↑

Properties

Label 2020.1
Level 2020
Weight 1
Dimension 268
Nonzero newspaces 12
Newform subspaces 22
Sturm bound 244800
Trace bound 13

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 2020 = 2^{2} \cdot 5 \cdot 101 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 22 \)
Sturm bound: \(244800\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2020))\).

Total New Old
Modular forms 2344 864 1480
Cusp forms 344 268 76
Eisenstein series 2000 596 1404

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 268 0 0 0

Trace form

\( 268 q - 14 q^{4} - 6 q^{5} - 4 q^{6} - 18 q^{9} + O(q^{10}) \) \( 268 q - 14 q^{4} - 6 q^{5} - 4 q^{6} - 18 q^{9} + 2 q^{13} - 12 q^{14} + 6 q^{16} - 2 q^{17} - 4 q^{20} + 8 q^{21} + 2 q^{23} + 4 q^{24} - 2 q^{25} - 4 q^{29} - 4 q^{30} + 2 q^{36} - 4 q^{37} - 4 q^{41} + 4 q^{43} - 8 q^{45} - 4 q^{46} + 2 q^{47} - 18 q^{49} - 4 q^{56} - 4 q^{61} - 14 q^{64} + 2 q^{65} - 8 q^{69} + 4 q^{70} + 4 q^{71} - 8 q^{76} + 4 q^{80} - 14 q^{81} - 50 q^{82} + 84 q^{84} - 2 q^{85} - 4 q^{86} - 4 q^{89} - 4 q^{94} - 12 q^{96} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2020))\)

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
2020.1.b \(\chi_{2020}(1011, \cdot)\) None 0 1
2020.1.d \(\chi_{2020}(2019, \cdot)\) 2020.1.d.a 1 1
2020.1.d.b 1
2020.1.d.c 2
2020.1.d.d 4
2020.1.d.e 12
2020.1.f \(\chi_{2020}(1819, \cdot)\) None 0 1
2020.1.h \(\chi_{2020}(1211, \cdot)\) None 0 1
2020.1.j \(\chi_{2020}(1303, \cdot)\) 2020.1.j.a 2 2
2020.1.k \(\chi_{2020}(1413, \cdot)\) 2020.1.k.a 4 2
2020.1.n \(\chi_{2020}(1101, \cdot)\) None 0 2
2020.1.p \(\chi_{2020}(1909, \cdot)\) None 0 2
2020.1.q \(\chi_{2020}(1213, \cdot)\) None 0 2
2020.1.t \(\chi_{2020}(1323, \cdot)\) 2020.1.t.a 2 2
2020.1.v \(\chi_{2020}(511, \cdot)\) None 0 4
2020.1.x \(\chi_{2020}(339, \cdot)\) 2020.1.x.a 4 4
2020.1.x.b 4
2020.1.z \(\chi_{2020}(219, \cdot)\) 2020.1.z.a 4 4
2020.1.z.b 4
2020.1.z.c 8
2020.1.bb \(\chi_{2020}(491, \cdot)\) None 0 4
2020.1.bc \(\chi_{2020}(163, \cdot)\) 2020.1.bc.a 8 8
2020.1.bf \(\chi_{2020}(137, \cdot)\) None 0 8
2020.1.bg \(\chi_{2020}(69, \cdot)\) None 0 8
2020.1.bi \(\chi_{2020}(41, \cdot)\) None 0 8
2020.1.bl \(\chi_{2020}(17, \cdot)\) None 0 8
2020.1.bm \(\chi_{2020}(363, \cdot)\) 2020.1.bm.a 8 8
2020.1.bp \(\chi_{2020}(131, \cdot)\) None 0 20
2020.1.bq \(\chi_{2020}(31, \cdot)\) None 0 20
2020.1.bt \(\chi_{2020}(279, \cdot)\) 2020.1.bt.a 20 20
2020.1.bt.b 20
2020.1.bt.c 40
2020.1.bu \(\chi_{2020}(19, \cdot)\) 2020.1.bu.a 20 20
2020.1.bu.b 20
2020.1.bx \(\chi_{2020}(29, \cdot)\) None 0 40
2020.1.bz \(\chi_{2020}(13, \cdot)\) None 0 40
2020.1.ca \(\chi_{2020}(3, \cdot)\) 2020.1.ca.a 40 40
2020.1.cd \(\chi_{2020}(7, \cdot)\) 2020.1.cd.a 40 40
2020.1.ce \(\chi_{2020}(37, \cdot)\) None 0 40
2020.1.cg \(\chi_{2020}(61, \cdot)\) None 0 40

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2020))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2020)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(404))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(505))\)\(^{\oplus 3}\)