - 8 q^{69} - 4 q^{70} - 2 q^{80} - 22 q^{81} - 8 q^{84} - 10 q^{85} - 4 q^{86} - 4 q^{89} + 8 q^{90} - 4 q^{94} - 4 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(820))\)

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
820.1.c \(\chi_{820}(411, \cdot)\) None 0 1
820.1.e \(\chi_{820}(819, \cdot)\) 820.1.e.a 1 1
820.1.e.b 1
820.1.e.c 8
820.1.f \(\chi_{820}(739, \cdot)\) None 0 1
820.1.h \(\chi_{820}(491, \cdot)\) None 0 1
820.1.i \(\chi_{820}(173, \cdot)\) None 0 2
820.1.l \(\chi_{820}(573, \cdot)\) None 0 2
820.1.m \(\chi_{820}(91, \cdot)\) None 0 2
820.1.o \(\chi_{820}(319, \cdot)\) 820.1.o.a 2 2
820.1.o.b 2
820.1.o.c 2
820.1.o.d 2
820.1.q \(\chi_{820}(493, \cdot)\) None 0 2
820.1.t \(\chi_{820}(73, \cdot)\) None 0 2
820.1.v \(\chi_{820}(161, \cdot)\) None 0 4
820.1.z \(\chi_{820}(167, \cdot)\) 820.1.z.a 4 4
820.1.ba \(\chi_{820}(3, \cdot)\) 820.1.ba.a 4 4
820.1.bb \(\chi_{820}(109, \cdot)\) None 0 4
820.1.bd \(\chi_{820}(359, \cdot)\) 820.1.bd.a 4 4
820.1.bd.b 4
820.1.bf \(\chi_{820}(51, \cdot)\) None 0 4
820.1.bh \(\chi_{820}(31, \cdot)\) None 0 4
820.1.bj \(\chi_{820}(59, \cdot)\) 820.1.bj.a 4 4
820.1.bj.b 4
820.1.bl \(\chi_{820}(77, \cdot)\) None 0 8
820.1.bn \(\chi_{820}(37, \cdot)\) None 0 8
820.1.bp \(\chi_{820}(39, \cdot)\) 820.1.bp.a 8 8
820.1.bp.b 8
820.1.bp.c 8
820.1.bp.d 8
820.1.br \(\chi_{820}(131, \cdot)\) None 0 8
820.1.bs \(\chi_{820}(113, \cdot)\) None 0 8
820.1.bu \(\chi_{820}(33, \cdot)\) None 0 8
820.1.bx \(\chi_{820}(29, \cdot)\) None 0 16
820.1.by \(\chi_{820}(47, \cdot)\) 820.1.by.a 16 16
820.1.bz \(\chi_{820}(7, \cdot)\) 820.1.bz.a 16 16
820.1.cd \(\chi_{820}(101, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(820))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(820)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 2}\)