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Properties

Label 580.1
Level 580
Weight 1
Dimension 72
Nonzero newspaces 7
Newform subspaces 13
Sturm bound 20160
Trace bound 4

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Defining parameters

Level: \( N \) = \( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 13 \)
Sturm bound: \(20160\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(580))\).

Total New Old
Modular forms 660 236 424
Cusp forms 100 72 28
Eisenstein series 560 164 396

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 72 0 0 0

Trace form

\( 72 q - 6 q^{4} - 4 q^{5} - 6 q^{9} + O(q^{10}) \) \( 72 q - 6 q^{4} - 4 q^{5} - 6 q^{9} - 4 q^{14} + 2 q^{16} - 7 q^{20} - 8 q^{21} + 20 q^{24} - 4 q^{25} - 14 q^{26} + 2 q^{29} - 6 q^{30} - 14 q^{34} + 22 q^{36} - 7 q^{40} - 4 q^{41} - 13 q^{45} - 4 q^{46} - 10 q^{49} - 14 q^{53} - 4 q^{54} - 4 q^{56} - 4 q^{61} - 6 q^{64} - 13 q^{65} - 8 q^{69} - 4 q^{70} - 14 q^{73} - 4 q^{80} - 14 q^{81} - 8 q^{84} - 8 q^{86} - 4 q^{89} - 14 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(580))\)

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
580.1.b \(\chi_{580}(291, \cdot)\) None 0 1
580.1.e \(\chi_{580}(579, \cdot)\) 580.1.e.a 1 1
580.1.e.b 1
580.1.e.c 2
580.1.e.d 4
580.1.g \(\chi_{580}(231, \cdot)\) None 0 1
580.1.h \(\chi_{580}(59, \cdot)\) None 0 1
580.1.i \(\chi_{580}(423, \cdot)\) 580.1.i.a 2 2
580.1.l \(\chi_{580}(249, \cdot)\) None 0 2
580.1.m \(\chi_{580}(57, \cdot)\) None 0 2
580.1.p \(\chi_{580}(117, \cdot)\) None 0 2
580.1.q \(\chi_{580}(41, \cdot)\) None 0 2
580.1.t \(\chi_{580}(307, \cdot)\) 580.1.t.a 2 2
580.1.v \(\chi_{580}(139, \cdot)\) 580.1.v.a 6 6
580.1.v.b 6
580.1.w \(\chi_{580}(51, \cdot)\) None 0 6
580.1.y \(\chi_{580}(179, \cdot)\) 580.1.y.a 6 6
580.1.y.b 6
580.1.y.c 12
580.1.bb \(\chi_{580}(111, \cdot)\) None 0 6
580.1.bd \(\chi_{580}(127, \cdot)\) 580.1.bd.a 12 12
580.1.bf \(\chi_{580}(21, \cdot)\) None 0 12
580.1.bg \(\chi_{580}(53, \cdot)\) None 0 12
580.1.bj \(\chi_{580}(13, \cdot)\) None 0 12
580.1.bk \(\chi_{580}(69, \cdot)\) None 0 12
580.1.bm \(\chi_{580}(3, \cdot)\) 580.1.bm.a 12 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(580))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(580)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 3}\)